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Numerical assessment of soil properties in relation to classification and genesis Sondheim, M. 1982

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NUMERICAL ASSESSMENT OF SOIL PROPERTIES IN RELATION TO CLASSIFICATION AND GENESIS by MARK WEISS SONDHEIM M.A., The University of Toronto, 1975 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE STUDIES Department of So i l Science We accept th i s thes is as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA Q) Mark Weiss Sondheim, 1982 In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l l m e n t o f the r e q u i r e -ments f o r an advanced degree a t the U n i v e r s i t y of B r i t i s h C o l u m b i a , I ag ree t h a t the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and s t u d y . I f u r t h e r agree t h a t p e r m i s s i o n f o r e x t e n s i v e copy i n g of t h i s t h e s i s f o r s c h o l a r l y purposes may be g r a n t e d by the Head of my Department or by h i s r e p r e s e n t a t i v e s . I t i s unde r s t ood t h a t c opy i n g or p u b l i c a t i o n of t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . Department of S o i l S c i e n c e The U n i v e r s i t y of B r i t i s h Co lumbia 2075 Wesbrook PI ace Vancouve r , Canada V6T 1W5 Date *Vb Y^. i i ABSTRACT Soi l properties are examined from two perspectives: (1), in re la t ion to classes and categories of c l a s s i f i c a t i o n systems, and (2), in terms of mathe-mat ica l ly t rac tab le , chemical and physical continuums. Through four indepen-dent studies, major l im i ta t i ons of each approach are defined and evaluated. The f i r s t study examines samples from s ix d i f fe rent types of horizons commonly found in podzolic s o i l s . The results suggest that in a chemical context the horizons do not represent d i s t i n c t e n t i t i e s ; rather they appear to dominate overlapping regions along a multidimensional chemical spectrum. The second study analyzes the extent to which V .J . Kraj ina ' s phytosociologi-cal c l a s s i f i c a t i o n of biogeocoenoses explains the v a r i a b i l i t y of a number of s i t e propert ies. It i s determined that many of the physiographic properties are s i gn i f i c an t l y related to the association category of the system, but that many of the pedologic properties are not. The two studies lead to a dichotomy concerning c l a s s i f i c a t i o n and the s t a t i s t i c a l re lat ionships both among so i l properties and between s o i l properties and other elements of an ecosystem. Where sampling i s r e s t r i c ted to comparatively l imi ted ranges along environmental gradients, re lat ionsh ips may be so weak that a c l a s s i f i -cat ion based on only a few properties or elements may not be that useful for associated properties and elements. On the other hand, because of the i i i implied high degree of v a r i a b i l i t y , attempts to develop a h o l i s t i c , i n te -grated c l a s s i f i c a t i o n are not l i k e l y to be highly successful e i the r . In the t h i r d study chemical and physical changes across a prograded beach chronosequence are examined. It i s found that s o i l development over both time and depth may be modelled by a non-linear regression equation. The l a s t of the four studies concerns an evaluation of the extent to which the inherent v a r i a b i l i t y of s o i l properties masks expected trends across a morainal chronosequence. For those properties most affected by vegetation succession, the same type of regression equation as used i n the previous study was applied with excel lent re su l t s . For the other, less dynamic propert ies, assumed trends were too obscure to model. The two studies suggest that, where s o i l properties are d i rec t l y influenced by strong env i -ronmental gradients, ordination techniques may be quite i l l uminat ing . In less b i o l og i ca l l y s t ressfu l environments and in those which have reached steady state, both the predict ive and explanatory capab i l i t i e s of such techniques may be r e l a t i ve l y low. These findings c losely pa ra l l e l those discussed e a r l i e r concerning c l a s s i f i c a t i o n . The thesis concludes that for many appl icat ions attempts to model and map the landscape as an integrated whole should be abandoned. Furthermore, instead of viewing the landscape from e i ther a c l a s s i f i c a t i o n or ordination i v perspective, d i g i t a l t e r r a i n models should be considered. Data for the models could be generated from regional ized, s t a t i s t i c a l , stochast ic, and determin i s t ic equations, ca l ib rated with ground t ruth observations. Tradi -t i ona l polygon and contour maps can also be transformed into d i g i t a l t e r ra in models. Landscape interpretat ions could then be t i ed d i r e c t l y to measured and estimated data. This approach involves a minimum loss of information and i s conceptually simple. V TABLE OF CONTENTS INTRODUCTION 1 CHAPTER 1: COMPARISON.OF SOME PODZOLIC HORIZONS USING CHEMICAL PROPERTIES AND THE MULTIVARIATE DENSITY EQUATION 4 CHAPTER 2: THE RELATIONSHIP OF SOIL AND PHYSIOGRAPHIC ATTRIBUTES TO AN ECOLOGICAL CLASSIFICATION SYSTEM 21 CHAPTER 3: NUMERICAL ANALYSIS OF A CHRONOSEQUENCE, INCLUDING THE DEVELOPMENT OF A CHRONOFUNCTION 48 CHAPTER 4: NUMERICAL ANALYSIS OF A CHRONOSEQUENCE, INCLUDING AN ASSESSMENT OF VARIABILITY 70 CONCLUSIONS 106 REFERENCES CITED 115 vi LIST OF TABLES 1.1 Comparison between Original and Second Generation Classifications 13 1.2 Values of S and Tr (Q)/N for the Four Classifications 15 1.3 Comparison between Original and Third Generation Classifications 16 1.4 Comparison between Original and Fourth Generation Classifications 18 2.1 Description of Properties 27 2.2 Nested Analysis of Variance Design 30 2.3 Significance Tests for the Nested ANOVA 31 2.4 Design and Significance Tests for the One-Way ANOVA 32 2.5 Significance Results, General Physiographic Factors 2.6 Significance Results, Soil Textural Characteristics 35 2.7 Significance Results, Mineral Soil Chemical Attributes 36 2.8 Significance Results, Forest Floor Chemical Attributes 37 3.1 Original Data 54 3.2 Component Loadings 59 4.1 Organic Carbon and Nitrogen for All 183 Observations 80 4.2 Original Data for 39 Observations 82 4.3 ANOVA Design for Full Set of 180 Observations 85 4.4 ANOVA Design for Subset of 36 Observations 86 4.5 Analysis of Variance Test for Regression Equation 89 4.6 Analysis of Variance Results 92 4.7 Oblique Factor Matrices 95 4.8 Estimates and 95% Confidence Intervals for Coefficients 99 vii LIST OF FIGURES 2.1 Synopsis of the Taxa 26 2.2 Graphs of Percent Cumulative Variance versus Category of the Hierarch, from the Nested ANOVA, for the General Physiographic Factors 38 2.3 Graphs of Percent Cumulative Variance versus Category of the Hierarchy, from the Nested ANOVA, for the Soil Textural Characteristics 38 2.4 Graphs of Percent Cumulative Variance versus Category of the Hierarchy, from the Nested ANOVA, for the Mineral Soil Chemical Attributes 38 2.5 Graphs of Percent Cumulative Variance versus Category of the Hierarchy, from the Nested ANOVA, for the Forest Floor Chemical Attributes 38 3.1 Cross-section Indicating Horizons and the 21 Sample Locations 53 3.2 Cross-section Showing Contours Based on Component I Scores 62 3.3 Cross-section Showing Contours Based on Component II Scores ... 63 3.4 Graph Depicting Pedogenic Development as a Function of Depth and Age 66 4.1 Percent Cover on the Moraines for the Five Plant Species 75 4.2 Percent, Bases on Value for the Oldest Moraine of Five Site Factors 76 4.3 Graphs of Percent Total Nitrogen versus Time and Depth 101 vi i i ACKNOWLEDGEMENTS Numerous people both in and out of the Department of Soi l Science have aided my doctoral research during the la s t several years. As adviser, colleague, and f r i end , Les Lavkulich supported t h i s work with enthusiasm and dedicat ion. Karel Kl inka kindly allowed me to make extensive use of his data co l lec ted at the Haney Research Forest; of equal importance, I spent many f r u i t f u l hours with him discussing the ecological s ign i f icance of my f ind ings. Glen Singleton provided me with his data from Cox Bay. Both he and W i l l i e Hendershot ass isted me a great deal by t he i r useful c r i t i c i s m of my manuscripts. Terry Rollerson brought the Robson chronosequence to my at tent ion. He and Jace Standish furthered my understanding of the pract i ca l s ign i f icance of c l a s s i f i c a t i o n systems through many long and enjoyable discussions. Both of them, Dave Spittlehouse, and Pat Teti helped me during the f i e l d work at Mt. Robson. Besides providing useful commentary on my manuscripts, Tim Bal lard steered me away from some less worthwhile avenues of invest igat ion in the early part of my program. Harry Quesnel gave me much good advise concerning the laboratory analysis of the Robson samples. Doug Wil l iams, Malcolm Greig, David Mark, and Mike Patterson helped me consider-ably in understanding the use and misuse of numerical and s t a t i s t i c a l techniques; in f ac t , without t he i r time and interest th i s thesis would not have been poss ible. Special thanks are also due to Richard Webster for ix kindling my interest in numerical analysis of soils data four years ago. In addition, I would like to thank: Patti Carbis, Val Miles, and Bev Herman for laboratory analysis; and Julie Armanini and Rick Thompson for drafting of figures. The logistic support at Mt. Robson was partially supported by the B.C. Ministry of Forests; I thank Ted Baker for his interest in the project. The thesis was greatly facilitated by the financial support provided by the British Columbia Forest Products Fellowship in Soil Science and by the Natural Science and Engineering Research Council (Grant Number A4463). The Terrestrial Studies Branch, B.C. Ministry of Environment, supported much of my computer work. Very special thanks are due to my family, Kathy, Daniel and Alison, for their continued encouragement and understanding. 1 INTRODUCTION In pedology as well as other natural resource sciences considerable e f f o r t has been expended on the development of sophist icated c l a s s i f i c a t i o n systems. Most of these systems work well when highly d i s s im i l a r objects are being compared. A well developed Podzol for example d i f f e r s from a well developed Chernozem on almost any scale of measurement. V i r t ua l l y any c la s s -i f i c a t i o n which places the so i l s or ecology of the West Coast Mountains into d i f fe rent groups from those of the Canadian P ra i r i e s i s l i k e l y to be of some merit , whether the objective of the scheme i s general, such as promoting a better understanding of environmental dynamics, or s pec i f i c , such as aiding in the evaluation of forestry or ag r i cu l tu ra l c apab i l i t y . However, both the u t i l i t y and v a l i d i t y of many c l a s s i f i c a t i o n systems cannot necessari ly be taken for granted, pa r t i cu la r l y where the differences among objects are less pronounced. Three reasons for th i s are related to the nature of the population d i s t r i b u t i o n , the choice of d i f f e ren t i a t i n g c r i t e r i a , and the existence of v a r i a b i l i t y which cannot be ascribed to def in -able environmental functions. F i r s t l y , i f the d iv i s ions among classes do not correspond to regions of minimum density along graphs of univariate or mu l t i -var iate population d i s t r ibut ions for properties of i n te res t , the c l a s s i f i c a -t i o n may appear as very a r t i f i c i a l and of l i t t l e value. Secondly, even though two groups of objects may d i f f e r markedly with respect to certa in a t t r i bu te s , they may s t i l l f a l l into the same c las s , should these att r ibutes neither be d i f f e ren t i a t i n g c r i t e r i a in the c l a s s i f i c a t i o n nor covary strongly 2 with those which are. F i n a l l y , i f the non-attr ibutable v a r i a b i l i t y composes a large proportion of the to ta l v a r i a b i l i t y of a set of given propert ies, then the classes of a c l a s s i f i c a t i o n based on those properties w i l l not be very d i s t i n c t from one another, even i f a l l other conditions are i d e a l . Recognition and resolut ion of these potential c l a s s i f i c a t i o n problems i s of p ract i ca l as well as academic value, especia l ly at a time when so much interes t i s being placed on intensive management of our natural resources. Planning and assessment a c t i v i t i e s by government and industry are frequently based on maps or evaluation guidelines which in turn are t i e d d i r e c t l y to one or more c l a s s i f i c a t i o n schemes. Consequently, the true information content of such schemes becomes an issue of central concern. This raises the questions of whether there are other systems which may prove more worthwhile. Instead of defining classes and categories, should ordination techniques be considered? Are there other approaches which merit consideration? Are or should the answers to these questions be influenced by the a v a i l a b i l i t y of high speed data processing to the natural resource d i sc ip l i nes ? The breadth of required c r i t i c a l analysis evoked by such questioning i s well beyond the scope of t h i s d i s se r ta t ion . Instead, certa in aspects have been rigorously tack led. Chapter 1 concerns a test of the d i s t inct iveness of various types of s o i l horizons. Chapter 2 analyzes in deta i l some of the pedological aspects of V .J . K ra j ina ' s c l a s s i f i c a t i o n of biogeocoenoses. Chapter 3 concerns the appl icat ion of data reduction and regression tech-niques to s o i l genesis. Chapter 4 also studies s o i l genesis, but with 3 considerable emphasis given to the v a r i a b i l i t y of the s o i l and also to the re lat ionsh ip between so i l and plant development. Thus, the f i r s t two chapters deal with the value of two commonly used c l a s s i f i c a t i o n systems. Though re s t r i c ted to only one or two of Hans Jenny's state factors , the las t two chapters t reat s o i l s and ecosystems as continuums; in so doing, they represent attempts at modelling the landscape in a non-c lass i f icatory manner. In a l l four chapters new numerical or s t a t i s t i c a l techniques are introduced to pedology. The conclusion of the d i s ser tat ion provides summaries of the four studies, an overview of the s ign i f icance of the f indings, and some proposals concerning the analysis and handling of natural resource data. 4 CHAPTER 1 COMPARISON OF SOME PODZOLIC HORIZONS USING CHEMICAL PROPERTIES AND THE MULTIVARIATE DENSITY EQUATION 5 Theories of pedogenesis and c l a s s i f i c a t i o n are based in large measure on the recognition of s o i l horizons and an understanding of t he i r development. A century ago Dokuchaev and his colleagues i n i t i a t e d the science of pedology with t he i r study of the development and d i s t r i bu t i on of Chernozems and Pod-zo l s , s o i l s both readi ly dist inguished in the f i e l d by t he i r charac te r i s t i c horizons. Marbut, wr i t i ng in 1920, l i s t e d eight features which should be used when defining a s o i l ; seven of these related d i r ec t l y to the horizons while the eighth was concerned with the geology of the s o i l s material (Bald-win et a l . , 1938). His thoughts were echoed th i r t y -n ine years l a te r from a d i f fe rent perspective by Simonson (1959); " So i l genesis can be viewed as cons ist ing of two steps; v i z , (a) the accumulation of parent mater ia l s , and (b) the d i f f e ren t i a t i on of horizons in the p r o f i l e . " This marriage of pedogenic theory and so i l c l a s s i f i c a t i o n has been r e i n -forced by the genet ica l ly or iented, s o i l taxonomies which have been promul-gated by the U.S. Soi l Conservation Service (Soil Survey S ta f f , 1975) and the Canada Soi l Survey Committee (1978). These c l a s s i f i c a t i o n systems are con-cerned fundamentally with the recognition of diagnostic horizons, each of which i s defined in terms of d i f f e r en t i a t i n g so i l properties having values with in spec i f ied ranges. Idea l ly , each of these properties has a number of acccessory properties which vary with i t (C l ine, 1949). If th i s occurs, the fol lowing thesis should hold true: where s o i l s have developed from l i t h o l o g -i c a l l y homogeneous parent mater ia ls, horizon types can be expected to be d i s t i n c t from one another in terms of those so i l properties related to pedogenesis. 6 A mult ivar iate space model can be constructed in which the coordinate axes are defined as s o i l properties (Norr is , 1970). Within th i s model each horizon sample in the data set i s plotted as a s ingle point; consequently, each type of horizon i s represented by a group of points. Two questions are relevant. F i r s t l y , to what extent do horizon groups occupy d i f fe rent regions of the space? Secondly, in a numerical or s t a t i s t i c a l context, to what extent can the grouping of the points into the horizon types be considered as an optimum grouping? The present discussion attempts to answer these ques-t ions using chemical data from s ix d i f fe rent types of horizons of Podzolic s o i l s . Several types of parent materials ex i s t in the study area, but they are a l l derived from granodiorite bedrock. DATA BASE The so i l s were co l lected as part of an ecosystem c l a s s i f i c a t i o n program conducted throughout the 5100 ha Univers ity of B r i t i s h Columbia Research Forest (Kl inka, 1976). Located in the f o o t h i l l s of the Coast Range Mountains of southwestern B r i t i s h Columbia, the Forest consists of rugged mountainous land which was heavily glaciated un t i l approximately 10,000 years ago. The s o i l parent materials are dominantly g l ac i a l t i l l and colluvium with assoc i -ated deposits of g l a c i o f l u v i a l , glaciomarine, and a l l u v i a l o r i g i n . The sedi -ments are coarse grained and have been derived from several var ie t ie s of granodiorite bedrock. In some bogs volcanic ash i s present as a d i s t i nc t layer. 7 The 158 sample plots were selected such that each plot would approximate a modal ecosystem i nd i v i dua l ; thus, t rans i t i ona l areas (ecotones) were excluded from sampling. Of the 158 pedons sampled from the centres of the p l o t s , 112 were members of the Podzolic Order (C.S.S.C., 1978). Included in these were 40 F horizons, 42 H horizons, 39 Ah horizons, 58 Ae horizons, 46 Bhf horizons, and 132 Bf horizons (K l inka, 1976). Thirty horizons from each type were randomly chosen with no regard to the frequency of sampling from each of the pedons. The F and H designated horizons were e i ther true F or H horizons or LFH horizons considered in the f i e l d to consist of 90 to 95 percent F or H mater ia l , respect ive ly. The Ah category included both Ah and Ahe horizons. For each horizon twelve properties were measured: pH; percent organic carbon; percent to ta l nitrogen; carbon/nitrogen r a t i o ; exchangeable calcium, magnesium, sodium and potassium; cation exchange capacity; percent base saturat ion; extractable i r on ; and extractable aluminum. CHEMICAL ANALYSIS The pH was measured in 0.01 M CaCl2 (1:2, Peech, 1965). Organic carbon was determined using the Leco analyzer. The semi-micro Kjeldahl tech-nique was used to establ i sh to ta l nitrogen (Bremner, 1965). Cation exchange capacity and exchangeable calcium, magnesium, sodium, and potassium were determined by the ammonium acetate method at pH 7 (Chapman, 1965). Iron and aluminum were extracted by sodium pyrophosphate (Bascomb, 1968). A l l cation concentrations in extracts were measured by atomic absorption spectrophoto-metry. 8 NUMERICAL ANALYSIS The mult ivar iate spat ia l re lat ionships of groups to one another are determined with the use of a measure and an associated objective funct ion. The approach i s s imi la r to the techiques used by Webster and Burrough (1974) and by de Gru i j te r (1977). By basing t he i r analysis on Mahalanobis distance and Wilks ' lambda, Webster and Burrough assume a common variance-covariance structure for a l l groups. Geometrically, th i s i s equivalent to assuming that the regions of the mult ivar iate space occupied by the groups' respective points are best represented by e l l i p so i d s of equal s ize and or ientat ion, de Gru i j te r uses euclidean distance and the average squared euclidean distance from a point to i t s group's centro id. In so doing he rejects the notion of covariance altogether and assumes a common variance structure for a l l groups; thus, in his mult ivar iate space model the groups of points are treated as res iding in equally s ized hyperspheres. The present study employs mult ivar iate density calculated on the ind iv idual group covariance matrices and an objective function developed by Scott and Symons (1971). It i s assumed that the variance-covariance struc-ture of each group may d i f f e r s i g n i f i c an t l y from those of the other groups. The geometric equivalent of th i s i s the assumption that the points for the groups may be perceived as enclosed in e l l i p s o i d s with s izes and orientations independent of one another. Since the groups in the study are d i f ferent types of s o i l horizons, each dominated presumably by d i f ferent pedogenic processes, th i s approach i s most appropriate. 9 Mul t ivar iate density i s defined as fol lows: where fj,|< i s the density of the k t n observation with respect to the j t n group, p i s the number of var iab les , Vj i s the covariance matrix for the j t h group, d^ i s the squared Mahalanobis distance, X|< i s the vector of values for each of the variables for the k t h observation, and Uj i s the vector representing the centroid coordinates for the j t h group. For the s i t u a t i o n where the kth observat ion comes from the j t n group, an alternate density, f*j,k» c a n be defined by replacing d 2 with d*2 : (Eq. 1.2) f * j k = (2ir)_-d * 2 = n2{n.-Z)dZ/{{n.-l)Z'{l-n.d2/{n.-l)2)) where nj i s the number of observations in the j t n group. (Eq. 1.1) f j , k " W •.5p -.5 -.5 • .5d* and 10 This formula (Halm 1976; Jennrich and Sampson 1977) represents a short cut to determining what the squared Mahalanobis distance would be i f the kth observation were not a member of the j t h group. It happens that with d 2 ^0, f * j , k i s always less than fj,|<. I t i s straightforward to determine to what extent predefined groups overlap. Let M be a c l a s s i f i c a t i o n matrix of order g x g with elements m-j t j where g i s the number of groups. Each element equals the number of . observations of group i for which density i s greatest with respect to group j . The quantity Tr(M)/N, where N i s the number of observations, equals the proportion of the observations which are i den t i f i ed with the groups to which they belong. The sum of opposed matrix elements across the diagonal, i . e . , m i » j + m j , i » i ' 4 ' ' * p rov ides i n fo rmat i on as to the extent of over lap between groups i and j . A matrix M* can be s im i l a r l y defined using f * j , k where appropriate instead of fj,k« It can be argued that the quantity Tr(M*)/N provides a less biased estimate of the robustness of the c l a s s i f i c a t i o n scheme. Note that Tr(M*)/N i s always equal to or less than Tr(M)/N. The re la t i ve goodness of a c l a s s i f i c a t i o n of N observations into g groups can be tested with an objective function developed by Scott and Symons (1971). The funct ion, referred to here as S, can be defined as fol lows: (Eq. 1.3) S = n W," J ; W. = (n . - l ) .V . •j = ^ J j j J where Wj i s the sum of squares and cross-products matrix for the j t h group. 11 The more compact the groups are, the smaller i s the value of S. For an optimum c l a s s i f i c a t i o n S i s a minimum. When N i s even moderately large, the number of possible combinations of N observations into g groups i s so great that there ex i s t s no pract ica l way to derive with certa inty the g lobal ly optimum c l a s s i f i c a t i o n . However, there are a number of i t e r a t i v e dynamic c luster ing routines for obtaining l o ca l l y optimum c l a s s i f i c a t i o n s . So long as the value of S decreases with each i t e r -a t i on , rea l locat ion can be e i ther random or based on the best value of a given measure. D i f ferent s ta r t ing points and d i f fe rent procedures may lead to a plethora of loca l optima; often though, the membership of the better of these c l a s s i f i c a t i on s w i l l be quite s im i l a r . The best of these, the one for which S i s smallest, may or may not be the global optimum. In the present work several dynamic c luster ing methods were t r i e d . The smallest value of S was obtained by the fol lowing method. For a l l observa-t ions the alternate density, f*j,k» i s calculated with respect to each of the or ig ina l groups. Next each observation i s a l located to the group for which the value of f * j , k i s greatest. For the resu l t ing second genera-t i on groups, centroids and covariance matrices are determined, and a new value of S i s ca lcu lated. Assuming S has decreased, the procedure proceeds again. For th i s i t e ra t i on f * j , k i s now based on the newly created groups. Reallocation leads to a t h i r d generation of groups. I terat ion of the process stops i f no real locat ions are made, i f S has not decreased, or i f any of the group covariance matrices are s ingular. 12 When dynamic c luster ing as outl ined above was t r i e d using f j |< instead of f * j , k , S decreased, but neither so quickly nor so f a r . With Mahalanobis distance as the measure, WiIks' lambda cont inual ly decreased, while S behaved e r r a t i c a l l y . Cluster ing was also t r i e d using euclidean d i s -tance as the measure. In th i s case the average squared euclidean distance of a point to i t s group's centroid decreased and S again behaved e r r a t i c a l l y . Unless the groups are well segregated in the mult ivar iate space, a resu l t ing optimum i s highly dependent on the measure and objective function used to define i t . Consequently, the choice of measure and function must be regarded as c r i t i c a l . Comparison between each new set of groups and the or i g ina l c l a s s i f i c a -t i on can be made by construction of a Q matrix, analogous to the M and M* matrices discussed e a r l i e r . Q i s composed of the elements qi,j» where i and j refer to membership in the 1 th o r i g ina l group and the new group, respect ive ly. Should the new c l a s s i f i c a t i o n be an optimum, and i f the Q matrix can be organized such that the largest value in each column f a l l s on the diagonal, then Tr(Q)/N serves as a simple indicator of the v a l i d i t y of the or ig ina l c l a s s i f i c a t i o n . RESULTS AND DISCUSSIONS Table 1.1 displays the matrix M* giving the degree of overlap among horizons using f * j |< as the measure. Interpretation of the matrix i s straightforward. Group 1 i s composed of those observations which are 13 Table 1.1: Comparison Between O r i g i n a l and Second Generation C la s s i f i ca t i on s G R 0 U P 1 2 3 4 5 6 F 20 10 0 0 0 0 H 15 13 2 0 0 0 Ah 0 4 17 0 7 2 Ae 0 1 2 20 3 4 Bhf 0 2 6 1 20 1 Bf 0 0 5 1 1 23 14 nearest, in the sense of a greatest f*j,|< value, to the F horizon cen-t r o i d . Group 2 i s related to the H horizon and so forth for the other groups and horizons. For example, of the 30 F samples, 20 have the highest f * j , k value with respect to t h e i r own group centroid and 10 have the highest f * j , k value with respect to the H horizon centroid. The major misal locat ions on the matrix involve the F and H horizons and the Ah and Bhf horizons. Of the 67 off-diagonal observations, 25 involve c r o s s - i den t i f i c a -t i on between the F and H groups and 13 between the Ah and Bhf groups. There are much smaller degrees of overlap present between a l l pairs of the mineral horizons and also between the H and the Ah, Bhf, and Ae horizons. Table 1.2 shows that the value of Scott and Symons' objective function i s IO 1* 5 6 for the or ig ina l horizon groups and 10 2 l + 1 for the s ix new groups. Thus in the mult ivar iate space these second generation groups appear to be more t i g h t l y defined. Also shown on Table 1.2 for the new groups i s the value of Tr(Q)/N, equal to (20+13+17+20+20+23)/180, or 0.63. Thus, 63 percent of a l l observations are closest to the centroid of the horizon to which they belong. Note that in th i s case the matrices M* and Q are i d e n t i c a l . Reiterat ion with the new groups as the s tar t ing point results in a t h i r d generation c l a s s i f i c a t i o n (Table 1.3). The major misal locat ions are again between the F and H horizons and between the Ah and Bhf horizons. As i n d i -cated on Table 1.2 the values of Scott and Symons' objective function and of Tr(Q)/N have dropped to 1 0 1 5 9 and 0.62 respect ive ly. 15 Table 1.2: Values of S and Tr(Q)/N for the Four C la s s i f i ca t i on s C l a s s i f i c a t i on S Tr(Q)/N Orig inal Horizon Groups : 1 0 4 5 6 not appl icable Second Generation Groups : 10^41 0.63 Third Generation Groups : IO * 5 9 0.62 Fourth Generation Groups : undefined 0.54 16 Table 1,3: Comparison Between Original and Third  Generation C lass i f i cat ions " G R O U P 1 2 3 4 5 6 F 23 7 0 0 0 0 H 11 18 1 0 0 0 Ah 0 8 15 0 6 1 Ae 0 2 5 16 1 6 Bhf 0 3 9 0 18 0 Bf 0 0 8 1 0 21 17 I terat ion another time produces the fourth generation c l a s s i f i c a t i o n (Table 1.4). C ros s - ident i f i ca t ion between the F and H groups and between the Ah and Bhf groups i s high, but i t i s also high between most other pairs of groups. The value of Tr(Q)/N i s given on Table 1.2 as equal to 0.54. Calcu-l a t i on of Scott and Symons' objective function i s meaningless because one of the groups contains only eight members, a number less than the number of variables used in the analys i s . When th i s condition occurs, the covariance matrix for that group i s said to be s ingular. For th i s same reason i t i s no longer possible to i te ra te with Equation 1.2. The t h i r d generation c l a s s i f i c a t i o n would appear to be an optimum in the sense that the objective function has the lowest definable value. On the other hand, since a l l of the observations do not have the greatest density, ^*j,k» w i t h respect to the group to which they belong, th i s optimum i s not very sa t i s factory . Regardless of the d i f f i c u l t i e s in defining a s t a t i s -t i c a l l y optimum c l a s s i f i c a t i o n , i t i s c lear that the or ig ina l horizon c l a s s i -f i c a t i on must be viewed as considerably less than optimum. The results of these i te ra t i ons suggest that while none of the horizons, e i ther singly or c o l l e c t i v e l y , forms an i so lated c lu s te r , each does tend to f a l l into a de f in i te region of the mult ivar iate space. If th i s were not the case the values of Tr(Q)/N in Table 1.2 would be much lower. The l imited degree of spat ia l reg iona l izat ion suggested here i s due in part to the presence of precise boundaries e x p l i c i t in the def in i t i ons of some of the groups, e.g., the percent carbon breaks between the organic and the mineral 18 Table 1.4: Comparison Between Original and Fourth  feneration u a s s m c a t i o n s " G R O U P 1 2 3 4 5 6 F 22 8 0 0 0 0 H 11 19 0 0 0 0 Ah 0 10 16 0 3 1 Ae 0 5 6 8 1 10 Bhf 0 3 10 0 16 1 Bf 0 0 12 0 1 17 19 horizons and between the Bhf and Bf horizons. However, in part i t i s probably a result of a d i f fe rent balance of pedogenic processes operating in each of the horizons. It may be that i f the F and H layers had been more precisely defined in the f i e l d then a greater degree of separation between them would have been manifest in the mult ivar iate space. A l te rna t i ve l y , i t has been suggested (L.E. Lowe, personal communication) that had d i f fe rent chemical properties been used, they may have appeared better separated. The confusion between the Ah and Bhf horizons i s somewhat more serious in that the physical d i f f e r -ences between them are often vague. Because the presence or absence of each of these horizons i s of d i rect importance to so i l c l a s s i f i c a t i o n , i t may be that the d i s t i nc t i on between them should be precisely defined. However, i t should be noted that t he i r re lat ionship at the Research Forest may be compli-cated by the possible presence of volcanic ash in the s o i l , a factor which could result in the Ah horizons having chemical properties s imi la r to those of the Bhf horizons (C.S.S.C., 1978). Although there i s no morphological evidence of ash in any of the pedons sampled, th i s p o s s i b i l i t y should not be dismissed completely, since ash i s known to ex i s t elsewhere in the Forest. CONCLUSION For the data in th i s study i t was shown that c ro s s - i dent i f i ca t i on between F and H horizons and between the Ah and Bhf horizons may be consid-ered as f a i r l y high. Nevertheless, an overal l evaluation of the horizon 20 c l a s s i f i c a t i o n system c lea r l y indicates that while none of the s ix horizons forms an i so lated c lu s te r , each of them appears to occur in a de f i n i t e region of the mult ivar iate space. S imi lar analyses of larger and more complete data bases would be of value. 21 CHAPTER 2 THE RELATIONSHIP OF SOIL AND PHYSIOGRAPHIC ATTRIBUTES TO AN ECOLOGICAL CLASSIFICATION SYSTEM 22 During the l a s t decade there has been increased interest in North America in an ecosystem approach to forest resource management (Kimmins, 1977). In western Canada th i s has led to the development and u t i l i z a t i o n of several types of ecosystem c l a s s i f i c a t i o n schemes. Among those successful ly applied in B r i t i s h Columbia i s the system developed by Krajina (1960, 1965, 1969, 1972, 1977) and his colleagues (Wali and Kraj ina, 1973; Kojima and Kraj ina, 1975; Hoefs et a l . , 1975; K l inka, 1976; Bei l et a l . , 1976; Kl inka and Skoda, 1977; Utzig et a l . , 1978; Annas and Coupe, 1979; Kl inka et a l . , 1979; Kojima and Krumlik, 1979; Kl inka et a l . , 1980). Discussions of the system may also be found in some standard textbooks (Mueller-Dombois and El lenberg, 1974; Daniel et a l . , 1979; Spurr and Barnes, 1980). Kra j ina ' s c l a s s i f i c a t i o n i s considered to be t ru l y ecological in scope; however, i t i s based pr imar i ly on the i d e n t i f i c a t i o n of climax plant communi-t i e s . Use of the system i s of pa r t i cu la r interest to s o i l s c i en t i s t s in B r i t i s h Columbia because of the fol lowing assumption inherent in the system: an ecological c l a s s i f i c a t i o n , e s sent ia l l y phytosociological in nature, can be employed prof i tab ly to explain the v a r i a b i l i t y of those so i l and physiogra-phic properties thought to interact strongly with the vegetation. An i n -depth analysis of t h i s assumption i s the object of th i s paper. The manner of invest igat ion i s discussed a f ter a b r ie f description of the c l a s s i f i c a t i o n system. Kra j ina ' s approach to c l a s s i f i c a t i o n involves several levels of integra-t i o n , two of which are relevant here. The f i r s t concerns the de f i n i t i on of a biogeocoenosis. Synonymous with the term ecosystem (Tansley, 1935), a 23 biogeocoenosis refers to a concrete ent i ty on the ground with f i n i t e boun-dar ies , containing both uniform vegetation and s i t e character i s t i c s (Sukachev and Dy l i s , 1964). Thus i t contains vegetative, faunal, microb io log ica l , c l i m a t i c , and so i l elements which are conceptualized as being in dynamic equ i l ibr ium. The vegetation with in a biogeocoenosis composes a phyto-coenosis, the plant community. Taxonomically, climax plant communities are c l a s s i f i e d into plant associat ions. Where d i f fe rent biogeocoenoses are characterized by the same assoc iat ion, t he i r overal l c l ima t i c , moisture, and chemical regimes are presumed to be approximately equivalent (Kl inka, 1976; Kl inka and Skoda, 1977). A second level of integrat ion of K ra j ina ' s system involves the construc-t i on of a phytosociological c l a s s i f i c a t i o n (Kraj ina, 1977). The c l a s s i f i c a -t i on follows Braun-Blanquet 1s taxonomy of plant communities (Braun-Blanquet, 1964), whereby associations are grouped h ie ra rch i ca l l y into a l l i ance s , orders and classes. The groupings are based mainly on the f l o r i s t i c properties of the ecosystems. It i s assumed that the higher the category of the taxonomy, the broader i s the spectrum of some of the associated pedologic and physio-graphic att r ibutes (Kraj ina, 1969). The phytosociological c l a s s i f i c a t i o n i s applied to biogeocoenoses as well as phytocoenoses. Consequently, the c la s s -i f i c a t i o n i s presumed to be va l id not only for vegetation, but also for those s i t e character i s t i c s which s i gn i f i c an t l y interact with the f l o r i s t i c elements of the ecosystem. The present study analyzes the re lat ionsh ip of forty pedologic and physiographic properties to the assoc iat ion, a l l i a n ce , and order categories 24 of the system. The class category i s not considered because of data base l im i t a t i on s and because of i t s very l im i ted usage in the l i t e r a t u r e . Two major issues are addressed. (1) To what extent does the v a r i a b i l i t y of each of the properties increase as the degree of general izat ion increases through the categories? (2) Ignoring the categorical rank, how much does the organization of the biogeocoenoses into associat ions, a l l i a nce s , and orders help explain the v a r i a b i l i t y of each of the properties? The two questions can be examined appropriately in a univar iate context with the use of nested and one-way analyses of variance, respect ive ly. Because univar iate analyses are used exc lus i ve ly , the study does not examine the ecological p r i nc ip l e of compensating factors . Note as well that the l e g i t i -macy of the taxonomy as a phytosociological c l a s s i f i c a t i o n i s not questioned. Rather the study simply attempts to ascertain the extent to which the three selected categories of K ra j ina ' s taxonomic system explain the v a r i a b i l i t y of a number of s o i l and physiographic propert ies. DATA BASE The data comes from a study by Kl inka (1976) at the University of B r i t i s h Columbia Research Forest located in southwestern B r i t i s h Columbia.* 1 The numbers of the plots in Kl inka (1976) from which the data were taken are as fol lows: 2, 3, 4, 5, 6, 7, 8, 12, 13, 14, 16, 19, 20, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 36, 37, 39, 41, 42, 44, 46, 52, 53, 54, 55, 56, 60, 62, 63, 74, 75, 79, 82, 87, 89, 90, 97, 99, 100, 104, 111, 114, 116, 119, 148, 150, 153, 155, 158. 25 The study groups the biogeocoenoses of the Research Forest into twenty-four associat ions. Of these twenty-four taxa, fourteen have complete environ-mental data and are adequately represented to be included here. The fourteen associations f a l l into eight a l l i ance s , and these in turn into three orders. Included in t h i s hierarchy are s ix ty biogeocoenoses, each of which was sampled once. Figure 2.1 displays the synopsis, the names of taxa, and the number of biogeocoenoses which each contains. The stands, a l l natural ly establ i shed, range in age from approximately 100 years to greater than 250 years; they represent mature to old growth stages of succession. Although the time factor has not been held constant, the e a r l i e r , most dynamic periods of ecosystem development have been excluded. The properties under invest igat ion include eight physiographic factors , four mineral s o i l textura l cha rac te r i s t i c s , f i f t een mineral s o i l chemical a t t r ibutes and th i r teen forest f l oo r (LFH) chemical a t t r i bu te s . Because mineral s o i l data were co l lected on a horizon basis, i t was necessary to take weighted averages for each of the nineteen mineral s o i l s propert ies. Both ar ithmetic and exponential weighting procedures were used, bringing the to ta l number of parameters up to f i f t y - n i n e . The properties with t he i r abbrevia-t ions are l i s t e d in Table 2.1. NUMERICAL METHODS For each of the mineral s o i l textura l and chemical propert ies, data for the horizons within the rooting zone of each pedon are reduced to a s ingle value. This was accomplished using both arithmetic and exponential weighting procedures. With the ar ithmetic method the s ingle pedon value i s defined as follows (Kloosterman and Lavkul ich, 1973): Figure 2.1: Synopis of the Taxa Sample Size Association Alliance Order 2 Lichen - Gaultheria - PC - BI Pseudoteuga menziesii 5' Stokesiella - Gaultheria - TH - PM Gaultheria - PM 5 Mahonia - Gaultheria - TH - PH 5 Plagiotheoium - HhytidiadeIphue - TH - PH Hhytidiadelphus - TH 2 Hyloaomium - Mahonia - TP - PM 4 Hyloaomium - (Polystiohum) - PMSTP - TH Hyloaomium - TH Tsuga heterophylla Gaultheria - Vaaainium - PM - TH 3 6 Rhytidiopeie - Vaooinium - AA - TH Vaooinium - TH 4 Blechnum - Vaooinium - AA - TH Blechnum - AA - TH 7 Polypodium - Polystiohum - PM - TP Polystiohum - PM - TP 5 Mahonia - Polystiohum - PM - TP 3 Tiarella - Polystiohum - TP Txarella - TP Thuja 6 Rubus - Polystiohum - TP plicata 3 Ribes - Oplopanax - TP Oplopanax - TP The names of trees species are abbreviated as follows: AA - Abies amabilis, PC - Pinus contorta, PM - Pseudotsuga mensiesii, TH - Tsuga heterophylla, TP - Thuja plicata 27 Table 2.1: Description of Properties Property Description Laboratory Reference — General Physiographic Factors EL Elevation SL Slope in percent RA Incoming solar radiat ion (month of May) Buffo et a l . , 1972 COSAS Cosine of aspect PRS % of ground surface as rock or stone PCF F ie ld estimate of % of s o i l as coarse fragments (>2mm) DPO Depth of LFH layer DPM Depth of rooting zone Soil Textural Character i s t i c s * COFR % Coarse fragments (>2mm) Sieve SAND % Sand (<2mm, >50um) Sieve and p ipette, Jackson, 1958 SILT % S i l t (<50ym, >2um) CLAY % Clay (<2ym) Mineral S o i l * * and Forest F loor * * Chemical Attr ibutes PHH pH-measured in water 1:1, Peech, 1965 PHC pH-measured in CaCl 2 so lut ion 1:2, Peech, 1965 C % carbon content Leco N % nitrogen content Semi-micro Kje ldah l , Bremner, 1965 CNR Carbon-nitrogen ra t i o CA Exchangeable calcium-meq/lOOg pH 7.0, Chapman, 1965 MG Exchangeable magnesium-meq/lOOg " NA Exchangeable sodium-meq/lOOg " K Exchangeable potassium-meq/lOOg " CEC Cation exchange capacity-meq/lOOg " BS % base saturation FEP Iron by pyrophosphate-ppm Bascomb, 1968 ALP Aluminum by pyrophosphate-ppm " FEO Iron by oxalate-ppm McKeague and Day, 1966 ALO Aluminum by oxalate-ppm " * For the mineral s o i l properties both ar i thmet ica l l y and exponentially weighted values for each s i t e were derived from the or ig ina l horizon data. * * Mineral Soi l Chemical Attr ibutes include a l l f i f t een properties l i s t e d . Forest Floor Chemical Attr ibutes include only the f i r s t th i r teen properties l i s t e d . 28 (Eq. 2.1) V a = S viti/i51 where V a i s the new, ar i thmet ica l l y weighted value, n i s the number of horizons, v"i i s the value of the i t n horizon, ^ i s the thickness of the 1^  horizon. With the exponential technique the weight of a horizon diminishes with depth. The s ingle pedon value i s thus determined by the fol lowing equation: .Z V i (exp(-0.02u i ) -exp(-0.02^)) (Eq. 2.2) V e = J L l i , where n Z (exp(-0.02u i)-exp(-0.021 i)) i= l 1 1 V e i s the new, exponentially weighted value, u-j i s the depth of the upper boundary of the i t h horizon, l i i s the depth of the lower boundary of the i t h horizon. Work by Russel and Moore (1968) and by Sondheim et a l . (1981) shows that for many so i l s the in tens i ty with depth of pedogenic development and of organic matter accumulation i s approximately proportional to the exponential term, exp(-0.02d), where d i s depth in cm. This term may also serve as a rough approximation of the a v a i l a b i l i t y of nutrients with depth within the mineral s o i l . Using Equations 2.1 and 2.2 two separate data sets for the mineral s o i l textural and chemical data were created. An a l ternat ive to the integrat ion techniques of these equations involves taking data from speci f ied horizons. For example, the pH of the f i r s t Bf horizon could be used as a var iab le . However, since a given type of horizon w i l l vary in i t s occur-rence, thickness, and depth, and in i t s re lat ionship to the rooting zone, th i s approach was not considered to be sa t i s fac to ry . 29 For the nested analysis of variance a random ef fects model i s used in which components of variance are assigned to each category of the hierarchy. Because the c l a s s i f i c a t i o n as tested i s unbalanced, i t i s necessary to resort to the approximation procedure developed by Gower (1962). The results for the calculated sums of squares and the estimated sums of squares and mean squares are shown in Table 2.2. The calculated mean squares, not shown, are equal to the calculated sums of squares divided by the respective degrees of freedom. Thus each of the variance components are readi ly evaluated. The to ta l variance, i s equal to the sum of the variance components a t t r ibutab le to the order, a l l i a n c e , and association categories, and random error within the association categories respect ive ly: (Eq. 2.3) a T 2 = a 0 r 2 + a A 1 2 + a A s 2 + o E 2 The proportion of the to ta l variance at t r ibutab le to each of the categories of the hierarchy i s readi ly obtained and graphed from th i s equation. The s t a t i s t i c a l s ign i f icance of the components can be determined approximately by a technique developed by Satterthwaite (1946). With th i s procedure quasi-F rat ios and associated degrees of freedom are calculated using the mean square values. Table 2.3 shows the resu lts for the assoc iat ion, a l l i a n ce , and order categories. The calculated mean squares of Table 2.3 represent the expected mean squares of Table 2.2. The a, 3 and y coe f f i c ient s on Table 2.3 are designated such that the expected mean square terms in the numerator and denominator of the quasi-F ra t i o are ident ica l with the exception of one term in the numerator spec i f i c to the level being tested. Table 2.2: Nested Analysis of Variance Design Source Degrees of Freedom Calculated  Sum of Squares Expectations of Sum of Squares Mean Squares Order Alliance Association Error 46 3 m^  MMk=i if, ( xi jkr x*i J k) z 2o E 2+9.4o A s 2+19.5o A 1 Z+38.4a 0 r 2 5a E 2+21.4o A s 2+31.5o A 1 2 6a E 2+24.5o A s 2 46oc a E 2 + 4 . 7 a A s 2 + 9 . 8 c A 1 2 + 1 9 . 2 o 0 r 2 o E 2 +4.3o A s 2 +6.3o A 1 2 o E 2 + 4 . 1 a A s 2 to o are n i Is the number of observations In the 1th order; is the number of alliances of the 1th order, n^j, n ^ , and similarly defined for the lower levels of the hierarchy, x* 1s the calculated grand mean. x* 1 Is the calculated mean of the 1th order; x *^ and x * 1 j k are similarly defined for the lower levels of the hierarchy. x 1 j k 1 Is the 1th observation of the kth association of the jth alliance of the 1th order. aQ 2 , o A ] 2 , a. 2 and ov 2 are the variance components attributable to the orders, alliances, associations, and the variabil ity within the associations (the error), respectively. Null 2 2 n U I Vt » • " - » T J ZJ. - — « g r °0r 0 MST^  2 M C 2 ~ r 7 1 2 M < . 2 U r n Qr M S 0 r . 6 Or H S As . y0r " 5 E s + 7 + I c Table 2.3: Significance Tests for the Nested ANOVA Degrees of Freedom E Quasi-F Ratio Numerator Denominator Coefficients Hypothesis (Nearest Integral Value) „ 2 - n U^S. 6 46 °As = 0 HS^ "Al H SA1 + 6A1 M S E (a A 1 MSA] 4 B A 1 MS £) 2 « „ - 4.1/4.3 w °A1 = 0 MST 2 M«. 2 , 2 H c 2 Al As «A1 H SA1 x 3A1 M S E S= + 17 "4T ° V M S 0 r + B 0 r " SAs ^ O r M S E ( c t 0r M S 0 r 4 3 Or M S As ^ O r M SE> ' M S A s Z + V 1 1 + — 4 T 2 6 °A1 " 4.1/4.3 8A1 = ^ A l °0r = 6.3/9.8 5 *0r " (4.3-4.7aQ r)/4.1 Y 0r = 1 _ a 0 r " B 0 r MS MS.,. MS. . and MSR are the calculated mean squares at the order, all iance, association, and error levels, Or* Al As E respectively. Table 2.4: Design and Significance Tests for the One-Way ANOVA's Order Alliance Association Null Hypothesis: o J ^ O Degrees of Freedom: 2 , 57 7 , 52 13 , 46 3 , 8 2 1 4 / Calculated Sums of Squares E n^x^ -x* ) 2 E n.tx^-x*) / " l ' x Y among Groups - SS 1=1 1=1 1 = 1 3 n i 8 n1 2 1 4 n1 2 Calculated Sums of Squares E E 1 (x,.-x*J 2 E E f x ^ - x M I A * x 1 j " X V within Groups - SSW 1=1 j-1 i j 1 1=1 J - l 1 J 1-1 M J Calculated Mean Squares SSfl/2 SSa/7 SSfl/3 w among Groups - MS, ro Calculated Mean Squares S V 5 7 SS^/52 S S ^ within Groups - MSw 2 2 2 2 2 2 Estimated Mean Squares o H +n0oA o y +n0oA o M +nQaA among Groups . . where n f l equals* 19-2 7.3 2 2 _ 2 Estimated Mean Squares » H °H within Groups F - Ratio MSa/MSw MSfl/MSw MSa/MSw 1 En . 2 — (En<- ), where g 1s the number of groups. * l z.n. 0 g-1 1 ""1 For each of the three independent tests: p is the grand mean and ^ Is the mean of the 1th class; x* Is the calculated grand mean and x^ 1s the calculated mean of the 1th class; n 1 Is the number of observations 1n the 1th class; x ^ 1s the jth observation of the 1th class; o ft 2 and o H 2 are the among group and within group variance components, respectively. 33 The one-way analyses were conducted using the one-factor analysis of variance, random ef fects model, with unequal numbers of observations (Snede-cor and Cochran 1967). This i s displayed for each of the categories of the hierarchy in Table 2.4. As before the to ta l variance can be broken into components. These components can be i den t i f i ed as the among group variance, a A 2 , and the within group variance, o^ 2. A s with the nested ana l -yses, the proportion of the to ta l variance at t r ibutab le to the components a A 2 a n c | a^2 -j s 0 f i n t e r e s t . The r a t i o of o A 2 to O A 2 + 0 W 2 i s referred to as the int rac lass cor re la t ion coe f f i c i en t , p p (Eq. 2.4) P j = a A 2/(a A 2 + a/) RESULTS Tables 2.5 through 2.8 display the s ign i f icance results for both types of analyses. For the one-way analyses the estimated int rac lass correlat ions are given only for those variables found s t a t i s t i c a l l y s i gn i f i c an t ; for the remaining variables the estimated corre lat ions are less than approximately 0.18, 0.14, and 0.11 for the assoc iat ion, a l l i a n ce , and order l eve l s , respec-t i v e l y ; such levels are too low to be of any in teres t . Figure 2.2 shows graphs of percent cumulative variance versus categorical l e v e l . The 2 2 2 2 2 2 percentages of the to ta l variance of , + , + a^ s + , and 2 2 2 2 a 0 r + a A l + aAs + °E a r e P ' ' o t t e d aga ins t the e r r o r , associat ion, a l l i -ance, and order categories, respect ive ly. As an example of the in terpre-tat ion of these tables and f igures , elevation w i l l be discussed in d e t a i l . 34 Table 2.5: S ignif icance Results - - General Physiographic Factors Property Nested ANOVA Assoc. A l l iance Order —One-Way ANOVA Assoc. A l l iance Order EL SL RA COSAS PRS PCF DPO DPM ** ** ** ** 0.64** 0.53** 0.19** 0.66** 0.35** 0.35** 0.32** 0.17* 0.64** 0.36** 0.15** 0.54** 0.21** 0.56** 0.51** 0.38** EL, e levat ion; SL, shape in percent; RA, incoming solar radiat ion (month of May); COSAS, cosine of aspect; PRS, % of ground surface as rock or stone; PCF, f i e l d estimate of % of s o i l as coarse fragments; DPO, depth of LFH layer ; DPM, depth of rooting zone. S ignif icance of the 95% and 99% levels of confidence are indicated by * and * * , respect ively. For one-way ANOVA re su l t s , the int rac lass cor re lat ion coe f f i c i en t s are given where the among group variance component i s judged s i g n i f i c an t l y d i f fe rent from zero at the 95% or 99% level of confidence. Table 2.6: Significance Results - - Soil Textural Characteristics Property Nested ANOVA One-Way ANOVA Arithmetic Exponential Arithmetic Exponential Assoc. Alliance Order Assoc. Alliance Order Assoc. Alliance Order Assoc. Alliance Order COFR SAND SILT CLAY ** ** 0.53** 0.36** 0.20* 0.14* 0.18* 0.21* 0.54** 0.36** 0.20* 0.19* 0.22** CO cn COFR, % coarse fragments; SAND, % sand; SILT, % s i l t ; CLAY, % clay, Table 2.7: Significance Results - - Mineral Soil Chemical Attributes Nested ANOVA One-Way ANOVA Arithmetic Exponential Arithmetic Exponential Property Assoc. Alliance Order Assoc. Alliance Order Assoc. Alliance Order Assoc. Alliance Order P H H ** ** 0.51** 0.36** 0.34** 0.50** 0.56** 0.38** PHC C N CNR CA MG NA K CEC BS FEP ALP 0.50** 0.54** 0.29** 0.49** 0.54** 0.31** 0.25** 0.15* 0.14* 0.15* 0.25** 0.26* 0.20* 0.23** 0.16* 0.20* 0.15* 0.20** o? 0.20* 0.22* 0.15* 0.13* 0.15* 0.21* 0.22* 0.26* 0.19* 0.23* 0.22* PEO , 0.28* 0.19* 0.33** 0.30** ALO 0.19* 0.20* PHH. pH in water; PHC, pH in CaCl 2 solution; C, % carbon, N, % nitrogen, CNR, carbon-nitrogen ratio; CA, exchangeable calcium; MG, exchangeable magnesium; NA, exchangeable sodium; K, exchangeable potassium; CEC, cation exchange capacity; BS, X base saturation; FEP, pyrophosphate extractable Iron; ALP, pyrophosphate extractable aluminum; FEO, oxalate extractable iron; ALO, oxalate extractable aluminum. 37 Table 2.8: Significance Results - - Forest Floor Chemical Properties Property -—Nested ANOVA ---One-Way ANOVA-----v 1 Assoc. Alliance Order Assoc. Alliance Order PHH PHC C N CNR CA MG NA K , CEC BS FEP ALP PHH. pH in water; PHC. pH in CaCl 2 solution; C, % carbon; N. % nitrogen; CNR, carbon-nitrogen ratio; CA, exchangeable calcium; MG. exchangeable magnesium, NA, exchangeable sodium; K, exchangeable potassium; CEC. cation exchange capacity; BS, % base saturation; FEP. pyrophosphate extractable Iron; ALP, pyrophosphate extractable aluminum. 0.41** 0.38** 0.41** 0.39** 0.41** 0.42** 0.22* 0.21* 0.20** 0.25* 0.28** 0.20** 0.23* 0.25** 0.28** 0.18* 0.18* 0.11* 0.23* 0.14* 0.47** 0.17* 0.17* 0.42 0.34** 0.39** 38 Figures 2.2 to 2.5: Graphs of Percent Cumulative Variance versus  Category of the Hierarchy from the Nested ANOVA E 1s error ; As 1s assoc iat ion; Al 1s a l l i a n c e ; Or 1s order. Where two graphs occur on the same set of axes, the upper refers to the arithmetic results and the lower refers to the exponential resu l t s . 39 Looking at the nested analyses of variance results on Table 2.5 f i r s t , i t can be seen that for elevation the association component of variance i s s t a t i s t i c a l l y s i gn i f i cant at the 99 percent level of confidence. At the 95 percent l e v e l , neither the a l l i ance nor the order component d i f f e r s s i g n i f i -cantly from zero. On Figure 2.2 i t i s c lear from the slope of the l i ne seg-2 2 ments that the estimate of i s larger than that for a A s . The former i s not s t a t i s t i c a l l y s i gn i f i can t because of the fewer degrees of freedom assoc-2 i a t e d w i th i t s assessment. The plot shows further that the estimate of a^r i s negative, a result which for p ract i ca l purposes can be equated with zero. When the association category i s considered as a separate, independent c l a s s i f i c a t i o n , the in t rac la s s cor re la t ion coe f f i c i en t for elevation i s e s t i -mated to be 0.64, as given on Table 2.5. This proportion, equal to approxi-mately two-thirds, i s s i gn i f i cant at the 99 percent level of confidence; i t also implies that among group variance, i s approximately twice as great as the within group variance o w2. T n i s S U g g e s t s that , in terms of understanding the v a r i a b i l i t y of elevation in the data set, knowledge of the association taxa i s quite he lp fu l . The a l l i ance and order categories are also tested as independent c l a s s i f i c a t i o n s . Their o^2 estimates are judged s i gn i f i c an t l y d i f ferent from zero at the 99 percent level and the i r i n t rac la s s corre lat ions are 0.53 and 0.19, respect ive ly. Though of s t a t i s t i c a l s i gn i f i cance, the l a t t e r value i s too small to be of much in terpret i ve use. 40 From th i s discussion the fol lowing points emerge concerning e levat ion. As independent taxa both associations and a l l i ances are valuable in that they each account for over half of the to ta l v a r i a b i l i t y . The h ierarchica l ar -rangement of ecosystems into associations also appears usefu l ; from the graph and the s ign i f icance re su l t s , i t i s c lear that the percentage of v a r i a b i l i t y explained by the association category i s comparatively large and s t a t i s t i -c a l l y s i gn i f i c an t . The grouping of associations into a l l i ances seems worth-while in spite of i t s apparent lack of s t a t i s t i c a l s i gn i f i cance. The order category appears to be of no value as a level of the hierarchy and of only marginal value as an independent c l a s s i f i c a t i o n . An examination of the other physiographic factors on Table 2.5 and Figure 2.2 shows that percent slope, percent of s o i l as coarse fragments ( f i e l d estimate), and percent of surface as rock or stone a l l behave quite s i m i l a r l y . In a l l three cases a^2 appears highly s i gn i f i cant and ex-pla ins well over 50 percent of the to ta l variance. Their association i n t r a -c lass corre lat ions are a l l above 0.5. The a l l i ances and orders,, as h ie r -arch ica l const ituents, are of no value; as independent classes the a l l iances account for only a l im i ted amount of the overal l variance, whereas the orders are of even less u t i l i t y . For incoming solar radiat ion the nested and the one-way results are of no s ign i f icance and of minor value, respect ively. Cosine of the aspect and depth of the LFH layer do not appear related to the taxa of the system in any way. From i t s cumulative component graph, depth of the rooting zone can be p a r t i a l l y explained by each of the categories, a l -though none are s t a t i s t i c a l l y s i g n i f i c an t . p T f o r both the associations 41 and the a l l i ance i s estimated as greater than 0.5, and for the orders i t i s nearly 0.4. Analyses of the textural data are provided on Table 2.6 and Figure 2.3. The upper and lower curves on each of the graphs represent the resu lts from the ar ithmetic and the exponential weighting procedures, respect ive ly. The marked s i m i l a r i t y between the two curves for each var iable i s noteworthy. For percent of s o i l as coarse fragments (laboratory determination) both the associations and the a l l i ances appear as va l i d h ierarch ica l categories; how-ever, only the association level i s s t a t i s t i c a l l y s i gn i f i c an t . The i n t r a -c lass cor re lat ion coe f f i c i en t i s over 0.5 for the associations and close to 0.4 for the a l l i ance s . Percent sand and percent clay are s i gn i f i can t at the 95 percent level of confidence for the a l l i ance category only on the nested re su l t s . From the graphs on Figure 2.3, percent s i l t behaves v i r t u a l l y i d e n t i c a l l y . For a l l sand, s i l t and clay one-way analyses, the estimated p I values are very low to non-s igni f icant for the association and a l -l iance categories. None of the textural variables show any re lat ionship to the order category. Table 2.7 and Figure 2.4 display the results for the mineral s o i l chem-i s t r y . Here as well the s i m i l a r i t y between the results for the arithmetic and exponential weighting procedures i s s t r i k i n g . For both measures of pH the component of variance at t r ibutab le to the a l l i ance category i s highly s i g n i f i c an t , accounting for approximately 50 percent of the to ta l variance. As independent c l a s s i f i c a t i on s a l l three categories are s t a t i s t i c a l l y s i g n i -42 f i c an t ; however, only for the associations and the a l l i ances i s the estimate o f °i at or above 0.5. Other s i gn i f i can t resu lts from the nested anal-yses include: calcium s i gn i f i can t for the order category, sodium for the order category for the ar ithmetic data only, and base saturation for the order category for the exponential data only. From the graphs on Figure 2.4 aluminum by pyrophosphate and iron and aluminum by oxalate appear to have major variance components for the a l l i ance category. Results from the one-way analyses ind icate that for the fol lowing variables one or more of the p I estimates was found s i gn i f i c an t : carbon, calcium, magnesium, cation exchange capacity, base saturat ion, iron and aluminum by both pyrophosphate and oxalate. Nevertheless the highest estimate of P j i s only 0.33 and i n most of these cases i t i s 0.20 or les s . For nitrogen, carbon-nitrate r a t i on , and potassium, none of the variance components i n any of the analyses are judged s i g n i f i c an t l y d i f fe rent from zero. Results from the analyses of the forest f l oo r chemical properties are contained in Table 2.8 and Figure 2.5. On the nested analyses, the order estimates of variance for both pH measures are s i gn i f i cant at the 99 percent leve l of confidence. For the association category the estimate of the nested variance component for cation exchange capacity i s highly s i gn i f i cant and accounts for over half of the to ta l variance. Other s i gn i f i cant results on the nested analyses include the estimates of variance for potassium for the associat ion category, for base saturation for the association and the order category, and for aluminum by pyrophosphate for the a l l i ance category. From the graphs on Figure 2.5 calcium and carbon-nitrogen ra t i o both appear to 43 have major variance components for the order category, though neither were found to be s i gn i f i c an t . Examining the results from the one-way analyses i t can be seen that a l l of the variables except carbon, i r on , and aluminum have s i gn i f i c an t variance estimates for at least one of the categories. None of the corresponding in t rac las s cor re lat ion coe f f i c i en t s are above 0.5 and only for the two pH measures, cation exchange capacity, and base saturation are any of the estimated P t values above 0.4. DISCUSSION When the c l a s s i f i c a t i o n i s viewed as h i e ra r ch i ca l , i t appears to be of l im i ted value as a means of pa r t i t i on ing the v a r i a b i l i t y of the physiographic factors or the s o i l a t t r i bu te s . The nested variance components were not judged s i gn i f i can t at a l l three levels of the hierarchy for any of the v a r i -ables examined. In one case, base saturation of the LFH layer, two of the components were found to be s t a t i s t i c a l l y s i gn i f i c an t . For fourteen of the properties only one of the components was found s i gn i f i c an t . A l l of the components on the remaining twenty-five variables were deemed not s i gn i f -i cant l y d i f ferent from zero. For some var iables, such as depth of the rooting zone, the components suggest a desirable trend, in spite of t he i r lack of s t a t i s t i c a l s i gn i f i cance. Provided that at least some of the variables are s i gn i f i cant at each of the three categories of the hierarchy, the c l a s s i f i c a t i o n system could be considered as a legit imate and valuable t o o l . This contention has been 44 suggested in regards to natural versus numerical s o i l c l a s s i f i c a t i o n systems (Kubiena, 1958). For the system under study, however, there appears to be no inherent log ic as to why certa in var iables are s i gn i f i can t for some categories but not for others. Consequently the worthiness of the c l a s s i f i c a t i o n as an eco log ica l l y v a l i d , h ierarchica l system must be ca l led into question insofar as the pedologic and physiographic properties tested here are concerned. When the d i f fe rent levels of the system.are considered as independent c l a s s i f i c a t i o n s , a complementary but very d i f fe rent picture emerges. With the one-way analyses only nine (ten with the exponential weighting) of the var iables are not s t a t i s t i c a l l y s i gn i f i can t at any of the three leve l s . The three levels though must be evaluated separately. At the association level var iables found s i gn i f i cant and with an estimated interc las s cor re lat ion coe f f i c i en t (pj) 0 f g.50 or greater include: e levat ion, slope, percent of surface as rock or stone, depth of the rooting zone, percent coarse f rag-ments ( f i e l d and laboratory estimates), and the two pH measures for the mineral s o i l . At the a l l i ance l e v e l , four variables have estimated Pj value of 0.50 or greater: e levat ion, depth of the rooting zone, and the two s o i l mineral pH measures. At the order level none of the estimated Pj values were equal to or greater than 0.50. Two further points emerge from an examination of the one-way resu l t s . F i r s t l y , of the three categories, the association c l a s s i f i c a t i o n appears to be the most v iable in terms of how i t relates to the forty variables included 45 in the study. Secondly, with the association category in pa r t i cu la r , those var iables best explained by the system are pr imari ly physiographic in nature. The only exceptions to th i s are the so i l pH measures. There are two explanations for the apparent s ign i f icance of many of the physiographic var iables. The f i r s t re lates to mapping procedures. A physio-graphic bias may result during mapping, when an attempt i s made for mapping convenience to l i nk landform boundaries to ecosystem del ineat ions; since the vegetation of these del ineations i s d i r ec t l y involved in the recognition and de f i n i t i on of taxa, a re lat ionsh ip between physiography and taxonomy can be expected. The second explanation, which also serves as j u s t i f i c a t i o n for the f i r s t , i s that physiography undoubtedly does exert a strong influence on ecosystems and thus in turn on associat ions. The nature of th i s influence would seem to involve the moisture (Soi l Survey S ta f f , 1975) and temperature regimes of the s o i l . E levat ion, slope, percent of surface as rock or stone, rooting depth, and percent coarse fragments are a l l c lea r l y related to the hydrologic dynamics within the rooting zone. To varying degrees these factors influence the s o i l ' s thermal character i s t i c s within the rooting zone as w e l l . The f inding that physiographic at t r ibutes are the major d i f f e ren -t i a t i n g c r i t e r i a in the research forest i s corroborated by the work of Eis (1962). The importance of physiography on climax communities i s also discussed by Daubenmire (1952). Most of the non-physiographic properties do not appear to show a strong re lat ionsh ip to the categories of the hierarchy examined. Data from a study 46 conducted in the i n t e r i o r of B r i t i s h Columbia (Wali and Kraj ina, 1973) i n d i -cate that the environmental tolerances of most species are s u f f i c i e n t l y wide that associations of these species may not f a l l within unique physical or chemical ranges. Other factors , such as f i r e h i s tory , past management prac-t i c e s , and seed dispersal patterns may also influence species l ocat ion . In theory these factors are i r re levant to the de f i n i t i on of a taxon defined on the basis of climax cha rac te r i s t i c s ; in pract ice i t may be d i f f i c u l t to d i s -count them completely. The existence of genetic v a r i a b i l i t y within i n d i v i -dual species also complicates the p icture. The p o s s i b i l i t y that a s ingle taxonomic system can explain a major proportion of the v a r i a b i l i t y of f l o r i s t i c , physiographic, and pedologic character i s t i c s may simply be asking too much. This would seem to be pa r t i cu l a r l y t rue, as in the case here, where that c l a s s i f i c a t i o n i s based on only the f l o r i s t i c att r ibutes of the ecosystems. CONCLUSIONS The study indicates that a s t a t i s t i c a l l y s i gn i f i can t re lat ionship ex i s t s between the ecosystem groupings, as defined by the plant associat ions, and many physiographic and so i l var iab les. For e levat ion, slope, percent of surface as rock or stone, depth of the rooting zone, and percent coarse f rag-ments, the association c l a s s i f i c a t i o n explains one-half to two-thirds of the v a r i a b i l i t y . It i s suggested that the s i gn i f i cant physiographic properties manifest t he i r ecological importance pr imar i ly through t he i r e f fects on the s o i l moisture and temperature regimes within the rooting zone. Of the mineral s o i l chemical propert ies, one-half of the v a r i a b i l i t y for pH i s 47 explained by the association c l a s s i f i c a t i o n . Of the forest f l oo r propert ies, 40 to 50 percent of the variance estimates for pH, cation exchange capacity, and base saturation are also explained by the association c l a s s i f i c a t i o n . Results for other properties are considerably lower. Whether viewed as cate-gories of a hierarchy or as independent c l a s s i f i c a t i o n s , the a l l i ances and orders appear to bear l i t t l e or no re lat ionship to most of the at t r ibutes included in the study. A p o s s i b i l i t y for improving the results for the a l l i ances and orders might be to redefine the classes and structure of the system such that environmental character i s t i c s are taken d i r ec t l y into account. However, such a redef in i t i on would resu l t in an increase of the var iat ion within the vegetation parameters. 48 CHAPTER 3 NUMERICAL ANALYSIS OF A CHRONOSEQUENCE, INCLUDING THE DEVELOPMENT OF A CHRONOFUNCTION 49 In 1941 Hans Jenny attempted to formalize much of the early Russian work on pedogenesis with the use of functional relat ionships employing mathe-matical symbolism. S p e c i f i c a l l y , he gives an "environmental formula of s o i l -forming fac to r s : " s = f ( c l , o, r, p, t . . . ) where s i s s o i l , c l i s c l imate, o i s organisms, r i s topography, p i s parent mater ia l , t i s time, and f indicates that s i s funct ional ly dependent on these f i ve factors (Jenny, 1941). Following Jenny's lead there have been a number of s o i l sequence studies aimed at i s o l a t i ng one or more of the factor s . Yaalon (1975) provides a review of much of th i s work. Most of the studies concerned with the determination of chronofunctions have presented the results only graphical ly or diagrammatically (e.g. Dickson and Crocker, 1953; Crocker and Major, 1955; Crocker and Dickson, 1957; Franzmeier and Whiteside, 1963; Ugo l i n i , 1968; Harr i s , 1971). Birkeland (1974, p. 176) gives schematics suggesting the time necessary to obtain a steady state for various s o i l properties and various s o i l orders; in a l l cases the curves have the c l a s s i c S-shape analogous to a b io log ica l growth curve. Ruxton (1968; Carson and Kirkby, 1972) i s one of the few authors to determine a regression equation. He found that the weathering of volcanic glass in north-east Papua followed an exponential decay with time. Lafon and Vacher (1975), working in a s t r i c t l y geological context, have attempted to model the time dependence of diagenetic a l terat ions in Bermuda sandstones 50 using a semi-stochastic d i f f e r e n t i a l equation. They claim that th i s approach i s necessary because of the tremendous complexity of natural diagenetic processes. Yaalon (1975) argues that the appl icat ion of s t a t i s t i c a l and stochast ic functions to pedogenic problems i s va l id and even necessary when the reactions are very complicated or when independent factors cannot be readi ly separated. Kl ine (1973) has proposed a semi-deterministic mathemat-i c a l simulation model of s o i l genesis based on systems theory; however, he goes no further than postulating the theoret ica l framework. The present study concerns the appl icat ion of numerical and s t a t i s t i c a l techniques to a well documented (Cordes, 1972; Hendershot et a l . , 1979; Singleton, 1978; Singleton et a l . , 1978) s o i l chronosequence at Cox Bay on the west coast of Vancouver Island, Canada. There are two aspects of i n -te re s t . One concerns the i d e n t i f i c a t i o n of the results of pr inc ipa l com-ponent analysis applied to chemical and physical data which characterize the ongoing s o i l processes. The other involves the evaluation of a non-linear equation defining pedogenic development as a function of time and depth. Before the numerical analyses are discussed, the data base i s reviewed. THE DATA BASE Site Character i s t ics The so i l samples were taken from seven s i tes along a 550-year-old chronosequence developed on a sandy, continuously aggraded beach at Cox Bay, 51 West Vancouver Island, B r i t i s h Columbia. The rate of aggradation has been determined independently by Cordes (1972) and Singleton (1978) to be f a i r l y constant at approximately 25 cm per year un t i l the early 1900's. At that time escaped logs from log booms began co l l ec t i ng on the beach, disturbing the natural rate of deposit ion. Dating in both studies was done by dendro-chronology. The headland rocks on e i ther side of the bay serve as the sediment source area and consist pr imari ly of greywacke with minor inclus ions of a r g i l l i t e . Results from X-ray d i f f r a c t i o n analysis (Singleton, 1978) of the less than 0.25 mm so i l f ract ion indicated that quartz, plagioclase fe ldspars, and amphiboles are the major const ituents. Comparison of the X-ray traces showed the mineralogy to be r e l a t i v e l y constant throughout the ent i re length of the transect. Topographically, the transect i s 110 m in length and i s oriented perpen-d i cu l a r l y to the beach. Elevation differences between any two sampling s i tes i s less than half a meter in a l l cases. The vegetation i s dominated by Sitka spruce (Picea s i tchens i s ) and sa la l (Gaultheria shal lon). Tree height varies asymptotically from roughly 8 m at the f i r s t s i t e , nearest the beach, to jus t over 40 m at the l a s t two s i t e s . The climate i s characterized by abun-dant r a i n f a l l and a lack of temperature extremes. Tofino A i rpor t , located 8 km from Cox Bay, has a mean annual p rec ip i ta t i on of 127 cm and a dai ly temp-erature mean and standard deviation of 9.0°C and 4.4°C, respect ively. It i s assumed that the climate has remained f a i r l y constant over the la s t s ix cen-52 t u r i e s . Differences among the samples should be explainable in terms of: (a) progressive degrees of pedogenesis, (b) distance from the marine i n f l u -ence, (c) b iocyc l ing , (d) water movement and water table e f f ec t s . Figure 3.1 shows a cross-section from the ocean through the las t s i t e , ind icat ing the horizons and the s i t e ages. The absence of an A horizon at s i te s 1 and 2 i s presumed to have resulted from i n su f f i c i en t time for devel-opment; there are no indicat ions that truncation has occurred. The s o i l s ranged from Typic Udipsamments at s i tes 1 and 2, to Typic Haplorthods from s i te s 3 through 6, to an Aquic Haplorthod at s i t e 7. At each s i t e , samples included in t h i s study came from the top B horizon, the horizon immediately below t h i s , and the lowest horizon sampled in the p r o f i l e ; th i s gives approx-imately equal weight to various types of horizons and to each of the s i t e s . The chemical and physical values for the samples were assumed to be represen-ta t i ve of the middle of the horizons, as shown in Figure 3.1. The actual data base (Table 3.1) consisted of the values for each of the 21 samples for the fol lowing s o i l propert ies: percent organic carbon; per cent nitrogen; extractable iron and aluminium; exchangeable calcium, mag-nesium, sodium and potassium; cation exchange capacity; pH; and percent f ines (<50um). The decision of which pa r t i cu la r variables to include was based part ly on convenience ( i . e . , only variables measured on continuous scales were included) and part ly on a subjective assessment of u t i l i t y in providing information on so i l genesis. Figure 3.1: Cross-section Indicating Horizons and the 21 Sample Locations SITE 127 (70 265 371 480 550 SURFACE AGE (yr) Table 3.1: Original Data OBS AGE yrs DEPTH cm PH C % Fe Al Ca Mg Na K meq/lOOg CEC FINES % 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 127 127 127 170 170 170 265 265 265 371 371 371 441 441 441 480 480 480 550 550 550 5.0 17.7 53.3 7.6 35.5 63.5 20.3 53.3 76.2 10.1 31.7 99.0 15.2 30.4 106.6 7.6 15.2 81.2 21.5 43.1 63.5 4.6 4.6 4.9 4.3 4.5 4.6 4.6 4.8 4.9 4.2 4.5 4.7 4.0 4.3 4.9 4.3 4.5 4.7 4.2 4.4 4.6 0.03 0.03 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.06 0.03 0.01 0.07 0.05 0.00 0.08 0.05 0.00 0.06 0.05 0.02 0.61 0.46 0.00 0.42 0.23 0.00 0.76 0.08 0.00 0.91 0.61 0.08 1.67 1.03 0.02 1.60 1.14 0.17 1.67 1.14 0.34 0.32 0.35 0.24 0.30 0.22 0.21 0.32 0.21 0.23 0.44 0.29 0.19 0.63 0.36 0.30 0.64 0.45 0.21 0.48 0.33 0.20 0.10 0.13 0.06 0.12 0.09 0.05 0.12 0.08 0.06 0.17 0.19 0.09 0.23 0.27 0.07 0.32 0.30 0.11 0.28 0.23 0.15 0.93 0.85 0.48 0.33 0.20 0.23 0.70 0.35 0.38 0.68 0.23 0.15 0.55 0.28 0.10 0.85 0.80 0.10 0.78 0.45 0.48 0.85 0.93 0.30 0.45 0.28 0.25 0.38 0.15 0.15 0.48 0.10 0.05 0.73 0.25 0.08 0.50 0.28 0.05 0.35 0.23 0.08 0.17 0.26 0.24 0.25 0.17 0.16 0.07 0.04 0.04 0.09 0.06 0.05 0.29 0.17 0.06 0.11 0.08 0.04 0.14 0.11 0.08 0.12 0.13 0.08 0.09 0.08 0.08 0.04 0.05 0.06 0.07 0.05 0.05 0.10 0.07 0.05 0.07 0.04 0.05 0.07 0.05 0.04 6.10 11.03 1.71 7.26 3.29 1.92 5.34 2.19 1.71 6.23 9.38 2.26 12.74 8.84 1.58 16.65 13.97 2.60 17.47 11.71 5.55 1.10 1.30 0.00 1.40 0.20 0.20 0.80 0.30 0.00 4.50 1.60 0.30 5.60 2.80 0.00 4.80 3.80 0.10 4.20 2.60 0.90 55 Laboratory Technique For th i s section of the thes i s , the fol lowing ana lyt ica l techniques were conducted. Total organic carbon was determined using the Leco analyser, as none of the horizons were calcareous. A semi-micro Kjeldahl technique was used to establ i sh to ta l nitrogen (Bremner, 1965). Iron and aluminium were extracted by c i t ra te -b icarbonate-d i th ion i te (Mehra and Jackson, 1960). Cation exchange capacity and exchangeable calcium, magnesium, sodium, and potassium were determined by the ammonium acetate method at pH 7 (Chapman, 1965). A l l cation concentrations were subsequently analyzed by atomic absorption spectrophotometry. The pH was measured in 0.01 M CaCl2 (1:2, Peech, 1965). Percent f ines was determined by the sieve and pipette method (Jackson, 1958) a f ter hydrogen peroxide pretreatment for organic matter removal. NUMERICAL METHODS Pr inc ipa l Component Analysis Pr inc ipa l component analysis with a normal varimax rotat ion was per-formed on the data matrix. P r inc ipa l component analys i s , as outl ined by Harman (1967), has been a major ana ly t i ca l tool in a number of so i l i n v e s t i -gations and consequently the mechanics of i t are not explained here. The varimax rotat ion (Kaiser, 1958) i s a modif ication to the basic procedure in which the s t a t i s t i c a l l y s i gn i f i can t components are rotated orthogonally in 56 the mult ivar iate space such that greater s imp l i f i ca t i on of the loadings matrix columns i s obtained. This implies that the loading for each component tends to be e i ther high or near zero. Thus fewer intermediate values re su l t . With th i s method, i den t i f i c a t i on of components with par t i cu la r processes i s f a c i l i t a t e d . An explanation of the mathematics behind the varimax c r i t e r i o n i s provided in the s o i l s l i t e r a t u r e by Webster (1977). Non-Linear Curve F i t t i n g It was decided to f i t component scores and so i l property values to non-l i nea r functions involv ing both time and depth. Non-linear here means that the equation cannot be l i near i zed by su i table transformations; thus the pro-cedure of mult ip le l inear regression cannot be employed. For such non-linear cases, i t i s generally possible to define an i t e r a t i v e least squares solut ion as fo l lows. F i r s t define the Function F as fo l lows: n 2 (Eq. 3.1) F = Z (y - y ' ) j = 1 j J The object i s to minimize F, where y ' j i s the estimated value of the property for observation j as determined by the non-linear equation, y j i s the actual value of the property for observation j , and n i s the number of observations in the set. Next a multi-dimensional space i s constructed, where each of the dimensions represents one of the coef f i c ient s in the non-57 l i near equation. If p i s the number of coe f f i c i en t s , then a p-dimensional space resu l t s . For each point in the space, F can be calculated. Thus the coordinates of the point at which F i s a minimum correspond to the optimum values of the coe f f i c i en t s in the non-linear equation. Once th i s has been accomplished, i t i s possible to determine r, the Pearson product-moment corre lat ion c oe f f i c i e n t : ( E q . 3.2) P . £(y-y*) - ( y - y ' * ) ((z(y-y*)2) • (s(y'-y'*)V/2 where y * and y ' * are the means of the y and y ' values, respect ive ly. There are a number of non-linear optimization routines for f inding the optimum point in the p-dimensional space. The technique used here i s termed a sequential simplex algorithm (Nelder and Mead, 1965). A s tar t ing point in the space i s f i r s t guessed; then p more points in the space are a r b i t r a r i l y defined around i t . Of the p + 1 points the point which gives the worst value for F i s ref lected through the hyperplane of the remaining p points. This new point plus the remaining p points form the new set of p + 1 points. Ref lect ion of the worst point occurs again, etc. Thus the continuously redefined p + 1 points move through the space towards a minimum on the hyper-surface determined by values of F. The f igure formed by the points, ca l l ed a simplex, can be forced to expand or contract in response to local curvature condit ions. 58 By such procedures i t i s possible to converge upon a minimum on the hypersurface. The reader i s referred to Nelder and Mead (1965) for a tech-n ica l discussion of the simplex method. Many computing centers have a v a i l -able the simplex technique as well as several other types of non-l inear optimization routines. A note of caution i s that for many non-linear equa-t ions there may be more than one minimum and that there i s no foolproof method of determining whether a pa r t i cu la r minimum i s in fact the global minimum. RESULTS AND DISCUSSION From Pr inc ipa l Component Analysis Results from the pr inc ipa l component analysis of the raw data indicated that there are two s i gn i f i can t components, with eigenvalues greater than 1.00, (Kaiser, 1960) and that these components explain 86% of the to ta l v a r i -ance. Table 3.2 gives the loading for the eleven so i l propert ies. The load-ings on the f i r s t component show that i t has strong pos i t ive corre lat ion with organic carbon, nitrogen, aluminum, i r on , cation exchange capacity, and percent f i nes . The pH i s also highly correlated with the f i r s t component, but negatively so, implying that low values of one w i l l generally be found with high values of the other. Looking at the second column of loadings, i t can be seen that potassium, magnesium, and sodium have high negative cor re la -t ions with component II. The loadings of calcium on both components are of intermediate magnitude, making i t s i d en t i f i c a t i o n with e i ther one suspect. 59 Table 3.2: Component Loadings No. Property Component I Component II 1 pH - .81 + .26 2 N + .95 - .15 3 C + .97 - .13 4 Fe + .89 - .28 5 Al + .96 + .10 6 Ca + .56 - .49 7 Mg + .30 - .91 8 Na + .11 - .87 9 K - .02 - .97 10 CEC + .92 - .18 11 Fines + .96 - .15 60 The loadings on the f i r s t component are c losely related to what i s con-sidered to be the dominant pedogenic process. This enta i l s the formation of i ron and aluminium sesquioxide coatings on the sand grains and the sloughing o f f of these coatings to form s i l t and c lay-s ized pa r t i c l e s . Intermixed with the sesquioxide material i s organic matter, suggesting a casual re lat ionship consistent with modern concepts of Spodosol genesis (Soi l Survey S ta f f , 1975). As would be expected, nitrogen co-varies with organic matter. Due to the low content of p h y l l o s i l i c a t e clay mater ia l s , the cation exchange capa-c i t y i s a function of the organic matter and the sesquioxides. With low absolute values for the basic cat ions, resu l t ing from high leaching rates, organic matter exerts strong control over the pH. The loadings on the second component ind icate that the d i s t r i bu t i on of the basic cations i s largely governed by other factor s , such as the marine environment (Etherington, 1967; Clayton, 1972) and possibly b iocyc l ing. Sea spray sweeping onto the i s land includes sa l t s of sodium, potassium, magnesium and calcium. Because the whole area i s forested, the section of the sequence nearest the beach i s most affected by the spray. Limited data from Cordes (1972) indicate that on the act ive beach sea spray annually deposits 250 g/m.2 0 f sodium, 8.9 g/m^ of potassium, 22 g/m^ of magnesium, and 7.0 g/m2 0 f calcium. Other data by Cordes (1972) suggests that at a distance of 250 meters from the beach inputs drop to less than 0.02 percent of these values. Moving inland from the shore, i t can be expected that the effects of b iocycl ing w i l l gradually begin to outweigh those of sea spray. 61 With the components being interpretable, i t was of interest to consider them separately. Figure 3.2 displays a hand-contoured cross sect ion, based on the scores from component I. The high level of concurrence between Figure 3.2 and Figure 3.1 shows that pedogenesis as discussed above correlates strongly with horizon development. This reinforces the fundamental tenet of pedology that in the absence of geomorphic causes horizon development i s a d i rect manifestation of pedogenesis. Scores for component II are mapped in Figure 3.3. It can be seen that the d i s t r i bu t i on of the bases follows a regular pattern quite d i s t i n c t from that on Figure 3.2. The comparatively high base values implied along most of the surface and at depth for the f i r s t two s i te s i s in keeping with the ideas on marine influence and b iocyc l ing discussed above. The i r r e g u l a r i t i e s of the l a s t three s i tes may be p a r t i a l l y explained by the observance at these p i t s in the winter of a near surface f luc tuat ing water tab le . However, neither regular monitoring nor sampling of the ground water has occurred as e i ther a part of th i s or previous studies. Results From the Curve F i t t i n g Because component I appears to act as a general index of pedogenic development i t was decided worthwhile to t ry to f i t component I scores to an empirical equation involving both time and depth. The equation used was: (Eq. 3.3) s = C j + C g ' e x p ^ d / C g ) • ( l + c 4 » e x p ( - t » c 5 ) ) " 1 where s i s component 1 scores, c-j , ( i = l . . .5 ) , are coe f f i c i en t s , d i s depth in cm and t i s time in years. Pedogenic development i s assumed to vary Figure 3.2: Cross-section Showing Contours Based on Component I Scores Figure 3.3: Cross-section Showing Contours Based on Component II Scores 64 exponential ly with depth. This i s analogous to temperature amplitude in an i so t rop i c s o i l , where C 3 i s termed the damping depth (Monteith, 1973). At depth d=C3 the magnitude of pedogenic development i s e " l or 0.37 times the magnitude at the surface. At depth d=3«C3 the magnitude i s e-3 or only 0.05 times that at the surface. The second part of the equation states that pedogenic development follows a l o g i s t i c curve over time. The l o g i s t i c , one of a family of S shaped curves, has been used to model b io log ica l growth, population dynamics, and economic development. The time coordinate of the i n f l e c t i o n point on the l o g i s t i c curve, tj.» i s given by: (Eq. 3.4) t T = (In c 4 ) / c 5 After several hundred i te ra t i ons using the simplex routine at the Uni-ver s i ty of B r i t i s h Columbia Computing Centre (Patterson, 1978), the best value for the f i ve coe f f i c i en t s were found to be: ci=-1.50, C2=7.23, C3=55.3, 04=10.4, 05=0.00531 Following Equation 2, r and r 2 were determined as 0.99 and 0.98, respec-t i v e l y . With twenty degrees of freedom th i s r value i s much greater than 0.67, the minimum value needed to be s i gn i f i can t at the 99.9 percent con f i -dence l e v e l . The s t a b i l i t y of the simplex results was checked by start ing from d i f fe rent points on the F hypersurface. It was found that within the v i c i n i t y of the minimum the hypersurface was quite regular and convergence on the minimum would always re su l t . Furthermore, the curvature of the hyper-surface near the minimum was rather pronounced, implying that the sampling variances of the estimates of the coe f f i c ient s are small. In conjunction 65 with the high r value, th i s means that i t i s reasonable to feel f a i r l y c on f i -dent about the estimates of the coe f f i c i en t s given above. The behavior of Equation 3.3 i s worth examining. Figure 3.4 shows a predicted three-dimensional map of the pr inc ipa l component I value plotted against time and depth. It should be noted that the l i nes in Figure 3.4 should not quite reach the so i l surface. This i s so because the balance of pedogenic processes in the A and & l horizons i s presumed to be very d i f fe rent from that in the B2, B3 and C horizons. A further graphical comment concerns the i n f l e c t i o n l i n e , occurring at 441 years at any depth. Of the seven s i te s four occur before th i s age, one at i t , and two fol lowing i t . The fact that a number of data points are located on both sides of the l i ne strengthens the argument for using an S-shaped curve. Although the data extend only from 127 to 550 years, i t was of interest to extrapolate the graph to zero and 1200 years. Two points emerge by doing t h i s . The f i r s t concerns the boundary condition at zero years. Along th i s l i n e pedogenic development should i dea l l y be zero yet the l i ne does show some curvature. Thus in the very i n i t i a l stages of pedogenesis, development occurs at a s l i g h t l y faster rate than indicated by the diagram. The second point concerns time to steady state. It can be seen that between 800 and 1000 years pedogenesis begins to level o f f ; at 900 years in fact development i s greater than 90 percent of the maximum. These f indings strongly corrob-orate the postulations by Birkeland (1974, p. 176) as presented in his graph of Spodosol development versus time. Figure 3.4: Graph Depicting Pedogenic Development as a Function of Depth and Age. From Equation 3,3 67 When invest igat ing the re lat ionsh ip between so i l a t t r ibute data and so i l c l a s s i f i c a t i o n , Russel and Moore (1968) assumed that the values for many physical and chemical properties decrease exponentially with depth in a manner analagous to the behavior of the fol lowing funct ion: (Eq. 3.5) w = c»exp(-c«d) where w i s a weighting factor , c a constant and d depth. For each property they converted a series of horizon values to a s ingle value representative of the pedon by mult ip ly ing w by a horizon value, integrat ing across the horizon boundaries, and summing the results for a l l horizons. Using c lus ter ing pro-cedures they found that with c equal to 0.02 there was a strong re lat ionsh ip between a s o i l ' s physical and chemical character i s t i c s and i t s c l a s s i f i c a t i o n category. The exponential part of Equation 3.3 can be transformed to a form equivalent to that of Equation 3.5 by simply defining C3=l/c and C2=k*c, where k i s an arb i t rary constant. Since C3 i s equal to 55.3, i t s rec ipro-cal i s 0.018, a value not s i g n i f i c an t l y d i f ferent from the 0.02 value mentioned above. The notion of a pedogenic damping depth i s i n t u i t i v e l y appealing because of the analogy to a thermal damping depth. As well i t i s potent ia l l y useful i n terms of the de f i n i t i on of a C horizon; th i s i s especia l ly true in those s o i l s in which the t ran s i t i on from B to C horizons i s comparable to var iat ion along a chromatographic column. Since many so i l s are approaching a steady s tate, i t would be easy to define a C horizon as that section of a pedon f a l l i n g below three damping depths for example. The c r i t e r i o n on which the 68 damping depth would be based could be e i ther a s ingle so i l property, such as organic carbon, or a factor representing a combination of chemical and physical properties thought to play major roles in the genesis of the par-t i c u l a r s o i l in question. Further numerical analysis of component II was not attempted because of i n s u f f i c i e n t data regarding sea spray input, b iocyc l ing, and water table dynamics. Simply comparing component II scores to tree height would be of l i t t l e value. Nevertheless, the regular i ty of the pattern displayed in Figure 3.3 suggests that , were an adequate data base ava i lab le , addit ional analysis might be worthwhile. CONCLUSION The Cox Bay deposits provide a very useful chronosequence. The homo-geneity of the parent mater ia l , the uniformity of topography, and the con-stant rate of aggradation make the area highly suitable for studying so i l development. Appl icat ion of pr inc ipa l component analysis with a varimax rotat ion appears to separate pedogenic processes from sea spray addit ions. Curve f i t t i n g analysis of the component associated with pedogenesis produces a model of so i l development over time and depth expressed as a s ingle empir-i c a l equation with both l o g i s t i c and exponential terms. Because only one chronosequence i s examined, the extent to which these results are s i t e spec-i f i c cannot be ascertained. Nevertheless, the general s im i l a r i t y between the findings here and those by other workers elsewhere i s encouraging. 69 The techniques employed may be appl icable to reclamation projects , where for example the leaching rates from mine t a i l i n g s might be modelled in a s im i l a r fashion. Instead of a purely s t a t i s t i c a l approach, i t may be pos-s i b l e to apply a stochastic analysis in which the autocorrelation of an observation to those observations adjacent to i t in both time and space i s taken into account. The general s t a t i s t i c a l relat ionships discussed in the present paper could be used as the basis of such a procedure. With a stochast ic approach i t would be preferable to sample in time and space at equal i n te r va l s . 70 CHAPTER 4 NUMERICAL ANALYSIS OF A CHRONOSEQUENCE INCLUDING AN ASSESSMENT OF VARIABILITY 71 A number of recent studies have examined the v a r i a b i l i t y of s o i l physical and chemical properties (Sondheim and K l inka, 1982; Burgess and Webster, 1980; Webster, 1978; Beckett and Webster, 1971; Webster and Beckett, 1968). A major conclusion of these works i s that the inherent, error assoc-iated v a r i a b i l i t y of most properties i s usually as great or greater than the v a r i a b i l i t y a t t r ibutab le to known fac to r s , such as differences in vegetation or te r ra in features. This suggests that i t may be d i f f i c u l t to measure accurately trends related to temporal or landscape cha rac te r i s t i c s . Of the large number of avai lable chronosequence studies (Jenny, 1980; Yaalon, 1975; B i rk land, 1974), none have had an experimental design allowing for an assess-ment of the v a r i a b i l i t y of propert ies. Rather, they a l l appear to have concentrated on modal descr ipt ions. In studies by Sondheim et a l . (1981) and Ruxton (1968) the time dependent changes in properties have been analyzed numerical ly, but the resu l t ing regression equations were based on compara-t i v e l y few points, with only one pedon representing each posit ion along the time ax i s . Previous numerical chronosequence studies to contain rep l i cat ions include works by Jenny (1965) and Olson (1958); however, in both cases not a l l points were repl icated and the notion of v a r i a b i l i t y was not addressed. The present study examines data from s ix moraines located adjacent to Mt. Robson in the Canadian Rockies. On each moraine ten p i t s were dug and samples were co l lected from three standard depth interva l s fol lowing a rigorous sampling scheme. Three major questions are addressed. 1) What are the major pedogenically related processes operating on the moraines? 72 2) To what extent does the inherent v a r i a b i l i t y of the parent material mask expected trends? 3) For selected properties does the inherent v a r i a b i l i t y l i m i t the usefulness of estimated chronofunctions? The techniques used to answer these questions include analysis of variance, factor analys i s , and non-linear regression. DATA BASE S i te Character i s t ics The terminal and f i ve recessional moraines under study are s ituated in front of the Robson G lac ie r , the largest g lac ie r on Mt. Robson. The mountain i s located just west of the continental d iv ide in the Canadian Rockies at 53°7'N l a t i tude and 119°9'W longitude. The moraines are readi ly i den t i f i ed on 20 chain (1:15,840) a i r photographs (F l ight Line BC7515, Nos. 147 and 148) which may be obtained from AIR B.C., Surveys and Mapping Branch, B r i t i s h Columbia Ministry of Environment, V i c t o r i a , V8V 1X5, Canada. Referred to here as Moraines A through F, they are located at a bearing of N45W at distances of 1.59, 1.45, 1.34, 1.25, 0.99 and 0.64 km, respect ively, from the snout of the g lac ie r as depicted on the photography. The mountain and moraines are s ituated at elevations of 3959 m and approximately 1676 ± 8 m, respect ive ly. 73 The chronology of the sequence has been documented by Cooper (1916) and Heusser (1956). Heusser's work shows that sometime between 1350 and 1650 the Robson Glac ier advanced roughly 0.5 km over an Engelmann spruce forest . It remained f a i r l y s t a t i c un t i l the late 1700's, at which time i t began to re t reat . As i t did so, i t deposited nearly twenty recessional moraines. The ages of the s ix most prominent moraines, these included in th i s study, were determined using tree r ing cores and an age-height growth curve for the moraines provided by Heusser (1956). The resu l t ing ages for Moraines A through F are 193, 96, 79, 65, 55 and 33 years before the 1979 f i e l d season, respect ive ly. For Moraines A, B, C, D and E, the ages are based on an average of three Engelmann spruce t rees . For Moraine F, only one spruce was examined. With reference to Cooper's terminology (1916), Moraine A i s the terminal moraine and Moraines B, C and D are the t h i r d , fourth and f i f t h recessional moraines. Plant succession along the moraines has been examined by Cooper (1916), Heusser (1956), Tisdale et a l . (1966), and again in the present study. Plots of f i ve metres radius were establ ished around each so i l p i t . Vegetation cover for each species was estimated by use of the Domin-Krajina cover abundance scale (Mueller-Dombois and El lenberg, 1974). For selected species categorical scale values were transformed to percentage values based on the corresponding category midpoints. The results were averaged for each moraine and in some cases a ltered s l i g h t l y a f ter examination of a i r and ground photo-graphy. 74 The pioneering species on Moraines E and F and on younger sediments are sweet vetch (Hedysarum mackenzi i), yellow dryas (Dryas drummondii), white dryas (Dryas octopetala), Indian paintbrush ( Ca s t i l l e j a p u l l i d a ) , dwarf f i r e -weed (Epilobium l a t i f o l i a ) , several wil low species (Sal ix glauca, Sal ix  v e s t i t a , var. erecta, Sal ix r i g i d a , and Sal ix brachycarpa), and Engelmann spruce (Picea engelmanii). Sweet vetch and the two dryas species, a l l involved in nitrogen f i x a t i o n , often appear to serve as centers of radiat ion for the other species. Also a f fect ing d i s t r i bu t i ona l patterns are some small scale geomorphic features; depressional areas, including miniature ket t les and f l u t e s , have a higher concentration of vegetation than the surrounding coarser and dryer mounds. The forest community on Moraine A appears to be more randomly dispersed. Dominant species include Engelmann spruce, red bearberry (Arctostaphylos rubra), glandular birch (Betula glandulosa), the willow and dryas species, soapberry (Shepherdia canadensis), carex (Carex  sc i rpo idea), alpine aster (Aster a lp inus ) , bracted wintergreen (Pyrola  bracteata), bracted lousewort (Pedicular is bracteosa), and assorted mosses and l ichens. The percent cover graphs (Figure 4.1) indicate that while for some species the change across the moraines i s gradual, for others i t i s dramatic. Engelmann spruce, glandular b i r ch , and red bearberry show compara-t i v e l y slow and continuous increases through the sequence. By comparison, for both sweet vetch and yellow dryas, a sharp increase and a sharp decrease are evident between Moraines F and B, a time span of only 63 years. Trends for to ta l vegetation cover, height of the dominant t rees , thickness of the l i t t e r layer, and rooting depth of the 1 mm roots, also show a wide var iety of patterns (Figure 4.2). 75 Figure 4.1; Percent Cover on the Moraines for Five Plant Species 76 Figure 4.2: Percent, Based on Value for the Oldest Moraine, of Five S ite Factors YEARS SINCE DEGLACIATION RD i s rooting depth; VC i s to ta l vegetation cover; DC i s depth of the Ck horizon; LH i s thickness of the LFH horizon; and TH i s dominant tree height. For Moraine A, the respec-t i v e values for the f i ve factors are 55 cm, 100%, 18 cm, 5.7 cm, and 11.3 m. Plotted data are expressed as a percentage of these f igures . 77 The bedrock of the headwalls and sidewalls of the Robson Glacier consists pr imar i ly of limestone, dolostone, argi l laceous limestone, ca lca r -eous shale, and limestone conglomerate, with smaller quant i t ies of non-calcareous shale and s i l t s tone also present. This i s ref lected in the c las t l i tho logy of the moraines and has been corroborated by the 1:250,000 mapping of the region by Mountjoy (1980). Mineralogical determination by x-ray anal -y s i s of the <2 mm f ract ion was performed on s ix samples. Two samples were taken from each of Moraines A, C, and F, with one of the samples coming from the 0 to 15 cm depth interva l and with the other coming from the 30 to 45 cm depth i n t e r v a l . The s ix traces were very s im i l a r . They a l l indicated the presence of c a l c i t e , dolomite, quartz, k a o l i n i t e , i l l i t e , c h l o r i t e , and vermicul i te. The nearest meteorological s tat ion to Mt. Robson i s at Red Pass Junct ion, 17.5 km to the southeast of the mountain and at an elevation of 1059 m. For the stat ion the mean da i ly temperature and mean to ta l p rec ip i t a t i on are 2.1°C and 73.7 cm, respect ive ly. The mean annual snowfall i s 391 cm or about 53 percent of the mean to ta l p rec i p i t a t i on . The mesoclimate at the moraines i s considerably harsher than that at Red Pass Junction. Not only i s there a difference in elevation of more than 600 m between the two s i t e s , but as w e l l , the moraines are subject to cold a i r drainage from the g lac ie r . Both r a i n f a l l and snowfall are probably several times greater on the moraines compared to Red Pass Junction. The so i l s on the moraines can be characterized as belonging to the very cold s o i l temperature class and the perhumid so i l moisture subclass (C.S.S.C., 1978). 78 Assuming that the mean annual s o i l temperature i s above 0°C, the s o i l s vary from Orthic Regosols on Moraine F to Orthic Eutr ic Brum'sols on the f i ve older moraines; otherwise, they range from Orthic S tat ic Cryosols on the three younger moraines to Brun i so l ic S ta t i c Cryosols on the three older moraines. Using d i l u t e HC1 ac id , a l l s o i l s effervesced to the surface of the mineral mater ia l . The average calcium carbonate equivalent i s over eighty percent. Organic carbon content of the surface horizon for the oldest moraine i s just under one percent, and the corresponding organic carbon-nitrogen ra t i o i s approximately 20. A l l s o i l s appeared well drained with no evidence of mott l ing. Moist colours varied very s l i g h t l y from l i gh t o l i ve grey (5Y 6/2) for the surface horizon of the oldest moraine to grey (N 5/0) for samples taken at depth or from anywhere on the younger moraines. The corresponding dry colours were both l i g h t grey (5Y 7/1 and N 7/0, respec-t i v e l y ) . F i e ld estimation of coarse fragment content ranged from for ty to seventy percent by volume, with no trends evident across the moraines or with depth. The texture of nearly a l l samples taken from the moraines was loam. By contrast the texture of several samples obtained from the edge of the ice was loamy sand. The morainal samples were extremely hard when dry, f irm when moist, and s t icky and p l a s t i c when wet. Weak horizonation was evident on a l l but the youngest moraine. A Bmk horizon overlying a Ck horizon was defined on the basis of a gradual change in structure (C.S.S.C., 1978). The Bmk was f ine subangular blocky with a granular secondary structure, whereas the Ck was medium subangular blocky with no secondary structure. The depth of the Bmk increased from zero to 18 cm across the moraines (Figure 4.2). 79 Sampling Design On each of the s ix moraines examined, the fol lowing sampling procedure was employed. A f i f t y metre chain was placed along or near the crest of the moraine on a section where the microtopography was r e l a t i ve l y smooth. In a l l cases th i s was around the middle of the moraine, as the surfaces of the two ends t yp i c a l l y were covered with miniature kett les and small mounds. The chain was subdivided from west to east into f i ve sequences: 0 to 10 m, 10 to 20 m, 20 to 30 m, 30 to 40 m, and 40 to 50 m; these were labe l led Segments 1 through 5, respect ive ly. In every segment two points were randomly chosen, and from each of these a random of f set up to 4.5 m in length was taken in a northerly d i rec t i on . A p i t was dug at each of the new points, provided that i t was at least a metre away from any major tree or shrub. If i t was not, a new offset was picked. The two p i t s were randomly labe l led as P i t 1 and P i t 2. In th i s fashion, two p i t s represented each segment, and the f i ve segments represented - each moraine. Bulk s o i l samples for a l l p i t s were co l lected at three standard depth i n te rva l s : Depth 1, 0 to 15 cm; Depth 2, 15 to 30 cm; and Depth 3, 30 to 45 cm. Add i t i ona l l y , three samples were obtained from the edge of the i c e , as indicators of time zero. Properties and Laboratory Methods Percent organic carbon (C), percent to ta l nitrogen (N), and the i r r a t i o (C/N) were determined for a l l 183 resu l t ing samples (Table 4.1). For a subset of 39 samples, the fol lowing properties were evaluated as well (Table Table 4.1: Organic Carbon and Nitrogen for a l l 183 Observations Organic Total Carbon Nitrogen n S P 0 •I A 1 1 1 0.878 0.0508 A 1 2 1 1.005 0.0457 A 2 1 1 0.779 0.0384 A 2 2 1 0.773 0.0412 A 3 1 1 0.341 0.0187 A 3 2 1 0.820 0.0352 A 4 1 1 0.689 0.0353 A 4 2 1 1.Z08 0.0585 A 5 1 1 0.710 0.0314 A 5 2 1 0.918 0.0500 A 1 1 2 0.221 0.0107 A 1 2 2 0.206 0.0154 A 2 1 2 0.248 0.0096 A 2 2 2 0.225 0.0120 A 3 1 2 0.174 0.0112 A 3 2 2 0.185 0.0116 A 4 1 2 0.268 0.0095 A 4 4 2 0.239 0.0159 A 5 1 2 0.224 0.0132 A 5 2 2 0.271 0.0146 A 1 1 3 0.133 0.0103 A 1 2 3 0.125 0.0100 A 2 1 3 0.226 0.0118 A 2 2 3 0.189 0.0097 A 3 1 3 0.183 0.0110 A 3 2 3 0.146 0.0086 A 4 1 3 0.206 0.0104 A 4 2 '3 0.184 0.0116 A 5 1 3 0.166 0.0099 A 5 2 3 0.233 0.0128 B 1 1 1 0.690 0.0384 B 1 2 1 0.286 0.0183 B 2 1 I 1.078 0.0566 (continued on next page) Organic Total Carbon Nitrogen N s P 0 - X C 1 1 1 0.512 0.0324 C 1 2 1 0.165 0.0119 C 2 1 1 0.731 0.0397 C 2 2 1 0.386 0.0232 C 3 1 1 0.552 0.0261 C 3 2 1 0.583 0.0345 C 4 1 1 0.761 0.0387 C 4 2 1 0.510 0.0328 C 5 1 1 0.490 0.0241 C 5 2 1 0.473 0.0256 C 1 1 2 0.239 0.0093 C 1 2 2 0.233 0.0126 C 2 1 2 0.369 0.0167 C 2 2 2 0.289 0.0141 C 3 1 2 0.283 0.0135 C 3 2 2 0.187 0.0127 C 4 1 2 0.270 0.0153 C 4 2 2 0.277 0.0154 C 5 1 2 0.207 0.0139 C 5 2 2 0.228 0.0120 c 1 1 3 0.142 0.0085 c 1 2 3 0.145 0.0109 c 2 1 3 0.215 0.0111 c 2 2 3 0.236 0.0133 c 3 1 3 0.145 0.0099 c 3 2 3 0.152 0.0093 c 4 1 3 0.149 0.0089 c 4 2 3 0.203 0.0103 c 5 1 3 0.205 0.0115 c 5 2 3 0.154 0.0096 D 1 1 1 0.214 0.0130 0 1 2 1 0.551 0.0301 0 2 1 1 0.372 0.0209 Organic Total Carbon Nitrogen M S P D % E 1 1 1 0.340 0.0176 E 1 2 1 0.235 0.0135 E 2 1 1 0.248 0.0174 E 2 2 1 0.231 0.0091 E 3 1 1 0.191 0.0129 E 3 2 1 0.272 0.01'.3 E 4 1 1 0.217 0.008a E 4 2 1 0.238 0.0126 E 5 1 1 0.337 0.0238 E 5 2 1 0.429 0.0241 E 1 1 2 0.188 0.0109 E 1 2 2 0.348 0.0239 E 2 1 2 0.151 0.0101 E 2 2 2 0.169 0.0078 E 3 1 2 0.113 0.0083 E 3 2 2 0.172 0.0098 E 4 1 2 0.114 0.0065 E 4 2 2 0.145 0.0079 E 5 1 2 0.221 0.0158 E 5 2 2 0.190 0.0129 E 1 1 3 0.143 0.0093 E 1 2 3 0.152 0.0107 E 2 1 3 0.139 0.0090 E 2 2 3 0.102 0.0077 E 3 1 3 0.086 0.0073 E 3 2 3 0.113 0.0055 E 4 1 3 0.086 0.0064 E 4 2 3 •0.080 0.0058 E 5 1 3 0.096 0.0112 E 5 2 3 0.162 0.0123 F 1 1 1 0.101 0.0086 F 1 2 I' 0.106 0.0076 F 2 1 1 0.089 0.0175 Table 4.1 (continued) Organic Total Carbon Nitrogen M S P D - X B 2 2 I 0.506 0.0249 B 3 1 1 1.142 0.0473 B 3 2 1 0.860 0.0403 B 4 1 1 1.127 0.0505 B 4 2 1 0.845 0.0450 B 5 1 1 1.174 0.0590 B 5 2 1 1.066 0.0582 B 1 1 2 0.240 0.0156 B 1 2 2 0.189 0.0114 B 2 1 2 0.286 0.0159 B 2 2 2 0.266 0.0113 B 3 1 2 0.392 0.0205 B 3 2 2 0.316 0.0201 B 4 1 2 0.335 0.0179 B 4 2 2 0.422 0.0238 B 5 1 2 0.370 0.0195 B 5 2 2 0.342 0.0199 B 1 1 3 0.164 0.0111 B 1 2 3 0.163 0.0096 B 2 1 3 0.274 0.0146 B 2 2 3 0.102 0.0060 B 3 1 3 0.255 0.0130 B 3 2 3 0.191 0.0092 B 4 1 3 0.230 0.0133 B 4 2 3 0.253 0.0137 B 5 1 3 0.192 0.0095 B 5 2 3 0.249 0.0130 Organic Total Carbon Nitrogen M S P D -X D 2 2 1 0.300 0.0153 D 3 1 1 0.436 0.0227 0 3 2 1 0.296 0.0171 D 4 1 1 0.529 0.0267 D 4 2 1 0.305 0.0184 D 5 1 1 0.303 0.0187 D 5 2 1 0.363 0.0178 0 1 1 2 0.134 0.0096 D 1 2 2 0.170 0.0095 0 2 1 2 0.161 0.0090 D 2 2 2 0.142 0.0079 D 3 1 2 0.191 0.0109 D 3 2 2 0.150 0.0103 D 4 1 2 0.130 0.0070 0 4 2 2 0.151 0.0081 D 5 1 2 0.158 0.0092 0 5 2 2 0.255 0.0123 D 1 1 3 0.102 0.0071 0 1 2 3 0.115 0.0087 D 2 1 2 0.139 0.0066 0 2 2 3 0.127 0.0095 D 3 1 3 0.155 0.0090 D 3 2 3 0.105 0.0068 D 4 1 3 0.111 0.0070 D 4 2 3 0.146 0.0079 D 5 1 3 0.144 0.0090 D 5 2 3 0.138 0.0074 Organic Total Carbon Nitrogen M S P D - X F 2 2 1 0.117 0.0062 F 3 1 1 0.109 0.0080 F 3 2 1 0.117 0.0081 F 4 1 1 0.207 0.0106 F 4 2 1 0.159 0.0101 F 5 1 1 0.121 0.0085 F 5 2 1 0.134 0.0068 F 1 1 2 0.079 0.0070 F 1 2 2 0.075 0.0064 F 2 1 2 0.101 0.0048 F 2 2 2 0.086 0.0054 F 3 1 2 0.087 0.0073 F 3 2 2 0.093 0.0056 F 4 1 2 0.079 0.0069 F 4 2 2 0.080 0.0070 F 5 1 2 0.103 0.0064 F 5 2 2 0.094 0.0064 F 1 1 3 0.093 0.0064 F 1 2 3 0.078 0.0061 F 2 1 3 0.090 0.0050 F 2 2 3 0.100 0.0061 F 3 1 3 0.105 0.0073 F 3 2 3 0.090 0.0049 F 4 1 3 0.087 0.0064 F 4 2 3 0.082 0.0062 F 5 1 3 0.093 0.0072 F 5 2 3 0.092 0.0070 I • 1 • 0.058 0.0045 I • 2 • 0.048 0.0054 I • 3 • 0.058 0.0056 M signifies the moraine, A through F, and I for the time zero, 1ce contact samples. S, P, and D signify segment, pit, and depth Interval, respectively. dj Table 4.2: Original Data For 39 Observations N S P 0 Organic Carbon Total Nitrogen pH CaCO, Equivalent Citrate-bicarbonate dlthlonlte extractable Fe Al Pyrophosphdte Extractable Fe Al Sand Clay 3 2 1 0.820 0.0352 7.68 76.14 0.277 0.025 0.035 0.005 26.25 19.98 A 4 1 1 0.689 0.0353 7.82 85.87 0.232 0.010 0.031 0.007 45.75 10.20 A 3 2 2 0.185 0.0116 7.83 80.08 0.205 0.015 0.031 0.002 41.50 20.73 A 4 1 2 0.268 0.0095 7.88 88.25 0.210 0.010 0.033 0.005 40.75 21.68 A 3 2 3 0.146 0.0086 7.89 83.92 0.220 0.015 0.031 0.002 42.75 19.55 A 4 1 3 0.206 0.0104 7.95 85.43 0.290 0.005 0.033 0.005 41.25 21.68 B 3 2 1 0.860 0.0403 7.54 83.59 0.197 0.017 0.034 0.004 45.00 17.76 B 4 1 1 1.127 0.0505 7.75 84.21 0.217 0.012 0.034 0.006 43.50 19.40 B 3 2 2 0.316 0.0201 7.70 75.91 0.187 0.010 0.034 0.003 44.25 18.56 B 4 1 2 0.335 0.0179 7.81 83.00 0.192 0.012 0.033 0.005 43.50 20.65 B 3 2 3 0.191 0.0092 7.84 81.60 0.187 0.012 0.034 0.002 46.75 20.81 B 4 1 3 0.230 0.0133 7.86 86.68 0.177 0.007 0.034 0.004 40.25 22.74 C 3 2 1 0.582 0.0345 7.83 80.29 0.217 0.022 0.034 0.003 44.25 19.04 C 4 1 1 0.761 0.0387 7.75 80.29 0.217 0.015 0.031 0.006 39.75 20.99 C 3 2 2 0.187 0.0127 7.97 80.98 0.202 0.010 0.034 0.003 42.25 21.17 C 4 1 2 0.270 0.0153 7.97 82.16 0.197 0.012 0.034 0.005 43.00 21.68 C 3 2 3 0.152 0.0093 7.96 82.67 0.207 0.010 0.034 0.004 41.00 22.01 C 4 1 3 0.149 0.0089 8.00 90.07 0.185 0.007 0.032 O.OOS 46.50 20.41 D 3 2 1 0.296 0.0171 7.84 85.05 0.180 0.012 0.034 0.002 40.75 23.21 D 4 1 1 0.529 0.0267 7.84 84.46 0.212 0.010 0.033 0.005 37.00 22.74 0 3 2 2 0.150 0.0103 7.92 77.83 0.187 0.010 0.035 0.002 40.75 22.44 D 4 1 2 0.130 0.0070 7.92 82.82 0.195 0.012 0.033 0.003 43.00 22.74 0 3 2 3 0.105 0.0068 7.94 77.96 0.180 0.010 0.035 0.002 42.00 21.12 D 4 1 3 0.111 0.0070 7.88 86.80 0.192 0.007 0.031 0.005 41.25 22.74 3 2 1 0.272 0.0149 7.86 80.58 0.177 0.020 0.033 0.003 42.75 21.16 4 1 1 0.217 0.0088 7.86 87.96 0.197 0.012 0.032 0.003 35.00 23.56 3 2 2 Q.172 0.0098 7.84 82.38 0.190 0.015 0.034 0.002 37.25 23.73 4 1 2 3.114 0.0065 7.88 83.57 0.180 0.012 0.034 0.005 35.75 24.01 3 2 3 0.113 0.0055 7.93 82.45 0.185 0.015 0.036 0.004 35.50 24.54 4 1 3 0.086 0.0064 7.94 84.30 0.1RO 0.015 0.035 0.004 35.00 26.59 3 2 1 0.U7 0.0081 8.02 78.50 0.165 0.015 0.032 0.002 48.75 19.44 4 1 1 0.207 0.0106 7.93 82.55 0.180 0.012 0.030 0.003 51.30 12.40 3 2 2 0.093 0.0056 8.09 84.33 0.167 0.007 0.033 0.003 40.50 22.84 4 1 2 0.079 0.0069 7.90 82.61 0.180 0.010 0.031 0.004 33.66 18.29 3 2 3 0.090 0.0049 8.08 83.30 0.180 0.012 0.035 0.002 39.00 23.23 4 1 3 0.087 0.0064 8.03 81.27 0.177 0.007 0.032 0.004 37.75 25.51 1 0.058 0.0045 7.92 89.05 0.125 0.002 0.025 0.001 82.50 5.29 1 • 2 0.048 0.0054 7.65 92.32 0.117 0.002 0.021 0.002 84.75 5.77 1 3 0.058 0.0056 7.81 100.02 0.127 0.002 0.024 0.003 80.50 5.77 CO r o M signifies the moraine: A through F, and I for the time zero. Ice contact samples. S, P, and D signify the segment, pit, and depth Interval, respectively. 83 4.2): pH (pH), percent calcium carbonate equivalent (CaC0 3), percent i ron by c i t ra te -b icarbonate-d i th ion i te extract ion (CBD-Fe), percent aluminum by the same method (CBD-A1), percent iron by pyrophosphate extract ion (Pyr-Fe), percent aluminum by the same method (Pyr -A l ) , percent sand (Sand), percent s i l t ( S i l t ) , and percent clay (Clay). The 39 samples were chosen a r b i t r a r i l y as the Segment 3, P i t 2 and the Segment 4, P i t 1 samples from each moraine, plus the three time zero samples. Organic carbon was determined t i t r i m e t r i c a l l y by the Walkley-Black method (A l l i s on , 1965). A semi-micro Kjeldahl technique was used to estab-l i s h t o ta l nitrogen (Bremner, 1965). The pH was measured in 0.01 M CaCl 2 (1:2, Peech, 1965). Percent calcium carbonate equivalent was measured by the gravimetric method for loss of carbon dioxide (A l l i son and Moodie, 1965). CBD extractable i ron and aluminum followed the indicated extract ion method (Mehra and Jackson, 1960), as was also the case for pyrophosphate extractable i ron and aluminum (Bascomb, 1968). A l l cation concentrations were analyzed by atomic absorption spectrophotometry. Percentages of sand and clay were determined by sieve analysis and the hydrometer method (Day, 1950), respec-t i v e l y , after pretreatment with hydrogen peroxide and calgon. A l l other properties were evaluated by ca l cu l a t i on . 84 NUMERICAL METHODS Analysis of Variance Linear models with random, f i xed , and nested ef fects were employed. For the 180 samples covering the s ix moraines, p i t s (P), segments (S), and moraines (M) were classed as random, with the p i t s nested in the segments and the segments nested in the moraines. Depth (D) was treated as f i xed . Inter-act ion between moraines and depth (MD) was also considered. For the subset of 36 samples on the s ix moraines, the p i t s were treated as nested d i r e c t l y i n the moraines. The analysis of variance designs for the two sampling schemes i s provided (Tables 4.3 and 4.4). The a 2 terms refer to the variance components associated with the random e f f ec t s , whereas the 2 <D term i s equal to the mean square of the dev i a t i on s a s soc i a ted w i t h the f i x e d depth e f f e c t . i s t n e e r r o r v a r i a n c e not explained by the model (Snedecor and Cochran, 1967). Any of the terms with an estimate less than zero was treated as equal to zero. The ANOVA program of the S t a t i s t i c a l Analysis System (Helwig and Counci l, 1969) was used for a l l analyses. Factor Analysis The method of factor analysis used involved three major steps. F i r s t l y , p r inc ipa l components were generated. Secondly, the s t a t i s t i c a l l y s i gn i f i cant components were rotated orthogonally by the varimax procedure as a means of 85 Table 4 .3 : ANOVA Design for Ful l Set of 180 Observations D.F. Source of Variat ion Parameters Estimated 5 Moraines a E 2 + 3ap2 + 6 a s 2 + 30oM2 24 Segments in Moraines a E 2 + 3a p 2 + 6a p 2 30 P i t s in Segments 2 , o 2 0£ + OOp 2 Depths °E 2 + 1 0 a MD 2 + 6 0 K D 2 10 Moraine Depth Interaction a E 2 + 10aM D 2 108 Error * E 2 86 Table 4.4: ANOVA Design for Subset of 36 Observations D.F. Source of Variat ion Parameters Estimated 5 Moraines a£ + 3op + Defy 6 P i t s in Moraines a E 2 + 3 a p 2 2 Depths a E 2 + 2 a M D 2 + 12K D 2 10 Moraine Depth Interaction °E 2 + 2 a MD 2 12 Error °E2 87 s impl i fy ing the columns of the loadings matrix (Kaiser, 1958). F i n a l l y , in order to s impl i fy the structure even fur ther , the components or factors were rotated again, t h i s time obliquely by the promax method (Hendrickson and White, 1964). With th i s approach the i den t i f i c a t i o n of factors with major processes i s f a c i l i t a t e d , especia l ly when i t i s thought that these processes may be related to one another. The strength of the relat ionships can be judged by the cor re la t ion coe f f i c i en t s between the pairs of oblique factor s . For the promax rotat ion k was set equal to 4, allowing the components to be moderately corre lated, provided that such corre lat ion ex i s ts in the data base. Varying the value of k around 4 changed the results only marginal ly. Results were also equivalent to those obtained by the d i rect oblimin method (Jennrich and Sampson, 1966) using the SPSS package (Kim, 1975). A detai led explanation of the pr inc ip les behind oblique rotations may be found in Harman (1967) or Mulaik (1972). The factor analysis presented here was produced by the FACTOR program of the S t a t i s t i c a l Analysis System (Helwig and Counci l, 1979). Non-Linear Curve F i t t i n g Organic carbon and nitrogen values were f i t t e d independently by non-l i nea r equations involving functions of time and depth. Instead of applying the sequential simplex algorithm (Nelder and Mead, 1965) as done in a previous paper (Sondheim et a l . , 1981), the Gauss-Newton method using the Taylor series was employed. This technique demands that the par t i a l der iva-t i ve s of the function be given with respect to each of the coef f i c ient s to be 88 estimated. Convergence on an optimal solut ion i s reached much more quickly than with the simplex method; more importantly, unl ike the simplex method, approximate standard errors and thus confidence l im i t s are generated readi ly fo r a l l estimated coe f f i c i en t s . Concise explanations of the method are found i n Snedecor and Cochran (1967) and in Helwig and Council (1979). The NLIN program of the S t a t i s t i c a l Analysis System (Helwig and Counci l, 1979) was used for a l l non-l inear curve f i t t i n g . The corre lat ion coe f f i c i en t between observed and expected values for each s o i l property tested was determined by the Pearson product-moment formula. Because the sampling design allows for the representation of each of the 18 depth-moraine combinations by ten independent samples, the regression equation can be tested further using a repeated measurements analysis of variance procedure (Draper and Smith, 1981). The to ta l sum of squares, SST, consists of the sum of squares explained by the regression equation, SSR, plus the residual or error sum of squares, SSE. The l a t t e r term may be subdivided into the sum of squares categorized as pure error , SSP, plus the sum of squares re f l ec t i ng lack of f i t of the regression equation, SSL. The pure error term i s the random var iat ion defined by the sum of the sum of squares of the ten repl icates from t he i r mean for each of the depth-moraine combinations. The lack of f i t term measures systematic var iat ion from the regression curve, and consequently, i t i s related to the adequacy of the regression model. It can be calculated by subtracting SSP from SSE. Both the regression equation and the lack of f i t may be tested for s t a t i s t i c a l s ign i f i cance (Table 4.5). SSP and SST may be used further to estimate the 89 Table 4.5: Analysis of Variance Test for Regression Equation Source of Sum of Degrees of f s t a t i s t i c and associated Var iat ion Squares Freedom degrees of freedom Regression SSR k-1 (SSR/(k-l))/((SSL+SSP)/(n-k)); k-1, Lack of f i t SSL o-k (SSL/(o-k))/(SSP/(n-o)); o-k, n-o Pure error SSP n-o Total SST n-1 k i s the number of constants estimated by the regression equation, o i s the number of observations representing each combination of the independent var iab les , and n i s the to ta l number of observations. In the case under study, k, o, and n are equal to 4, 10, and 180, respect ive ly. 90 maximum proportion of var iat ion which could possibly be explained by a regression equation. The proportion, referred to as Max-r 2, i s estimated as (SST-SSP)/SST. RESULTS AND DISCUSSION From the Analyses of Variance The to ta l variance of a so i l property may be part i t ioned into a number of separate and independent variance components. These f a l l into three gross classes: (1) variance associated with differences in process related charac-t e r i s t i c s ; (2) variance associated with locat ional differences not readi ly related to ongoing processes; and (3) variance remaining a f te r a l l of the previously defined sources of var iat ion have been taken into account. Into the f i r s t class f a l l variances a t t r ibutab le to differences in age of the 2 2 m o r a i n e s , O M j i n d e p t h , K d t and i n t h e i n t e r a c t i o n of age w i th depth, Var iances r e l a t e d to d i f f e r e n c e s among the 2 segments on the moraines, O S j a nd between the p i t s w i t h i n the 2 segments, a p ) belong i n the second c l a s s . The e r r o r component, 2 °E, which l i e s in the t h i r d c la s s , i s the variance unexplained by the other terms. Presumably, i t i s associated with l a te ra l or horizontal var ia t ion within a p i t , with var iat ion resu l t ing from minor differences in sampling technique, and with var iat ion a t t r ibutab le to the method of labora-tory determination. 91 Following standard analysis of variance procedures (Snedecor and Cochran, 1967), the amount of var iat ion a t t r ibutab le to each of a number of sources may be estimated. By summing the a2 and K 2 components (Tables 4.3 and 4.4), the percentage of the to ta l var iat ion determined by the i n d i -vidual components i s readi ly ascertained. Note that the legitimacy of such percent i le comparisons depends on the recognition that for the f ixed ef fects the associated K 2 values represent very spec i f i c quant i t ies ; in the case at hand they refer d i r e c t l y to the depth interva l s examined. Another point concerning the approach used here i s that , i f the d i s t r i bu t i on of a property d i f f e r s markedly from the Gaussian d i s t r i b u t i o n , the data should be trans-formed to approach greater normality. Organic carbon and nitrogen were both found to be lognormally d i s t r i bu ted ; thus t h e i r logarithmic equivalents were used in the analysis of variance. Examination of the organic carbon results (Table 4.6) shows that approx-imately 90 percent of the var iat ion i s explained by the moraine, depth, and moraine-depth interact ion terms. The fact that the interact ion term d i f f e r s very s i g n i f i c an t l y from zero suggests that the true re lat ionship of ln(C) as a function of depth and age may be non-l inear. Var iat ion among the means of the segments within the moraines accounts for only three percent of the tota l and var iat ion between the p i t s within the segments accounts for only two percent. Thus, while these differences in locat ion are judged s i gn i f i can t , they are of minor importance. Analysis of the differences among the means for the three depths and for the s ix moraines i s accomplished by use of Duncan's New Mult ip le Range Test. The results ind icate that Depth 1 has Table 4.6: Analysis of Variance Results Property No, of Samples % of Sum of ANOVA Components Duncan's H Listed ew Multiple Range Test Highest to Lowest °P 2 °MD <o2 °M2 Depths Moraines ln(C) 180 7 2* 3* 8** 44** 37** 1 2 3 B A c D E F 1n(N) 180 9 2* 3* 9** 47** 30** I 2 3 B A _C D_ _E f_ C/N pH 180 62 7 1 3 7* 19** 1 2 3 B A c D E F 36 13 14 NA 5 28** 40* 3 2 1_ F_ c 0 E A B CaC03 36 53 40 NA 5 1 0 CBO-Fe 36 25 8 NA 10 13* 44* I 2 3 A c B D E F CBD-A1 36 37 35 NA 0 28** 0 I 2 3 CBO (Fe + Al) 36 23 13 NA 10 19* 36* 1 2 3 A c B D E F Pyr-Fe 36 65 31 NA 5 0 0 Pyr-Al 36 18 66* NA 16 0 0 Pyr (Fe + AD 36 53 7 NA 28 0 12 Sand 36 71 0 NA 15 0 15 Si lt 36 50 2 NA 36 0 12 Clay 36 52 0 NA 4 22* 22 3 2 1 Significance at the 95% and 99% levels of confidence 1s Indicated by * an«L**, respectively. Results from Duncan's New Multiple Range Test are provided where r 0 £ or orf are found significantly different from zero. Depths or moraines joined by underlining are judged to have means not s i gn i f i -cantly different from one another at the 95X level of confidence. For the subset of 36 samples the o§ component Is not applicable, (NA). 93 s i g n i f i c an t l y more organic carbon than Depth 2 and that Depth 2 has s i gn i f -i cant l y more than Depth 3. The s ix moraines have means s i gn i f i c an t l y d i f f e ren t from one another. With the exception of Moraine B, the older the moraine the greater i s i t s organic carbon content. The results for nitrogen are es sent ia l l y the same as those for organic carbon. Other properties with a high degree of variance explained by the moraine, depth, and interact ion terms are pH, CBD extractable i r on , and CBD extractable iron plus aluminum. Values for pH increase with depth and tend to decrease with age. The l a t t e r two properties both decrease with depth, but generally increase with age. It i s c lear from the i r values (Table 4.2) that in the analysis of CBD extractable iron plus aluminum, the ef fects of the iron far outweigh those of the aluminum. For a l l the remaining var iab les , the error , p i t , and segment terms explain more than one-half of the to ta l variance. Nevertheless, the carbon-nitrogen ra t i o shows a s i gn i f -icant decrease with depth and a s i gn i f i can t increase with age. CBD extract -able aluminum decreases s i g n i f i c an t l y with depth, whereas percent clay increases s i g n i f i c an t l y with depth. From the Factor Analysis The factor analysis was performed on the corre lat ion matrix for the fo l lowing eight propert ies: organic carbon, nitrogen, pH, calcium carbon equivalent, the sum of iron plus aluminum by both extract ion methods, percent sand and percent c lay. The cor re lat ion between organic carbon and nitrogen 94 was based on a l l 183 samples; a l l other corre lat ions were based on the subset of 39 samples. Accounting for eighty-three percent of the to ta l variance, two pr inc ipa l factors were judged s i gn i f i can t with eigenvalues greater than 1 (Kaiser, 1960). The results from rotat ing these factors obl iquely are displayed in the pattern matrix and the structure matrix (Table 4.7). The squares of the coe f f i c ient s in the pattern matrix indicate the d i rect c o n t r i -butions of the factors to the variances of the propert ies. Thus, the pattern matrix i s used to del ineate the groupings of propert ies. The structure matrix consists of the cor re la t ion coe f f i c i en t s between the properties and the factor s . The squares of these coe f f i c i en t s give the to ta l contributions of the factors to the variances of the propert ies. The to ta l contributions are composed of both d i rect and ind i rect contr ibut ions, the l a t t e r resu l t ing from the non-zero corre lat ions among the factor s . The ind i rect contributions may be e i ther pos i t ive or negative, as scrutiny of Table 4.7 shows. In an orthogonal so lut ion, such as that provided by pr inc ipa l component ana lys i s , there are no ind i rect contr ibutions since by de f i n i t i on the compo-nents or factors are completely uncor rec ted; orthoganality also implies that the pattern and structure matrices are i d e n t i c a l . It follows that the smaller the corre lat ions between factors in an oblique so lu t ion , the more s im i l a r w i l l the pattern matrix be to the structure matrix. Examination of the two matrices (Table 4.7) shows small differences between the respective coe f f i c i en t s . The corre lat ion between Factor 1 and Factor 2 i s 0.20. Thus, from a s t a t i s t i c a l perspective the factors and the processes i den t i f i ed with them cannot be assumed to have a simple l i near re lat ionship to one another. 95 Table 4.7: Oblique Factor Matrices Pattern Matrix Structure Matrix Property Factor 1 Factor 2 Factor 1 Factor 2 C 0.13 0.94 0.31 0.96 N 0.10 0.94 0.29 0.96 pH 0.35 -0.85 0.18 -0.78 CaCC-3 -0.71 -0.06 -0.72 -0.20 CBD (Fe + Al) 0.68 0.48 0.78 0.61 Pyr (Fe + Al) 0.89 0.11 -0.97 -0.13 Sand -0.98 0.07 -0.97 -0.13 Clay 0.93 -0.35 0.86 -0.17 96 Perusal of the pattern matrix shows that organic carbon, nitrogen and pH are strongly related to Factor 2. From the signs of the coef f i c ient s i t i s c lear that higher values of organic carbon occur with higher values of nitrogen and lower values of pH. A l l three of these properties were deter-mined to have s i gn i f i can t depth and age components in the analysis of variance. Increases in vegetation development and associated microbial a c t i v i t y lead to increases in organic carbon and nitrogen. The corre lat ion coe f f i c i en t between these two properties i s 0.98, ind icat ing that the nitrogen produced by symbiotic f i x a t i on as well as by other mechanisms quickly attains equi l ibr ium with respect to organic carbon. The changes in pH appear to be contro l led largely by the production of acids associated with organic matter. Carbonic acid as a constituent of p rec ip i ta t ion or as a product of non-bio log ica l ly produced carbon dioxide and water in the s o i l i s tenta t i ve l y discounted as a major influence on pH. This i s l og i ca l not only because of the re lat ionship of pH and organic carbon in the factor pattern, but also because the two properties reach t he i r minimum and maximum values, respect ive ly , on Moraine B, not Moraine A (Table 4.2). Since Moraine A i s twice the age of Moraine B, i t s s o i l should be less a lka l ine i f a b i o t i c a l l y generated carbonic acid were the main cause of decreases in pH. The remaining properties may be i den t i f i ed with Factor 1. The pattern coe f f i c i en t s suggest that decreases in percent sand are related to increases in percent c lay , to increases in percent iron plus aluminum by both extrac-t i on methods, and to decreases in percent calcium carbonate equivalent. Percolation of r a i n f a l l and snowmelt through the so i l should lead to weather-97 ing from carbonation, which as argued above, seems largely independent of the state of vegetation development. Dissolution of carbonate in the surface layer results in the destruction of sand grains and the creation of clay-sized particles; some of these particles are translocated downward in the profile by infiltrating water, as suggested by the analysis of variance results. Increases in percent extractable iron plus aluminum can be explained by the freeing of amorphous material during the weathering process. The decrease in percent CBD extractable iron plus aluminum with depth is a reflection of the lesser intensity of weathering with depth. It is assumed that only percent clay and percent CBD extractable iron plus aluminum show significant variation with depth and that only the latter property shows significant variation across the moraines (Table 4.5) because of the inherent variability of the parent material. From the Non-linear Curve Fitting In a previous chronosequence study Sondheim et al., (1981) defined a multivariate measure of pedogenic development in terms of an equation with an exponential soil depth term and a logistic age term. The same equation is used here with first percent organic carbon and then percent total nitrogen as the dependent variable. (Eq. 4.1) P = C j + c2*exp(-d/c3)•(1 + c4«exp(-t«c5))_1 where P is the soil property, c^  through c5 are coefficients, d is depth in cm and t is time in years. The value of c^  is defined as the mean 98 organic carbon value or the mean nitrogen value for the three time zero so i l samples. The values for the other coe f f i c i en t s are such that for e i ther a zero value for t or a very large value of d, P becomes approximately equal to c i . The data base for the two analyses consisted of the 180 samples from the s ix moraines, with ten repl icates for each of the eighteen depth-age combinations. The midpoints of the depth i n te r va l s , 7.5, 22.5 and 37.5 cm, are taken as the values of d. The cor re lat ion coe f f i c i en t s between the observed and the equation estimated values were 0.89 ( r 2 = 0.79) for orga-n ic carbon and 0.88 ( r 2 = 0.78) for nitrogen. The corresponding Max-r 2 estimates are 0.81 and 0.83, respect ive ly. Thus, of the var iat ion which hypothet ical ly could be explained by a regression model, Equation 4.1 accounts for 97 percent (100 x .79/.81) for organic carbon and 94 percent (100 x .78/.83) for nitrogen. Examination of the c oe f f i c i en t s ' estimates and the i r 95 percent c o n f i -dence interva l s shows (Table 4.8) that for C3, C 4 and C 5 the values for the two properties are very s im i l a r . For C£ the values for organic carbon are a l l approximately 20 times the corresponding values for nitrogen. This i s close to 17, the carbon-nitrogen ra t i o for the 180 samples. The con f i -dence interva l s for C3 are f a i r l y narrow, those for C4 quite wide, and those for C2 and c 5 somewhere in between. Thus the estimates for C 3 should be judged as reasonably r e l i a b l e . In an e a r l i e r paper (Sondheim et a l . , 1981) C 3 was i d en t i f i ed as a chemical damping depth, analogous to a physical damping depth (Monteith, 1973). At depths of C3 and 3 * 0 3 , or approximately 14 and 43 cm, the values for the s o i l properties can be 1 99 Table 4.8: Estimates and 95% Confidence Intervals for  Coeff ic ients of Eq. 4.1 Percent Organic Carbon Percent Total Nitrogen Estimate Lower Upper Estimate Lower Upper c i 0.0547 0.00517 C2 1.30 1.15 1.46 0.0641 0.0559 0.0723 C3 14.8 13.0 17.1 13.7 11.9 15.9 c 4 226 -81.9 533 252 -122 625 c 5 0.0790 0.0579 0.100 0.0815 0.0582 0.105 f 100 expected to be only 37 percent and f i ve percent, respect ively, of those at the surface of the mineral s o i l . This suggests that the buildup of organic carbon and nitrogen i s heavily concentrated at and near the surface. The results of the repeated measures analysis of variance provided two f s t a t i s t i c s for each property, one for the regression equation and the other fo r lack of f i t . The f values for the lack of f i t are 4.86 and 8.30 for organic carbon and nitrogen, respect ive ly, both with s ix and 170 degrees of freedom and both s i gn i f i can t at the 99.9 percent level of confidence. The f values for the regression equation are 210 for percent organic carbon and 202 for percent to ta l nitrogen. With three and 176 degrees of freedom, these would normally be s t a t i s t i c a l l y s i gn i f i can t well beyond the 99.9 percent leve l of confidence. However, since the lack of f i t i s s t a t i s t i c a l l y s i g n i f -i can t , i t i s not rea l l y leg it imate to test the s ign i f icance of the regression equation. Thus, the regression model appears to account for a highly s i gn i f -icant proportion of the variance for both propert ies, but whether i t f a i t h -f u l l y represents a l l the trends in the data seems doubtful. This apparently anomalous s i tuat ion i s c l a r i f i e d by examination of the graph of Equation 4.1 for percent t o ta l nitrogen with the appropriate means plotted (Figure 4.3). Two major systematic deviations between the observed and the expected values are evident. At a l l three depths Moraine B has the highest level of nitrogen. It i s postulated that Moraine A does not have a higher nitrogen percentage because of the sharp decrease in the plant species included in nitrogen f i x a t i on (Figure 4.1). The other major systematic 101 YEARS SINCE DEGLACIATION Triangles, open c i r c l e s , and f i l l e d c i r c l e s are used to designate the horizon means for Depths 1, 2, and 3, respec-t i v e l y . For Depth 1, error bars on each side of the mean represent the standard error of the mean based on the pooled standard deviation within s t r a ta . 102 deviation concerns the re la t i ve magnitudes of the means of the second and t h i r d depth i n te rva l s . The curves ind icate a much wider spread between the values than i s in fact the case. Also, for a l l s ix moraines the means of the lowest depth interva l are above the regression l i n e . These factors suggest that the chemical damping depth may be smaller than the equation indicates and that the background nitrogen level may be gradually increasing over time, as a result presumably of percolat ing water carrying minute quantit ies of nitrogen throughout the s o i l . Organic carbon i s not discussed here since i t s behaviour i s nearly ident ica l to that of nitrogen. A further comparison between the plotted points and curves for nitrogen and the graphs of sweet vetch and yellow dryas (Figure 4.1) i s in order. The percent cover for both species reaches i t s maximum values on Moraines C, D and E, the same moraines exh ib i t ing the greatest increase in nitrogen content. Where the percent cover i s low at the beginning and end of the graphs, the rate of nitrogen increase i s also low. This suggests a func-t i ona l re lat ionsh ip between the level of nitrogen in the so i l at any given time and the to ta l sum of nitrogen added to the s o i l since time zero. A p rac t i ca l impl icat ion of th i s hypothesis i s that appl icat ion of nitrogen f e r t i l i z e r at an early stage of ecosystem development may lead to long term increases in the s o i l ' s nitrogen content. Armson (1977) discusses a s imi la r notion with respect to degraded s o i l s . Concerning the small but de f i n i te decrease in nitrogen from Moraine B to Moraine A, i t i s speculated that i t may be a product of a s i gn i f i can t increase in the nitrogen uptake by the t rees . The graphs of dominant tree height and thickness of the l i t t e r layer 103 (Figure 4.2) ind icate considerable tree growth between the oldest two moraines. S imi lar results were obtained by Ugolini (1968) and by Crocker and Major (1955). In t he i r chronosequence studies at Glacier Bay, Alaska, they found that percent nitrogen reached a maximum within a century of deglacia-t ion and then decreased as Engelmann spruce replaced a lder. Examination of the graphs (Figures 4.1, 4.2 and 4.3) and the apparent cor re la t ion between s ize of the error bars and age (Figure 4.3) suggests a further supposition. Strong corre lat ions may ex i s t between certa in so i l and vegetation properties during spec i f i c periods of ecosystem development or whenever high levels of pedological ly related or pedological ly induced stress are placed on the plant community. D ivers i ty of an ecosystem, as indicated by the complexity of the vegetation structure and the number of plant species with in a given area, may be related to the v a r i a b i l i t y of s o i l propert ies. For the study at hand ecosystem d i ve r s i t y appears to increase as steady state (Figure 4.3) i s approached. Thus, steady state may represent a stage of development during which the s t a t i s t i c a l interdependences among the elements of an ecosystem are at comparatively low l eve l s . This hypothesis i s corrobo-rated by the findings of Sondheim and Klinka (1982) in t he i r study of the re lat ionsh ips between so i l properties and a phytosociological c l a s s i f i c a t i o n system. The question of the time to steady state remains to be addressed. Because of the absence of data between Moraines A and B i t i s unclear whether the oldest moraine has in fact reached steady state. If i t i s assumed that 104 no further decrease in nitrogen content i s expected, then steady state probably occurs somewhere between 130 and 190 years. The graph of Equation 4.1 v i r t u a l l y reaches i t s age related asymptote at 130 years, but for reasons given above, the v a l i d i t y of th i s estimate may be questionable. By compari-son to much older forest communities nearby, the successional status of the oldest moraine would s t i l l be considered as se ra i . F ie ld examination of the s o i l s of these older ecosystems showed them to have the morphological charac-t e r i s t i c s of a Podzol. Thus, there ex i s t s the p o s s i b i l i t y that the community on Moraine A is approaching an edaphic climax. The graphs of rooting depth, depth of the Ck horizon, and to ta l vegetation cover a l l suggest the culmina-t i on or near culmination of a phase of ecosystem development. However, even i f i t were the case that one or more components of the ecosystem have reached steady state condit ions, major changes in both the pedological and b io log ica l cha rac te r i s t i c s of the moraines are l i k e l y to occur once the percentage of carbonate in the so i l begins to decrease subs tant ia l l y . The time required for th i s to begin to happen cannot be extrapolated from the data, since percent calcium carbonate equivalent did not show s ign i f i cant differences across the moraines. CONCLUSIONS The Robson moraines appear to reach pedogenic steady state in less than two centuries a f ter deg lac iat ion. For organic carbon and nitrogen the near surface values for the oldest moraines are greater than t he i r time zero counterparts by approximately an order of magnitude. This comparatively 105 large increase has been i den t i f i ed with highly v i s i b l e changes in the vegeta-t i on ecology of the moraines. A non-l inear regression model, with an expo-nentia l term for depth and a l o g i s t i c term for time, explains nearly four-f i f t h s of the var iat ion for both propert ies. Decreases in pH are associated with increases in organic carbon and nitrogen. For percent calcium carbonate equivalent, percent i r on , percent aluminum, percent sand and percent c lay , the primary mechanism of change appears to involve the process of ab i o t i c a l l y induced carbonation. However, the evidence to substantiate th i s in terpreta -t ion i s clouded by the high degree of inherent v a r i a b i l i t y exhibited by these propert ies. 106 CONCLUSIONS This thesis examined some fundamental concepts of s o i l c l a s s i f i c a t i o n and genesis, using a var iety of s t a t i s t i c a l and numerical techniques. Chapter 1 concerned an evaluation of the extent to which horizons can be d i f f e ren t i a ted from one another on the basis of chemical propert ies. The horizons studied included F, H, Ah, Ae, Bhf, and Bf and were taken from Podzolic so i l s developed on granodiorite derived sediments in southwestern B r i t i s h Columbia. The determination of the degree to which the horizons form d i s t i n c t groups in a mult ivar iate context was performed using a grouping procedure based on the mult ivar iate density equation. It was found that 63 percent of the observations were nearer to t he i r own horizon centroid than to any of the other centroids. When horizon membership was a ltered in an attempt to form optimal groupings, the membership of 54 percent of the obser-vations was unchanged. Considerable overlap was show to ex i s t between the F and H horizons and between the Ah and Bhf horizons. Otherwise the picture that emerged was one in which the horizons did not form d i s t i n c t c lusters but did tend to f a l l into de f i n i te regions of the mult ivar iate space. In Chapter 2 the a b i l i t y of an ecological c l a s s i f i c a t i o n system to explain the v a r i a b i l i t y of s o i l and physiographic properties was tested. S ixty stands from a research forest in southwestern B r i t i s h Columbia are defined in terms of three categorical levels of the ecosystem taxonomy of V . J . Kraj ina. The stands belong to fourteen associat ions, eight a l l i ances , and three orders. Using these taxa, nested and one-way analyses of variance were performed on forty s o i l and physiographic properties of the included 107 ecosystems. Because the hierarchy tested was unbalanced and the samples were of unequal s i z e , the estimates and s ign i f icance of the variance components for both analyses were determined by approximation techniques. The results from the nested analyses indicated that for most of the properties the h ierarch ica l structure was of l i t t l e value as a means of explaining v a r i -a b i l i t y . The results from the one-way analyses showed that for mineral s o i l pH and for most physiographic factors between one-half and two-thirds of the v a r i a b i l i t y can be att r ibuted to the c l a s s i f i c a t i o n of the ecosystems into associat ions. For the other properties and for the a l l i ances and orders, t h i s proportion was t y p i c a l l y much lower. The study suggested that for general pedologic and environmental character izat ion there may be l i t t l e j u s t i f i c a t i o n for using the a l l i ance and order categories. In Chapter 3, mult ivar iate techniques were applied to eleven chemical and physical properties of s o i l samples co l lected along a prograded beach chronosequence, located on the west coast of Vancouver Island, B r i t i s h Columbia. The samples were taken from three horizons at each of seven s i t e s . The twenty-one samples were considered as independent observations. Appl ica-t i on of pr inc ipa l component analysis with a normal varimax rotat ion gave highly interpretable resu l t s . The f i r s t component was readi ly i den t i f i ed with podzolic pedogenic processes, whereas the second component appeared to re la te closely to sea spray input. A non-l inear optimization procedure was used to f i t the f i r s t pr inc ipa l component to an empirical equation incor-porating a l o g i s t i c term for time and an exponential term for depth. A cor re la t ion coe f f i c i en t value of 0.99 was obtained. The notion of a pedo-genic damping depth analagous to a thermal damping depth was suggested. 108 Chapter 4 involved an interpretat ion of 183 so i l samples from 60 p i t s co l l ec ted from a sequence of moraines located i n front of the Robson G lac ie r , Mt. Robson, B r i t i s h Columbia. Univariate analysis of variance, oblique rota -t i on factor analys i s , and non-linear regression were employed to ascertain the major processes operating on the moraines and to determine whether expected trends were masked by the inherent v a r i a b i l i t y of the parent mater ia l . Properties exh ib i t ing s i gn i f i c an t differences with respect to s o i l depth and moraine age included organic carbon, nitrogen, and pH. Assumed to be funct iona l ly re lated, these properties were also i den t i f i ed with one of two s i gn i f i cant factors from the factor analys is . The values for organic carbon and nitrogen were f i t t e d to non-l inear equations involving an exponen-t i a l term for depth and a l o g i s t i c term for time; the resu l t ing cor re lat ion coe f f i c i en t s were 0.89 and 0.88, respect ively. Percent calcium carbonate equivalent, percent iron plus aluminum by c i t rate-b icarbonate-d i th ion i te ext rac t ion , percent iron plus aluminum by pyrophosphate extract ion, percent sand, and percent clay showed generally l i t t l e or no relat ionship to depth and age. These properties were related to the second factor from the factor ana lys i s , which was i den t i f i ed with water i n f i l t r a t i o n and a b i o t i c a l l y induced carbonation. The absence of stronger depth and age trends for these properties was presumed to be caused by a high degree of v a r i a b i l i t y within the parent mater ia l . Extrapolations The major conclusions and suppositions from the chapters may be extended to paint a more cohesive p ic ture . The basic points are as fo l lows. 109 In a s t a t i s t i c a l context s o i l horizons do not always represent well defined e n t i t i e s , as discussed in Chapter 1. Instead they may be arb i t rary d iv i s ions along a continuum. This suggests that in many cases the use of constant depth in terva l s may be as informative as the use of horizons. Sampling from constant depth interva l s can be cost e f fec t i ve in terms of the number of laboratory samples needed to characterize a plot and in terms of the level of expertise required by the f i e l d surveyor. As w e l l , management oriented interpretat ions may be easier to make since comparisons among pedons are more d i r e c t . Chapter two suggests that a t i g h t l y defined functional re lat ionsh ip between vegetat ion and s o i l p r o p e r t i e s t y p i c a l l y may not e x i s t . Consideration of the extremes of environmental gradients may lead to assumptions regarding the nature and intens i ty of interact ions which are not necessari ly appl icable to more common s i tuat ions . At least when re s t r i c ted to r e l a t i ve l y small geographic areas, attempts to derive a h o l i s t i c c l a s s i f i c a t i o n useful for a var iety of ecological data may be i l l fated. It may be better to handle the data for each d i s c i p l i n e separately, combining i t only as demanded by various algorithms designed to meet very spec i f i c interpretat ion object ives. Treatment of so i l as a mathematically t ractable continuum may be useful not only in interpret ing processes, but also in predict ing values across a landscape, as shown in Chapter 3. Add i t i ona l l y , representation of chemical and physical s o i l dynamics by simple mathematical en t i t i e s may be more informative than by taxonomic nomenclature. Fundamental pedological and 110 ecological p r inc ip le s may be helpful as guides in the development of regres-sion equations, simulation models, and the l i k e . L imitat ions to such tech-niques imposed by the presence of random noise, or non-attributable va r i a -b i l i t y , also apply to more t r ad i t i ona l c l a s s i f i c a t o r y methods. The results of Chapter 4 corroborate many of the assertions made above. Use of constant depth interva l s for sampling was highly bene f i c i a l , as i t allowed for straightforward analysis of the data. Some so i l and vegetation properties were c l ea r l y related to one another, but the strength of the re lat ionsh ips appeared to drop when steady state was approached. For the majority of s o i l properties measured, expected trends were vei led by a high degree of v a r i a b i l i t y not a t t r ibutab le to any readi ly def inable, environ-mental functions. F i n a l l y , the employment of regression and data reduction analyses f a c i l i t a t e d data i n te rp re ta t ion , where dependence on taxonomy would have been of l i t t l e value. Perspectives The rat ionale behind s o i l taxonomy i s based on two proposit ions. (1) The taxonomy establishes a conceptual model. It serves as a data reduction mechanism by providing the user with a compre-hensible vantage point of what i s generally a very large number of raw data. This in turn f a c i l i t a t e s communication among users and generally allows for the widespread appl ica-t ion of the taxonomy. I l l (2) The def in i t i ons inherent in the taxonomy demand the develop-ment and maintenance of data standards. The standards ensure that temporal and areal comparisons can be made. Addit ion-a l l y , the conceptual model and the data standards together may be used to support s o i l mapping. From both points i t may be assumed that more e f f o r t directed at the develop-ment and refinement of sophist icated pedologic and ecologic taxonomies i s worthwhile. This assumption was probably va l i d in the past. It i s question-able today and w i l l become more so in the future. The reasoning behind t h i s claim centers on the advent of e lect ron ic data storage and manipulation. The importance of the conceptual model i s discussed f i r s t . Increasingly the degree of general izat ion i m p l i c i t in the model w i l l be viewed as unneces-sary and undesirable in a pract ica l context. The emphasis more and more in mapping w i l l be to define polygons in as much deta i l as possible with respect to a large set of raw a t t r ibu tes . The maps w i l l be d i g i t i z ed and entered into a computer, along with rough estimates of the att r ibutes for each polygon. Using algorithms operating on th i s data base, the surveyor w i l l be able to create computer produced, simple interpret ive maps. Since the raw f i e l d and laboratory data for sampled pedons w i l l also be stored in the computer, the surveyor w i l l have the option of using his or ig ina l pedon data in the development of predict ive models and the l i k e . Standardized algo-rithms in conjunction with the data standards w i l l gradually replace the role of taxonomy as a communications device. Extensive use of the computer w i l l 112 give the surveyor the opportunity to create maps, guidel ines, and other i n te rp ret i ve aids more r igorously and with less dependence on taxonomy and t r ad i t i ona l c l a s s i f i c a t i o n concepts. Some users of the Canada Soi l Informa-t i on System have begun taking t h i s approach in recent years. The imminent introduction in B r i t i s h Columbia of second generation s o i l information systems w i l l make th i s l i ne of thinking very r e a l i s t i c to pursue. The second point made e a r l i e r , concerning the re lat ionship of data stan-dards to taxonomy, w i l l also be influenced heavily by e lectron ic data proces-s ing. The dr iv ing force behind standardization w i l l become the existence of la rge, integrated data base management systems. Major changes in the stan-dards w i l l enta i l major changes in system design, programming, and documenta-t i o n . System updating i s always very expensive and w i l l only be done when there i s substantial evidence that such a revis ion i s required. This argu-ment refers pr imar i ly to the storage, re t r i eva l and i n teg r i t y requirements of the raw pedon and polygon data. Advances in s t a t i s t i c a l and numerical methods are less of a concern, since they are usually incorporated quite quickly into standard analysis systems, such as SAS, SPSS, and BMD. Assuming that a l ink has been established between the data management and analysis systems, the surveyor w i l l be able to analyze his data very read i ly . Two complementary avenues of invest igat ion are suggested from the pre-vious discussions. One concerns d i g i t a l t e r ra in models and the other involves v a r i a b i l i t y . From a d i g i t a l t e r r a i n model of e levat ion, companion models can be derived of slope, aspect, curvature, upslope distance, distance 113 to the nearest water body, etc . Maps of p rec ip i t a t i on , temperature, bedrock, and rego l i th thickness and composition could be d i g i t i z ed and added to the data base to help establ i sh gross chemical and physical propert ies. Crude ind icat ions of surface and canopy conditions could be gleaned from remotely sensed imagery in or converted to a d i g i t a l format. Mathematical models of s o i l moisture and temperature dynamics could be applied to the data base using actual f i e l d measurements for loca l c a l i b r a t i o n . Other s o i l properties might be predicted through regression and corre lat ion techniques based on the re lat ionsh ips between elements in the data base and ground truth observations sampled where possible in accordance with a vigorous experimental design. Through modelling and analys i s , the o r i g ina l data base could be extended so that for every point on the d i g i t a l landscape a value could be estimated for a large number of var iables. Many interpretat ions commonly attempted from so i l s maps or ecosystem descr ipt ions probably could be made fa s te r , cheaper, and more accurately through the use of simple algorithms operating on the extended data base. Conceptually, such a d i g i t a l landscape approach i s very straightforward; as much emphasis as possible i s placed on the data and as l i t t l e emphasis as possible i s placed on higher levels of abstract ion. Random noise, or non-attr ibutable v a r i a b i l t y , poses an ult imate l i m i t a -t ion to the usefulness of t h i s approach or any other. It would be of interest to determine the re lat ionsh ip between noise and more manifest land-scape cha rac te r i s t i c s . D i f ferent environments could be placed re l a t i ve to one another on a noise scale. Predict ive techniques would be less successful with noisy environments as compared to quieter ones. S im i l a r l y , in a high 114 noise environment differences in accuracy between reconnaissance and inten-s ive surveys would not be as great as one would normally expect. Extra survey e f fo r t might be more prof i tab ly spent in a low noise environment. There may ex i s t re lat ionships between noise and physiographic and ecological complexity. It seems l i k e l y that, at the meso-scale, noise can be broken in to two main components: that related to the development of microenviron-ments and that inher i ted from the parent mater ia l . Juvenile ecosystems and ecosystems under high stress conditions probably display comparatively l i t t l e noise, pa r t i cu l a r l y i f they occur on homogeneous parent mater ia ls . Low s t ress , climax ecosystems developed on heterogeneous parent materials would represent the opposite extreme. 115 REFERENCES CITED A l l i s o n , L.E. 1965. Organic carbon. In C A . Block (ed.) Methods of Soi l Analys i s , Part 2. Agronomy 9: 13F7-1378. Amer. Soc. of Agronomy, Madison, Wisconsin. A l l i s o n , L.E. and CD . Moodie. 1965. Carbonates. In C A . Block (ed.) Methods of Soi l Analys is, Part 2. Agronomy 9: 1379-T396. Amer. Soc. of Agronomy, Madison, Wisconsin. Annas, R.M. and R. Coupe. 1979. 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