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Factors affecting the distribution of permafrost, Mackenzie Delta, N.W.T. Smith, Michael William 1973

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/ 7 Z ZSf ' ' ' t\ FACTORS AFFECTING THE DISTRIBUTION OF PERMAFROST MACKENZIE DELTA, N.W.T. by MICHAEL WILLIAM SMITH M.A. University of Georgia, 1968 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF Doctor of Philosophy in the Department of GEOGRAPHY We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA October 1973 In p r e s e n t i n g t h i s t h e s i s in p a r t i a l f u l f i l m e n t o f the r e q u i r e m e n t s f o r an advanced d e g r e e a t the U n i v e r s i t y o f B r i t i s h C o l u m b i a , I a g r e e t h a t t h e 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 a g r e e 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 c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y p u r p o s e s may be g r a n t e d by the Head o f my Department or by h i s r e p r e s e n t a t i v e s . It i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o n o f t h i s thes . is 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 . The U n i v e r s i t y o f B r i t i s h Co lumbia Vancouver 8, Canada Department Date ABSTRACT Variations in ground temperature regime and permafrost distrib-ution were studied in a small area about 50 km northwest of Inuvik, N.W.T., in the east-central part of the Mackenzie Delta. The ground thermal regime is influenced by surface conditions, the nature of which varies spatially and temporally. Relationships obtained for the present set of environmental conditions are applied to the analysis of perma-frost dynamics where surface boundary conditions have changed. The Delta is an area of active sedimentation and erosion and about 50 percent of the study area is covered by water bodies. A major distributary in the study area is undergoing lateral migration and the local configuration of permafrost is closely related to the history of river migration. Further, vegetation shows a successional sequence related to river migration, and there is thus a complex interaction between vegetation, topography and microclimate. The major objectives of the study were: 1) To describe the permafrost and ground temperature variations in the study area. 2) To understand how local environmental factors influence the ground temperature field. 3) To analyse the development of the present ground temperature field in terms of its position in a long-term geomorphological sequence. Temperature boreholes were drilled to various depths up to 30 m. Temperatures were measured with thermistors, and these measurements were augmented with seismic and resistivity surveys. Lake and river temperatures were also recorded, and ground materials were sampled from boreholes. In summer, active layer temperatures, net radiation and ground heat flux were recorded at five sites. Measurements of ground i i temperatures, snow depths and ice cover were made in winter. Permafrost is generally perforated in nature, being absent be-neath the river channel and larger lakes. Ground temperatures are warmer close to water bodies, and permafrost plunges steeply beneath cut banks. Observations indicate permafrost thicknesses of between 50 to 65 m in stable, spruce-covered areas. Calculations show that the maximum thickness in the area is about 100 m, at sites most distant from water bodies. Beneath slip-off slopes ground temperatures are warmer than beneath cut banks, and permafrost is between only 2.5 to 9 m thick. Here, permafrost thickens away from the river, and wedges out towards i t ; permafrost is absent in some places, where the winter snow drifts are deep. Significant differences in thermal regime exist under the various types of vegetation. In summer, higher ground temperatures are assoc-iated with high values of net radiation and ground heat flux. Mean daily 25-cm temperatures varied from 0 .7 ° to 11.2°C between sites. In winter, snow cover is the decisive factor affecting ground temperatures. Significant variations in snow accumulation occurred between sites, and winter 1-meter temperatures varied from - 6 . 4 ° to -0.6°C within 12 m. Through the framework of simple heat conduction theory, a con-sistent explanation of permafrost distribution in terms of local environ-mental factors is developed. The heat conduction models are suitable for ground temperature prediction, with agreement typically within +0 .5 ° of observed values for most sites. Calculations of the thermal disturb-ance due to channel shifting are in general agreement with observations, although omission of the latent heat term leads to some errors. ACKNOWLEDGEMENTS During this research and in the preparation of this thesis, I have received help and encouragement from many sources. Foremost I wish to thank my wife Pauline, who acted very capably as f i e l d assistant, lab assistant, reviewer and factotum, and who gave me continuous and much needed encouragement. Thanks also to Dr. J. R. Mackay, who suggested the i n i t i a l ideas from which this study developed, and who provided continued and superior help and support during the fieldwork and in the writing of the thesis. Grateful appreciation is extended to Peter Lewis, who f i r s t introduced me to the area, and for his valued help in the f i e l d and in discussion. Thanks also to the people who helped me with f i e l d work: Gerry Allen, Ian Chapman, Dave Dickins, Blair Fitzharris, Ronald Good, Albert Oliver, and Oliver Oliver. In Inuvik, I was most fortunate to receive help and hospitality from Julian Inglis. The f i e l d work for this study was supported by the Geological Survey of Canada and by research grants from the Department of Indian Affairs and Northern Development and the National Research Council to Dr. J. R. Mackay, Department of Geography, University of British Columbia. I would also like to thank the Inuvik Research Laboratory, particularly John Ostrick, for the help that they provided. Imperial Oil Ltd., through G. Rempel, generously provided travel f a c i l i t i e s on occasions, and Gulf Oil cooperated in d r i l l i n g a number of boreholes. Thanks also to D. K. MacKay, for the loan of some equipment. During the writing of the thesis I received helpful and valued advice from Michael Church, Dr. T. R. Oke and Dr. 0. Slaymaker. Dr. R. El l i s also provided comments. I also benefitted from many discussions with my fellow graduate students, and with Dr. C. T. Hwang. I wish to thank Dean R. Wendt and Carleton University for a grant to help cover the costs of preparation, and I extend my grateful appreciation to those who typed the manuscript, particularly Mrs. Pat Stothart, and to Elizabeth Crux who drew the diagrams. v TABLE OF CONTENTS Chapter P a g e 1. Introduction 1 2. Background to the Present Study . 1. Permafrost in the Mackenzie Delta 7 2. The Thermal Effect of Water Bodies 10 3. Permafrost Configuration and River Migration . . 15 4. The Study Area 16 5. The Present Study 23 3. Experimental Design and Measurement 1. Areal Scale 30 2. Between-Site Scale 34 3. Around-Site Scale 38 4. The Distribution of Permafrost: Observed and Predicted 1. Major Features of Permafrost Distribution in the Study Area 39 2. Ground Temperatures and Heat Conduction Theory . 49 3. Present Application of Heat Conduction Theory . . 65 4. Summary 88 5. Variations in Microclimate 1. Introduction 92 2. Annual Thermal Regime 93 3. Summer Microclimate 104 4. Winter Conditions 123 5. Summary 142 6. Conclusions 144 Appendices 1. Glossary of terms 150 2. Computer program for steady-state thermal effect of water bodies 151 3. Computer program for thermal effect of a shifting river 165 4. Monthly ground temperatures at five micro-climatic sites (1/9/69 - 1/7/71) . 170 5. Calculation of surface heat flux values, using the temperature-integral method 176 6. Net radiation and ground heat flux data at five microclimatic sites (July-August 1970) . . . 178 Bibliography 179 vi LIST OF TABLES Table Page 1. Summary of Climate Data for Selected Stations, N.W.T. . 9 2. Depth of Penetration of a Temperature Disturbance as a Function of Time(t) and Thermal Diffusivity(a) . 27 3. River- and Lake-Temperature Data 42 4. Permafrost Thicknesses for Spruce-Covered Areas . . . . 41 5. Ground Temperatures Beneath a Cut Bank and a Slip-Off Slope 43 6. Permafrost Thicknesses for Slip-Off Slopes . . . . . . 43 7. Variation of Permafrost Thickness with Distance Away from River . . . 45 8. Permafrost Thicknesses for Areas of Salix-Alnus . . . . 48 9. Physical and Thermal Properties of Some Soil Samples 53 10. Calculations for Apparent Diffusivity, using data from Boreholes #2-6 and #2-8 57 11. Theoretical Thermal Effect (°C) of Lake #2 on Ground Temperatures at Various Depths at Site #6-3, as a Function of Time 65 12. Observed and Predicted Temperatures, Cut Bank Section . 68 13. Observed and Predicted Temperatures, with Transient Correction, for Boreholes on a Slip-Off Slope . . . . 74 14. Sample Calculations to Illustrate Effects of Latent Heat Term on Depth of Freezing and Ground Temperature Calculations 87 15. Analysis of Variance - Active Layer Depths in Five Terrain Segments (July 1970) 94 16. Characteristics of Five Microclimatic sites 95 v i i Table Page 17. Analysis of Variance - Mean Daily Air Temperatures at Five Microclimatic Sites: a) A l l days (July-August 1970) b) Sunny days (July-August 1970) 106 18. Analysis of Variance - Mean Daily Surface Temperatures at Five Microclimatic Sites (July-August 1970) . . 107 19. Analysis of Variance: a) Minimum Daily Surface Temperature b) Maximum Daily Surface Temperature at Five Microclimatic Sites (July-August 1970) ". . I l l 20. Analysis of Variance - Incident Light Values around Five Microclimatic Sites (July 1970) 114 21. Analysis of Variance - Mean Daily 10-cm Temperatures at Five Microclimatic Sites (July-August 1970) . . 116 22. Average Daily Net Radiation and Ground Heat Flux at Five Microclimatic Sites (July-August 1970) . . 119 23. Mean Daily Maximum and Minimum 10-cm Temperatures at Sites 1, 2 and 3 (July-August 1970) . . . . . . . . 119 24. Analysis of Variance - Mean Daily 25-cm Temperatures at Five Microclimatic Sites (July-August 1970) . . 122 25. Analysis of Variance - Half-Hourly 10-cm Temperatures: a) at Three Microclimatic Sites: 1, 4, 5 (August 23-24, 1970) b) at Three Microclimatic Sites: 1, 2, 3 (August 25-26, 1970) 124 26. Analysis of Variance - Snow Depths: a) in Six Terrain Segments (March 1971) b) in Three Terrain Segments (December 1970) . . 127 27. Snow Depths in Five Terrain Segments (March 1970) . . 128 28. Snow Cover Characteristics Along Two Transects Across a Slip-Off Slope 133 29. Outward Heat Flow From the Top-One-Meter Ground Layer at Sites on a Slip-Off Slope (December 1970 to March 1971) 137 30. Temperature Data from a Transect Through the Snowbank Zone, Slip-Off Slope 138 31. Temperature Data from Snowbank Transects 5 and 7 . . . 141 v i i i LIST OF FIGURES Figure Page 1. The Study Area - Location and Salient Surface Features 8 2. Diagrammatic Cross Section Through a Shifting Channel Area 19 3. Temperature Borehole Network on a Slip-Off Slope . . . . 35 4. Temperature Boreholes: Slip-Off Slope Sites 40 5. Temperature Boreholes: Spruce-Covered Sites 40 6. Resistivity Sounding Data, for Sites on Slip-Off Slopes 44 7. ' Details of Permafrost Configuration Beneath a Slip-Off Slope 47 8. Resistivity Profile Across a Slip-Off Slope 47 9. Material Characteristics of Some Sample Boreholes . . . 51 10. Examples of Temperature--Depth Curves used for Calculation of Apparent Diffusivity 55 11. Method of Dividing a Given Surface Area into Sectors of Circles. (For summing the temperatures under the apex of each sector) 59 12. Steady-State Permafrost Configuration Under Rivers 30, 45, 60, 70, 80 and 100 meters Wide . . 62 13. Permafrost Regression, with Time, Under a River (100 m wide) . . . . . . . . . 63 14. Ground Temperatures and Permafrost Distribution Along a Cut Bank Transect (SYMAP) 70 15. Computed Temperature Field Under a Traverse Line . . . . 72 16. Temperature Wave Simulating River Shifting 77 17. Diagram to Illustrate Sample Solution of Transient Model 81 ix Figure Page 18. Permafrost History Under a Shifting Channel: a) I n i t i a l Position b) Present-Day 83 19. Predicted Mean Annual Ground Temperatures in the Vicinity of the Snowbank Zone, Slip-Off Slope . . . . 85 20. Effect of River Shifting Rate on Magnitude of Thermal Disturbance 89 21. Ground Temperature Isotherms at Five Microclimatic Sites (September 1969-February 1971) 98 22. Calculated Values of Average Daily Surface Heat Flux at Four Microclimatic Sites (April 1970-April 1971) 103 23. Mean Diurnal Surface Temperature Regimes at Five Microclimatic Sites (July-August 1970) 108 24. Daily Radiation Totals for Five Microclimatic Sites (July-August 1970) 112 25. Mean Diurnal 10-cm Regimes at Five Microclimatic Sites (July-August 1970) 117 26. Mean Diurnal 10-cm Temperature Regimes at Two Sites in the Picea Segment (July-August 1970) . . . . 121 27. Effect of Snow Depth on the Temperature at the Ground Surface (March 1970) . . . 131 28. Temporal Variation of One-Meter Temperatures at Ten Sites Across a Slip-Off Slope (August 1970-July 1971) 135 29. One-Meter Temperatures Plotted Against Snow Depth at Ten Locations Across a Slip-Off Slope . . 135 ,30. Details of Permafrost Configuration Along Various Transects Across a Slip-Off Slope 140 x LIST OF PLATES Plates Page 1. Study Area and Vicinity (Portion of Air Photograph A19946-13) 18 2. Aspects of Riverbank Erosion: a) Thermo-Erosional Niche Along a Cut Bank b) Cut Bank Collapse Following Undercutting . . . . 20 3. Spatial Arrangement of Terrain Segments 22 4. D r i l l i n g Equipment at a Borehole on a Slip-Off Slope (Bare Ground Segment) 33 5. Microclimatic Sites: a) Salix(1) b) Salix(2) c) Salix-Alnus d) Picea 96 6. Snow Cover over Bare Ground on a Slip-Off Slope . . . . . 130 7. Snowbank Zone on a Slip-Off Slope 130 xi Chapter 1 INTRODUCTION Permafrost is defined exclusively on the basis of temperature, and is interpreted in this study to include rock or s o i l material, with or without included moisture or organic matter, that has remained below 0°C for some period of time--the minimum period being given by R. J. E. Brown (1969) as: Permafrost includes ground which freezes in one winter, remains frozen through the following summer, and into the next winter (p.14). This definition, therefore, includes the pereletok''" of other authors. Permafrost and associated phenomena were f i r s t comprehensively described in English by Muller (1945). More recent monographs include those of Stearns (1966), Corte (1969), and R. J. E. Brown (1970). Authoritative Russian works include "Principles of Geocryology" (translated, in numer-ous volumes, by N.R.C. since 1959), and Dostovalov and Kudryavtsev (1968). The words "freezing" and "thawing", commonly referring to the change of state between water and ice, w i l l be used here as i f these processes actually take place at 0°C. Permafrost may be ice free below 0°C, i f the moisture i t contains i s saline, or i f i t contains no moisture at a l l . In most s o i l s , and especially those with a clay fraction, substantial amounts of water, in the liquid phase, can persist at tempera-tures below 0°C (see P. J. Williams 1967). Ice in permafrost can occur as coatings, grains, veinlets, or massive beds; in unconsolidated A glossary of terms is presented in Appendix 1 2 materials i t often acts as a cementing agent, making the material rock-like. It has become common to divide permafrost occurrence into two broadly geographical zones, continuous and discontinuous. In the continuous zone, permafrost is present everywhere beneath the surface, except perhaps under large water bodies whose mean annual temperature is above 0°C. It is normally continuous to i t s lower surface, and may reach a thickness of hundreds of meters. Continuous permafrost is more formally defined by a temperature of -5°C or colder at a depth of about 15 m (R. J. E. Brown 1967). In lower latitudes the permafrost becomes thinner and the thickness more variable; ground temperatures are close enough to 0°C so that at some sites, under favorable local environmental conditions, permafrost may not be present, although nearby i t may s t i l l be quite thick. Under these conditions the permafrost is said to be discontinuous. The general pattern of distribution in Canada has been mapped by R. J. E. Brown (1967). Many studies have been concerned with the qualitative effect of differences in climate, vegetation, topography, geology and hydrology on the distribution of permafrost. Although obviously basic to a general understanding of the problem, such an approach cannot provide specific information on the local configuration of permafrost, which depends on that set of processes controlling the thermal regime. The quantitative aspects of the thermal relationships between the ground temperature f i e l d and i t s environment, and the details of permafrost configuration, can be resolved only by geothermal investigations. The writer agrees with the point of view expressed by Kudryavtsev (1967) : Only concrete studies of frozen layers, their distribution, occur-rence, structure and composition, in relation to the general complex of the geologic-geographic situation can yield full-value i n i t i a l material for general theoretical studies (p.5). 3 J. R. Williams (1970) identifies, in more specific terms, some problems worthy of attention: Quantitative data are needed to calculate the thermal effects of rivers, lakes, glaciers, the ocean, and vegetation on ground temperature...Measurements of ground temperature at the surface and to depth, and measurements of thermal conductivity of earth materials are needed to determine the history of permafrost and the degree to which its thickness reflects present ground surface temperature (p. 76). To understand thoroughly any geothermal studies, there must be a correlation with the properties of the ground materials, the surface cover, topographic position, past history, and present climatic conditions. Analysis of temperatures, and their gradients, may then make it possible to determine whether permafrost at any locality is aggrading or degrading, and in turn may provide basic information on the physical environment of the present, and perhaps the past. Although the permafrost literature is replete with information on details of permafrost occurrence from many different locations, there has been less progress towards an integrated, formal and, at the same time, practicable formulation (with predictive capability) of the interrelation-ships between the thermal regime of permafrost and the characterisitcs of its environment. Numerous studies have identified, and described in general terms, aspects of this relationship (for example, see Kudryavtsev 1959; Shvetsov 1959; Tyrtikov 1959; R. J. E. Brown 1960, 1965, and 1966; Barnett 1963; Annersten 1966; Benninghoff 1966). Valuable contributions from Lachenbruch (1957a, b, 1959, 1962, 1970), Mackay (1962, 1963, 1971), W. G. Brown (1963a, b) and W. G. Brown et al (1964) have shown that physical theory developed in the field of heat conduction might profitably be applied to the analysis of the ground thermal regime in the natural physical environment. (The theory of classical heat conduction is widely developed, and cannot be discussed here. A comprehensive survey is con-tained in Carslaw and Jaeger (1959); Ingersoll, Zobel and Ingersoll (1954) 4 contains many examples on the ground thermal regime.) Since the groundwater in permafrost regions is generally immobilized as ice, so that only localized groundwater circulation can occur, then "For the most part permafrost temperatures are determined almost entirely by conductive transfer" (Laehenbruch et al 1962, p. 792). Thus heat conduction models can be used with some confidence. Russian workers have called attention to the role of infiltration and ground-water circulation in the development of taliks beneath water bodies (for example, see Efimov 1964; Mel'nikov 1964; Romanovskii and Chizhov 1967). Although measurements of "filtration coefficients" are often quoted, i t is difficult to find any analysis of the actual importance of mass transfer in the thermal regime of permafrost areas. Dostovalov and Kudryavtsev (1968) discuss, in general terms, the degradation of perma-frost caused by groundwater flow through fractures and fissures in rock (pp. 319-321). Tiutiunov (1961) and Leschikov and Zarubin (1967) describe field situations where taliks have been formed in bedrock by this process. Some' aspects of heat conduction theory have found widespread application in ground temperature studies--for example, the surface periodic forcing functions and periodic heat flow; Stefan-like problems. Far fewer studies, however, have attempted a comprehensive analysis of observed spatial and temporal variations in the ground temperature field. The value of permafrost research is more than purely intrinsic; the rapidly expanding economic interest in the north has led to the recognition of permafrost as a pre-eminent factor in the arctic environ-ment. Thus i t has become necessary to develop a more rigorous under-standing of the thermal regime of permafrost, especially with respect to the effects of surface heat sources and sinks. Engineering operations 5 of any kind change, to some extent, the thermal regime of the ground, and therefore an understanding of the dynamics of permafrost under various "environmental" changes is important. Some of the problems associated with mining, dri l l ing, pipelines and roadbeds were the concern of the Third Canadian Permafrost Conference (1969) and the Canadian Northern Pipeline Research Conference (1972), and included consideration of structural instability due to permafrost degradation, frost heaving, and icing conditions. A recent paper by Ferrians et al (1969) discusses similar problems with examples from Alaska. An important and intriguing problem, therefore, both from a scientific and an engineering viewpoint, is to determine the disturbance of subsurface temperatures that results when the temperature at the ground surface within a finite region differs from the surface temperature characteristic of the area outside the region. Such conditions might correspond to: i) the presence of natural features such as lakes and rivers] i i ) a region in which the thermal properties of the surface cover are appreciably different from those characteristic of the area in general; i i i ) modifications of the surface as a result of erecting buildings, stripping off the vegetation, or emplacing a gravel f i l l ; (Lachenbruch 1957a; p. 52). The application of heat conduction theory to this general class of problems has been treated by Lachenbruch (1957a, b, 1959) and W. G. Brown (1963a, b). A current major objective of applied permafrost research is the development of numerical heat flow models designed to predict the effects of introduced sources (and sinks) on the thermal regime (see Lachenbruch 1970; Hwang et al 1972). Numerical models must be appealed to when irregularities of problem geometry or initial/boundary conditions make any analytic solution impossible. 6 An explicit objective of the present study is to arrive at an understanding of the development of the permafrost configuration over an area in terms of its changing thermal environment, both in a spatial and temporal sense, through the application of heat conduction theory. Specifically, it is concerned with permafrost dynamics in an area of geo-morphic change; no such study has appeared in the literature, although reference to similar situations has been made by some authors (see Epshtein and Chernyad'ev 1963; Efimov 1964; Pewe' 1965). Chapter 2 BACKGROUND TO THE PRESENT STUDY 1. Permafrost in the Mackenzie Delta The Mackenzie Delta i s a low, flat area, covering more than 13,000 km^ , spotted with thousands of lakes, and dissected by an intricate anastomosing network of several large channels and numerous smaller winding channels. The channels rarely meander, in the geomorphic sense, although they may be sinuous, and they do wander (Mackay 1963, p. 105) . The present study was carried out in the east-central part of the modern Mackenzie Delta, some 50 km north-west of Inuvik, encompassing an area of about 10 km2 (Figure 1). Aspects of the physical geography of the region have been described by Mackay (1963), whilst the vegetation and geomorphology in the study area has been investigated by G i l l (1971). The climate of this part of the Delta i s transitional between arctic and subarctic (see Table 1 for some relevant climatic data): The coastal portion of the Mackenzie Delta area li e s in the arctic, the southern portion in the subarctic...Aklavik and Inuvik are in the subarctic...The location of Reindeer Station is transitional. (Mackay 1963, p. 153) R. J. E. Brown (1967) uses the 17°F (-8.3°C) mean annual air isotherm to delimit the region of continuous permafrost. Aklavik and Inuvik have mean annual air temperatures below 17°F (Table 1). Were i t to conform to the broad geographical patterns of permafrost distribution, the region would thus be included in the continuous zone. However, 7 8 Figure 1 THE STUDY AREA - LOCATION AND SALIENT SURFACE FEATURES I fl II * 2 II l i i i i II y i n i i i i i i ?. ?. ?..° ?. ?. ?, ?. ?. ?. ?. ?. I l i l i g . l i l § 5 l 3 .=>. p. p. .°. ?. ?. P. p. p. P. p. 11111 s 11 y i ° = «• •? <=• = = =•=• = <? 5 = 35 a a ° - =' s = o 6 d d ™ W a s s '- ? - : « r. f, 2 ~ "! t a s S S 7. 2 = » t z ?. ? 2 : s s : ? s i s •? * °! " ~: 7 ° S 5 i 2 2 * - r: "! *-. * •". K 2 ^ " " - 7 f s a ~ 1 7 7 S 2 : 1 I 1 ii 7 7 7 " 1 -19.9 -16.5 -23.3 1.8 s = ».-!• ' 7 7 7 " 1 10.4 5.5 f .5 9.4 14.3 4.5 1.9 i ° * i J -22.6 -17.6 -27.5 1.0 ! 1 € I 5 1 5 3 1 P f i 1-•I 1 * H ~ ' .=; i l 1 I i i ? .7 7 ?. i l l s I I I I 7 .°. ? ?. 3 I S.I.I i l I III S i l l f i l l i l l ! ° 5. = ?. S 2 I 1 n l i i c 5 « 10 on a ground temperature basis, the region is seen to form an outlier of the discontinuous zone--Mackay (1967) quotes temperatures (at a depth of 15.2 m) for various Delta locations of between - 2 . 4 ° to -3 .8 °C. Other data published by Mackay (1967) indicate that Arctic Red River is close to the boundary (a temperature at 15.2 m of between -4° and -5 °C) , but that Fort McPherson should properly be classified as dis-continuous (a temperature at. 15.2 m of about -3 °C) . Investigations by Johnston and Brown (1964) revealed that permafrost was absent beneath a small lake in the Delta. At Aklavik, several piles were driven into the bottom of the Peel Channel, and no frozen ground was encountered (R. J . .E . Brown 1956). The Mackenzie Delta is thus marginal between the two zones, and permafrost is physically discontinuous there; permafrost thicknesses are probably generally less than 100 m (see Johnston and Brown 1964). This pattern is undoubtedly due to the thermal influence of the large amounts of surface water which occupy up to 50% of the surface area in some parts of the Delta (Mackay 1963; p. 98). On nearby tundra just a kilometer or so from the Delta, a permafrost thickness of about 365 m has been measured (Jessop 1970). 2. The Thermal Effect of Water Bodies The thermal effects of water bodies in high latitudes consti-tute the greatest local departure of the ground temperature field from the systematic geographical patterns determined by climatic factors. Mean annual temperatures beneath water bodies are often anomalously high; this is associated with the high heat capacity of water, combined with the reduction in the winter loss of heat due to the insulation afforded by an ice (and snow) cover. The Mackenzie. Delta is icebound for almost eight months of the year. 11 The influence of water bodies on permafrost configuration is often quite dramatic--Hopkins et al (1955) reported that "Permafrost is absent or lies at great depths beneath lakes and ponds throughout Alaska." (p. 117). If a fresh water body is deeper than the maximum thickness of winter ice, i t s bottom sediments wi l l have a mean annual temperature of. greater than 0°C. In high latitudes, where the mean annual ground surface temperature may be -10° to -15°C, the maximum accumulation of ice on water bodies is generally only 1.8 to 2.1 m (Lachenbruch 1962). At Barrow, Alaska, the mean annual air temperature is approximately -12°C, but lakes over 1.8 m deep in the area do not freeze to the bottom (Brewer 1958b). Hence, beneath even relatively shallow bodies of water, depression of the permafrost table w i l l presumably occur, and this has been confirmed by various investigators (see Brewer 1958a; Grigor'ev 1959; Vturina 1960; Johnston and Brown 1964; Anisimova 1966). Often, however, the information is of a qualitative nature, and l i t t l e suitable published data are available to test the physical efficacy of models proposed for these processes by, for example, Lachenbruch (1957a, b) and W.G. Brown (1963, 1964). Johnston and Brown (1964) investigated the distribution of permafrost under and around a small lake, about 275 m in diameter, in the Mackenzie Delta. The lake is shallow, with a maximum depth of only 1.5 m, at low water. (The lakes in the Mackenzie Delta are typically shallow—see Mackay 1963, pp. 130-135). However, the maximum thickness of ice was only 0.75 m, and they state that "It is unlikely that the lake freezes to the bottom, even during the most severe winter." (p. 173)*. D r i l l i n g to a depth of 70 m beneath the Depths in excess of the winter ice thickness must be consistently 12 lake they did not encounter permafrost, whereas in a borehole 168 m away from the lake, permafrost is over 90 m thick. At a distance of 40 m from the lake, permafrost is about 76 m thick. They concluded that: It is evident that the lake, although quite small and shallow, has a very marked influence on the distribution of permafrost. The thawing effect of the lake is confined, however, to the ground lying under the lake, as indicated by the presence of permafrost at the shoreline. (p. 172) . The permafrost surface is shown as plunging at a steep angle from the lake edge (see their Figure 9, p. 174). They detected that the thermal effect of the lake extends into the surrounding area for some distance away from the shore. In a subsequent paper, W. G. Brown et al (1964) employed aspects of heat conduction theory to model this physical situation. Using a solution due to Lachenbruch (1957a), they computed the ground temperature field under and around the lake and reported that: The computed results... .show that the entire region under the lake, as indicated by the position of the 320F (0°C) isotherm, is unfrozen, whereas under surface areas not covered by water the ground remains frozen to depths of up to several hundred feet, (p. 153) ...Theory supports the general field findings of no permafrost under the central region of the lake. (p. 154) Brewer (1958b) presents a temperature profile from beneath a lake near Barrow, Alaska; the depth to the permafrost table is 58 m, whereas permafrost in the region is over 275 m thick. The average annual surface temperature in the area is about -9 to -10°C, whereas for the unfrozen part of the lake it is +1 .2 ° to +1.8°C (p. 284). The modification of ground temperatures in the vicinity of a present in a large number of delta lakes, since the region is an important habitat for the muskrat, which lives in lakes with unfrozen pools (Mackay 1963, p. 135). 13 water body is illustrated by the following data (Vturina 1960, p. 138) Distance from lake (m) Temperature at 5 m (°C) 0 -1.8(?) 15 -4.5 30 -5.7 45 -7.0 60 -8.2 Permafrost is depicted here also as plunging downwards at a very steep angle (see her Figure 6, p. 138). Thermal effects associated with rivers should be similar to those of lakes, except that water flowing in from elsewhere will be important in determining the mean annual river temperature. Virtually no temperature data are available from beneath rivers in permafrost regions. Almost a l l the information on permafrost occurrence in these situations is of a qualitative nature--relating to the presence or absence of frozen ground, inferred mainly from dril l ing operations for groundwater and mining exploration. An excellent review of such information for Alaska is presented by J. R. Williams (1970). Apparently, the only temperature records from beneath rivers reported in the North American literature, are in an engineering site study in northern Quebec (Samson and Tordon 1969). In an area where the mean annual air temperature is between -10 .5 ° to -8.5°C (13° to 17°F) they found that: Subsurface investigations at three river sites...have disclosed the presence of permafrost at shallow depth below the river bed. (p. 25) Borehole results and ground temperature measurements show that the river bed is perennially frozen below depths of six to nine feet (1.8 to 2.7 m). Thermocouple readings... in the centre of the river...show the ground temperature at the depth of 50 feet (15 m) to be 26°F ( -3 .3 °C) . This ground temperature is somewhat higher than the ground farther from the river (19° to 20°F or - 7 . 2 ° to - 6 . 7 ° C ) . (p. 26) This river channel is about 38 m wide, is underlain by about 18 m of 14 granular alluvium, and in winter was found to be frozen to the bottom. Permafrost was also encountered at two other river sites: At Deception River, permafrost occurs at a depth of about 12 feet (3.7 m) and the ground temperature measured at 40 feet (12 m) below the river bed is 24°F ( -4 .4 °C) . At Murray River, permafrost was encountered below the river bed...and observations made in late winter 1966 showed that the river was frozen to the bottom. (p. 26) Almost al l other information relates to the presence or absence of permafrost, and further, most of this pertains to conditions along river banks or on floodplains--although it does appear to confirm the presence of taliks beneath the rivers themselves. For example: At Beaver (which is on the Yukon River, in the discontinuous-permafrost zone of Alaska), on a low gravel terrace...the alluvium is unfrozen for a distance as much as 100 feet (30.5 m) back from the bank. (J. R. Williams 1970, p. 33) Wallace (1948) found that frozen ground was uncommon beneath recently abandoned channels. Cederstrom (1950) also found evidence of this, and further writes that: In the vicinity of major streams and rivers permafrost is ordinarily absent...on the slip-off side of the stream, but...maybe close beneath the surface near a steep cut bank. (p. 3) Wells up to 80 m deep on the newer parts of meander scrolls in the Kuskokwim River floodplain (discontinuous zone) are permafrost-free (Fernald 1960). On the older parts of the scrolls, permafrost was penetrated at depths of 4.5 to 15 m. Writing about the continuous permafrost zone in Alaska, J. R. Williams (1970) states that: Only the largest rivers produce a temperature anomaly that is great enough to form an unfrozen zone through the permafrost. In northern Alaska, the Colville River has formed an unfrozen zone several hundred feet deep beneath its bed. (p. 19, p. 27) Brewer (1958a) found that the Colville River does not freeze down to its bed during the winter, and thus the mean annual temperature of the bottom sediments must be above 0°C. Borehole data from a sand bar in the middle of the Shaviovik River revealed that the temperature at 41 m 15 was 3° C. warmer there than on either side of the channel, but s t i l l frozen (Brewer 1958a, p. 26). J. R. Williams (1970, p. 19) reports that drillings beneath smaller streams in the continuous zone revealed the existence of permafrost at shallow depths. In the discontinuous zone, borings reveal permafrost to be thin or even non-existent in floodplains and terraces, so that through-taliks probably exist beneath most large and medium-sized, rivers. In the U.S.S.R. unfrozen zones are known to exist beneath large lakes and rivers (Svetozarov 1934; Grigor'ev 1959; Vturina 1960; Efimov 1964; Mel'nikov 1964; Anisimova 1966; Nekrasov 1967; Romanovskii 1967) . : In general, water bodies which do not freeze to the bottom in winter will have a mean annual temperature above 0°C. Some form of talik will therefore be present beneath them. Where the water freezes through, there will s t i l l be a warming effect, but a talik as such may not exist. 3. Permafrost Configuration and River Migration Migration of a river across the land surface can be expected to cause migration of the talik beneath the river. The thermal effects of the river on the surrounding ground temperature field depend not only on the strength of this source, but also upon the length of time available to the thermal processes, which is a function of the speed of migration. (Figure 13 illustrates the changing configuration of permafrost, over time, in the vicinity of a strip-shaped disturbance at the surface). The local configuration of permafrost, therefore, is closely related to the history of river migration. As the river migrates, it erodes the frozen deposits along its cut bank and deposits new material along the slip-off slope. The 16 deposits on the cut bank side are less influenced by the ameliorating effect of the river than the deposits along the slip-off slope; these latter deposits are init ia l ly unfrozen, but gradually freeze under the influence of below-zero mean annual temperatures. Thus one should expect ground temperatures on the cut bank side of the river to be colder than those on the slip-off slope. Mordvinov (1940; quoted in J. R. Williams 1965) has described such a pattern of ground temperature observations in a similar geomorphological situation. Beneath the slip-off slope, and further inland, temperatures decrease, and hence perma-i frost thickens, with distance away from the river; as one moves away from the river, the thermal state of the ground exhibits an increasing degree of recovery following the disturbance induced by a former position of the channel. Pewe (1965) has described the distribution of permafrost beneath a slip-off slope on the Yukon River. He found that the frozen alluvium forms a wedge-shaped mass that is thin near the river, but thickens away from i t . J. R. Williams (1970) described the distribu-tion of permafrost in the floodplains of the Tanana and Chena Rivers near Fairbanks. Based on data from over 5100 wells and borings, he summarised the pattern of occurrence as follows: The progressive increase in permafrost thickness from the flood-plain to successively older terraces suggests that permafrost thickness and continuity are partly a function of the time elapsed since removal of the warming influence of the river, (p. 37) 4. The Study Area The Mackenzie Delta is an area of active sedimentation and erosion. Shifting channel courses, as evidenced by abandoned channels, point bar deposits and undercut banks, are a conspicuous element of the landscape. Local relief generally does not exceed 3 to 4 m, excluding channel cross-sections; between levee systems, relief is generally minor. Vegetation shows a sequential distribution: actively forming sections near the channels are bare of vegetation, willow (Salix spp) and alder (Alnus crispa) grow away from the rivers, and the inactive parts of the floodplain are populated by spruce (Picea glauca), which is the typical climax community in the lower valley and delta of the Mackenzie River (Plate 1). The study area contains many lakes, which range in size from 2 2 0.01 km up to 0.5 km (Figure 1). About 50% of the area is covered by water bodies. Mackay (1963, p. 130-135) states that well over 90% of a l l the delta lakes are floodplain lakes, and that they are typically shallow. Lakes in the study area that were sounded were found to have maximum depths of 1.5 to 2.5 m (at low water), which is greater than the winter ice thickness. In March 1971, ice thicknesses varied from 0.85 to 1.0 m; in March 1970, they were about 15 cm thinner, and in March 1969, about 20 to 25 cm thicker. Maximum ice thicknesses on four Delta lakes, measured in 1965-66, ranged between 1.0 to 1.2 m (Inuvik Research Laboratory 1968). These ice thicknesses are less than those reported from the Arctic Coastal Plain (see p. 11); the lower temperatures and less snowfall in that region may be the reason. A major distributary, 120-170 m wide, flowing through the area, is erosionally active, exhibiting lateral migration (Plate 1). The channel bottom profile is fairly smooth and broadly U-shaped, with an average maximum depth of about 4-6 m. In March 1971, the ice thickness varied from 1.0 to 1.3 m. On the outside bends of meanders the river is cutting into a mature, spruce-covered surface in excess of 300 years old (as indicated by tree cores), with consequent degradation of permafrost. The undercut slope is marked by a levee which maintains its altitude and backslope as Plate 1 Study Area And Vic in i ty ( P o r t i o n Of A i r Photograph A19946 -13 ) co 19 it erodes back. Bank erosion is a function of two major processes; relatively warm water thawing the frozen sediments, and flowing water mechanically eroding and transporting material (see Efimov 1964; Walker and Arnborg 1966; Walker and McCloy 1969). These processes create a thermo-erosional niche, which weakens the bank and eventually leads to block collapse (Plate 2). As the cut bank recedes, new deposits are formed on the slip-off slope, and under the influence of low mean annual surface temperatures permafrost will form there ab init io (Figure 2). The process of geomorphic change is accompanied by a vegetation succession which produces a complex interaction between topography, vegetation and microclimate, and the thermal regime of the ground. The interactions between vegetation and permafrost have been studied by various authors (see Benninghoff 1952, 1966; Tyrtikov 1963; R.J.E. Brown 1965; Viereck 1970). This biomass gradient introduces other levels (sources) of variation in the ground temperature field, which it may or may not be possible to differentiate from the major source, that identi-fied with the process of geomorphic change. Land surface conditions vary from bare, newly exposed alluvium, close to the river, through to mature stands of spruce in the most inactive areas. It is possible to identify various terrain segments: because of the close association between vegetation and topographic location, along the successional transect, terrain segments wi l l , for expediency, be designated mostly by vegetation names. The five major terrain segments in the successional sequence are termed: l)bare ground; 2)Salix (1) (snowbank zone); 3)Salix (2); 4)Salix-Alnus; 5)Picea (see Figure 2, Plate 3). For a full description of the relationships between vegetation and topography in this area see Gi l l (1971). 20 Figure 2 DIAGRAMMATIC CROSS SECTION THROUGH A SHIFTING CHANNEL AREA Relationships of permafrost to the river and vegetation type Plate 3 Spatial Arrangement of Terrain Segments 23 5. The Present Study The present study focusses its attention on the environment of the ground climate system. The aspect of ground climate of special concern to this study is the thermal regime. Since temperature is the end result of the ground heat balance, i t is viewed as the fundamental index of the energy status of the ground. Further, with knowledge of the thermal conductivity, k(cal cm * sec * °C , and heat capacity, C(cal cm ^ °C )^ , i t is possible to determine the heat flow and the heat storage in the ground, from temperature observations. Variations in the ground temperature field, and permafrost configuration, are logically viewed as responses to spatial and temporal variations in external factors, principally those comprising the surface energy regime (i.e. aerial climate and surface cover), with certain constraints imposed by the thermo-physical properties of the ground materials (internal factors). Because the formation and existence of permafrost depends upon the mean surface temperature, permafrost configuration (thickness and areal extent) is directly affected by the nature and extent of surface features. The spatial pattern of mature delta surface, cut bank, river channel, slip-off slope and fossil cut bank is sequential. It is assumed to be analogous to a time series on a "geomorphic" time scale; something of the order of 500-1000 years. The modern Delta is thought to have aggraded at a mean rate of about 5 mm/yr for the past 7000 years or so (Johnston and Brown 1965). According to Ritchie and Hare (1971), it is likely that climatic conditions conducive to the existence of permafrost have persisted for at least 5500 years (i.e. the "geologic" time scale). If, as part of the current hypothesis, however, i t is assumed that permafrost is totally destroyed by the presence of the 24 river above i t , then the permafrost at any location will only be as old as the time elapsed since a river, or lake, last occupied the surface above i t (see P. J. Williams 1968, p. 1386). Thus the changing configuration of the ground temperature field previously described is wholly compatible with the time scale of geomorphic change (assuming some equivalence of spatial and temporal scales): relationships obtained for the present set of environmental conditions must be inter-preted in terms of the degradation and re-establishment of permafrost when the surface boundary conditions are changing. Variations in the surface energy regime can also, of course, be brought about by changes in climate itself. But since the surface temperature regime is so complexly related to the aerial climate, it is impossible to express quantitatively the effects of climatic variations. Certainly, variations have occurred and are presumably s t i l l occurring. Various data have been analysed for trends by the method of least-squares (see Panofsky and Brier 1958, pp. 136-138). Only linear trends were sought, and no analysis was directed towards cyclical variations. The significance of linear trends was assessed by testing regression coefficients with the F-test. For the long term, some Mackenzie Delta tree-ring data (abstracted from Giddings 1947) were analysed. Values for ring-widths were taken from his Figure 1 and regressed against time. Without implying any specific relationships to climate, no significant linear trend in tree growth rates between 1460 and 1940 was detected. For the recorded past, analysis of climate data for Aklavik (1926-1960), revealed no signifi-cant linear trends in any parameters tested (M. Church, pers. comm.).^  Apart from annual values, only summer data were analysed. 25 For mean annual temperature, the regression coefficient b = -0.0138 (S.E. = 10.0347, d.f. = 24), and for annual precipitation b = 0.0111 (S.E. = 10.0673, d.f. = 23). A similar analysis of Fort McPherson data (1935-1970), however, revealed a significant (at the 2^% level) decline in mean annual temperature (b = -0.1101, S.E. = +0.0397, d.f. =24 -Table 1). This seems to be mainly due to the significant decreases in winter temperatures. However, over the same time period there have been significant increases in snowfall for November, December and February (Table 1), so that it is difficult to assess the effects of the changes in air temperature on the ground thermal regime. Mean annual air temperature has also been declining at Fort Good Hope (1928-1966), but the b value (-0.0514, S.E. = +0.0.280, d.f. = 36) is not significant at the 5% level. The record for Inuvik (1957-1971), which is really too short to permit meaningful analysis, contains no significant trends, except that of decreasing April precipitation (Table 1). For the period of the present study (1969-1971), climatic condi-tions were generally within one standard deviation of the mean values (Table 1). Exceptions were the partly cool summer of 1969, the light snow cover in 1969-1970, and the cool autumn in 1970. The mean annual temperatures, however, were each within one standard deviation of the mean. It is to be supposed, then, that every change in environmental conditions, both external and internal, may either increase or decrease the heat content of the ground; or some part of i t . Where the surface regime is changing, any variations in the ground temperature field and permafrost configuration must necessarily be considered in relation to a definite period of time, which is compatible with the time rate of 26 change of the surface conditions. Variations of heat exchange at the earth's surface, at the same time and at the same place but with different periods, penetrate to different depths (Table 2). There is a correspondence between the time period of heat content variations, and the depth to which they penetrate; for example, annual periodic variations will generally penetrate to only 15 to 20 m. One must obviously maintain a consistency between the time and space (depth) dimensions. The viewpoint adopted here is that a number of aggrada-tional and degradational processes can occur simultaneously, perhaps, for example, representing short, medium and long-term changes in the thermal regime. The variation in external (and internal) factors relates to a variety of environmental processes, over a.wide span of spatial and temporal scales — section 2.4 has illustrated some of these variations in the study area. In the present study, analysis of ground temperature variations is restricted to the following scales: 1. The "areal"scale -- at this scale the distribution of permafrost over the study area is analysed, with respect to the influence of water bodies as local heat sources, including the pattern of degradation and aggradation associated with the process of geo-morphic change. The configuration of permafrost is thus viewed in terms of the spatial distribution of these heat sources, and, where appropriate, their spatial variation with time. (Their strength is assumed not to vary over time, i .e . long-term climatic variations are not considered). 2. The "between-site"scale --. at this scale the effect of different surface conditions on the ground climate is investigated; the temperature borehole network includes sites in different terrain Table 2 Depth of Penetration of a Temperature Disturbance as a Function of Time (t) and Thermal Diffusivity, a(m2/day) Depth of Penetration (m) Time, t a = 0, .04 a = 0.06 a =\0.08 h day 0, ,5 0.6 0.7 6 months 9, .4 11.5 13.2 1 year 13. ,2 16.2 18.7 10 years 41. .9 51.3 59.0 50 years 94, ,0 115.0 132.0 100 years 132. ,0 162.0 187.0 200 years 187. .0 230.0 265.0 500 years 296. ,0 363.0 419.0 1000 years 419, .0 513.0 592.0 5000 years 936, .0 1147.0 1324.0 10000 years 1324. ,0 1622.0 1873.0 Notes: i) The depth of penetration, z (m) , was calculated from z = /12oCt (Terzaghi 1952, p .22). Here, z is the depth within which the temperature of the ground has perceptibly increased (sic) during a given time t. This formula assumes that the ground is homogeneous. Further, latent heat effects are neglected; this leads to an over-estimate of z. i i ) If t represents the half period of a surface disturbance, then the z values are the depths to which the disturbance will penetrate before it is damped out. i i i ) If the surface disturbance in question is of the form of a monotonic step change, then the Table shows how quickly this change penetrates through the ground, towards the establishment of a new steady state. segments (representing the successional sequence). The variation in microclimate is studied on the basis of differences in the annual, seasonal and diurnal thermal regimes. 3. The "around-site" scale -- at this scale the variation in ground climate within a terrain segment is considered. This is an attempt to gauge the representativeness of sites selected for comparison at the between-site scale. 4. The "at-site" scale -- variation of T(z) in real (present) time. Whilst the scales are given spatial connotations, this is mainly for the sake of expediency, for they also relate to distinct time domains. They should not be regarded as necessarily comprising the total picture. With the foregoing in mind, the major objectives of the present study can be stated as follows: 1. To determine the first-order variations in the ground temperature field. If ground temperature is viewed as some function of space (s) and time (t) (f(s,t)), then the first-order variations per-tain to one of these variables being held constant (c^,C2) (i.e. f(s,ci) and f ^ . t ) ) . Determination of first-order variations is by field observation, and this information forms the basic input into the rest of the study. (Scales: at-site; real time). 2. To understand how the process and material sets influence the ground temperature field; for example, through variations in microclimate. Observed variations in ground temperatures must reflect variations in external and internal factors. (Scales: around-site, between-site; real time). 3. To analyse the development of the present temperature field. Geomorphic and biological evidence shows that the surface boundary conditions are changing over time, so that the present 29 temperature field has to be interpreted as a part of some sequential pattern. This is approached through the attempt to: i) demonstrate the consistency of the ground temperature field, when viewed in the framework of simple heat conduction theory, and thereby, i i ) derive a predictive model for the ground temperature field. (Scales: areal; geologic ("equilibrium") and geomorphic time). Chapter 3 EXPERIMENTAL DESIGN AND MEASUREMENT The scales, and their associated degrees of v a r i a b i l i t y , intro-duced in Chapter 2, make specific sampling demands. A major problem, common to most research, was how to accommodate these demands as effectively as possible. In the present study, two specific practical problems faced were the restrictions on spatial sampling and the in a b i l i t y to monitor parameters on a regular year-round basis. These problems have different impacts at the various scales of the study. 1. Areal scale At the areal scale, the primary concern is with the pattern of permafrost distribution, as i t relates to factors of i t s environment. A somewhat generalised picture i s sought, in that the longer-term variations associated with the process of geomorphic change are investigated, with most of the shorter-term variations in the thermal regime being ignored. (For example, the annual periodic variations are not considered at this scale.) Ground temperatures. Temperature is viewed as the fundamental index of the energy status of the ground. At the areal scale, "mean" values are sought, and assumed to be representative over the long term. Boreholes were a basic requirement, and temperature was measured with thermistors (Yellow Springs Instrument Co. part no. 44033), which were encapsulated at intervals along multiconductor cable. The pods contain-ing the thermistors were covered with rubber sealant and then self-30 31 vulcanising rubber splicing tape. Temperatures were mostly read manual-ly using a simple bridge circuit, and absolute accuracy with this type of thermistor is +0.1°C* Any individual thermistor could easily be read with a resolution of +0.02°C, but slight variations in calibration between thermistors reduce overall accuracy. On some occasions, temp-eratures were recorded on a chart recorder (Rustrak) and resolution is not as good as with the manual measurements (+0.1°C). The recorders were calibrated daily against a precision decade resistance, and over-all accuracy was probably maintained at +0.25°C. Given that only a limited number of boreholes could be drilled, and that boreholes cannot be moved around, the problem of obtaining an adequate and representative spatial sample was faced. The geomorphic sequence previously described was selected as a focus, and major borehole transects were strategically located along i t (Figure 1). In 1969, time and equipment limited these major boreholes to a total number of 7, and to a depth of 15 m--the approximate level of zero annual amplitude. (Numerous other shallower holes were also drilled, however.) The boreholes were arbitrarily located, along a transect, so that each of the terrain segments would be represented. It was not possible to d r i l l under water bodies, but holes were located as close as possible to the channel. In 1970, some 30 boreholes were drilled, to depths up to 30 m, which proved to be the deepest practical; 18 of these were located at regular intervals along a second major transect (Figure 1). All holes were drilled with a 10-HP Winkie Dri l l , using a three-wing drag Thermistors were calibrated after being encapsulated. The bridges used were regularly calibrated against a precision decade resistance. One source of error, which cannot be accounted for, however, is that which could result from stress following installation in a borehole, as the cable freezes in. 32 bit , giving a hole about 5-6 cm in diameter. An auxiliary pump was used to circulate f l u i d during d r i l l i n g (Plate 4). In 1969 a calcium chloride solution was used, in order to prevent the possibility of freeze-up in the hole, during d r i l l i n g . Unfortunately, this caused the magnesium-zircon rods to corrode and subsequently fracture. In 1970, ordinary lake and river water, at temperatures of 10-20°C, was used, without any problems. Following the d r i l l i n g disturbance, a borehole has to re-equil brate; observations showed that this took approximately two to three week by which time the temperatures below the depth of annual variations had become stable. Ground materials. Since the cuttings were flushed to the surface by pumped water, this d r i l l i n g procedure was unsuitable for sampling ground materials. However, in March 1970, an opportunity arose to obtain some samples when a seismic line was located in the v i c i n i t y of the study area (Plate 1). Through the cooperation of Imperial Oil Limited and Gulf Oil Limited, ten boreholes were d r i l l e d , the deepest to 32 m. D r i l l i n g was performed using compressed air, and i t was possible to collect 3-meter integrated samples over the depth of each borehole. These samples were subsequently analysed for total moisture content, grain-size characteristics, and organic content, with the view to estimating thermal properties. Other data. The knowledge of permafrost distribution obtained from the ground temperature network was extended in 1971 through the use of r e s i s t i v i t y surveys (see Barnes 1966, D. K. MacKay 1969). The Schlumberger configuration was used to determine the lower permafrost boundary, after successful checking at sites with ground temperature control data. Some profiling was also carried out, using the Wenner array. Also, a limited amount of seismic work was carried out in 33 Plate 4 Drilling Equipment at a Borehole on a Slip-Off Slope (Bare Ground Segment) 34 1970. 2 Estimates of mean annual lake- and river-bottom temperatures were obtained from regular measurements of water temperature. 2. Between-site Scale Nested within the o v e r a l l pattern o f permafrost degradation and aggradation are the va r i a t i o n s i n the ground thermal regime associated with the changes i n the nature of the surface cover, pro-gressing from bare, newly exposed sediments to mature spruce forest. It i s to be expected that such surface v a r i a t i o n s would produce differences i n microclimate between s i t e s . Ground temperatures. The major expression of v a r i a t i o n at t h i s between-site scale i s the difference i n the annual ("periodic") ground temperature regime, i . e . the mean and the flu c t u a t i o n s about the mean, extending down to the l e v e l of zero annual amplitude. For t h i s purpose thermistors were located at depths of 0.5 and 1.5 m in the major boreholes along Transect 2, i n addition to those at depths of 3, 6, 9, 12 and 15 m. Where environmental gradients were steep, such as at the boundary of t e r r a i n segments ( e s p e c i a l l y across the s l i p - o f f slope), the major borehole network was i n t e n s i f i e d by loca t i n g intermediate holes (Figure 3). Also, s p e c i a l temperature transects were established across the s l i p - o f f slope to investigate the influence of d i f f e r e n t i a l seasonal snow accumulation on ground temperature. Although the major environmental gradients run normal to the r i v e r , the magnitude of lo n g i t u d i n a l gradients was investigated The seismic work was c a r r i e d out by Mr. Ronald Good, of the Geological Survey of Canada. 6-13 i 6-12 Salix/Alnus Fossil Cut Bank Snowbank Prolile 7 0-0 Indicates 20m or 30m borehole 0-0 Indicates 9m borehole 0-0 Indicates 3m borehole Snowbank profile borohcies are 1.5m 0 meters I i 1 1— R i v e r Figure 3 T E M P E R A T U R E B O R E H O L E NETWORK ON A SLIP-OFF S L O P E 36 by repeating borehole transects at other locations along the s l i p - o f f slope (Figure 3). Energy balance components. A convenient means of comparing the microclimate of different surface types, in the same aerial environ-ment, is to examine the relative magnitudes of surface energy balance components. The net available radiative energy at the ground surface, R , i s dissipated via sensible heat (H) and latent heat (LE) transfer to the air, and by conduction into the ground (G) (e.g.see Sellers 1965, p.100). The relative importance of these energy balance terms can vary enormously, depending upon prevailing atmospheric and surface conditions. The ground surface thermal regime is a function of the mutual inter-action of these energy transfer processes. A comprehensive energy balance approach was beyond the scope of the present study, and con-sideration was restricted to R^  and G only. It i s recognised, however, that evaporation, for example, is an important term in producing cooling of the surface. One problem in this aspect of the study was that data collect-ion was restricted to the summer months, with only short v i s i t s being possible during the winter. It was decided, therefore, to combine the analysis of the annual temperature variations with a study of micro-climatic variations, over a 6-7 week summer period, between sites located in the five major terrain segments. A meteorological site was maintained throughout the summer, for measurements of solar radiation, temperature and humidity. Air and active layer temperatures were measured with thermistors, and recorded continuously on Rustrak recorders. The a i r temperature sensor was an ordinary thermistor (YSI 44033), wrapped with aluminum 37 f o i l , and subject only to natural ventilation. No determination of response time was carried out. A l l temperatures were logged once per 15 minutes. Net radiation and s o i l heat flux were measured with Thorn-thwaite systems—miniature net radiometer or s o i l heat flux disc, together with a matched microvolt recorder, powered by a 12-volt battery. Absolute accuracy of the radiation measurements depends on, more than any other single factor, the sensors and their assigned calibration (Weaver 1969). The calibrations used were those supplied with the instruments. The resolution of the net radiation systems was -1 -2 0.01 ly min (0.698 mW cm ), and for the s o i l heat flux systems -1 -2 0.003 ly min (0.209 mW cm ). The radiometers were mounted 1 m above the ground. They were checked daily for damage (by animals) and signs of moisture accumulation; when the latter was noted, the sphere was purged with dry a i r . The polyethylene domes were cleaned as necessary. Great care was given to maintaining consistency in the instruments and methods of data collection and reduction. The zero calibration of each system was checked at frequent, but irregular, intervals, and the systems were cross-checked against each other. The overall maximum error in the radiation measurements i s estimated to be -0.04 ly min* _2 (2.792 mW cm ). Accuracy of s o i l heat flux measurements depends, in addition to sensor calibration, on the careful emplacement of the disc in the ground. Discs were placed at a depth of 1.5 cm - as close to the surface as possible. Because only two systems were available, i t was not possible to measure the v a r i a b i l i t y of s o i l heat flux around a site. Thus there is no check on the representativeness of the measured values. The two systems used were cross-checked, and the maximum error is est-imated at +0.012 ly min -* (0.836 mW cm - 2). Ground materials were sampled at each site; they varied from sandy-silt to organic matter. Strip charts were digitised (on a potentiometric d i g i t i s e r ) , and appropriately summarised by computer. Reduction errors are within the basic precision of the measurement systems. On some occasions data loss did occur, either as a result of sensor troubles or recorder malfunctions. Winter data. During the winter v i s i t s , information was collected on seasonal snow cover distribution, snow density, bottom temperatures of lakes and channels, and low water extent of water bodies. In addition, a l l thermistors were routinely read. Around-site Scale To assess the representativeness of sites selected for between-site comparison, i t was necessary to gauge around-site va r i a b i l i t y . Fairly simple measures were employed because of equipment limitations. Measures included determination of active layer depths, ground temperatures at 10 cm depth (including diurnal variation) , variation in incident and reflected visible light (using a camera light-meter). Results are discussed in Chapter 5. Chapter 4 THE DISTRIBUTION OF PERMAFROST: OBSERVED AND PREDICTED 1. Major Features of Permafrost Distribution in the Study Area Before proceeding with the application of the heat conduction models, the major features of permafrost configuration in the study area will be summarised. Where a permafrost "thickness" is quoted, this is measured down from the ground surface. It thus includes the active layer, which is not strictly correct, but convenient. Where mean annual temperatures are quoted, they refer to mean values calculated over the period of field observations (either 1 or 2 years). Temperature data were collected irregularly over this period; al l data were fitted to a Fourier series (using UBC FCT), from which intermediate values were generated, and the means calculated. The maximum thickness of permafrost locally exceeds 65 meters, as indicated by thermistor measurements in boreholes. Linear extra-polation of the temperature profile at #6-3 (Figure 4) yields a thickness of about 65 meters; a seismic reflection was obtained at a depth of 66 meters at this locality. Linear extrapolation is only valid, of course, for a steady-state situation, with homogeneous ground material. The maximum permafrost thicknesses are found in locations which have a mature spruce cover, and are farthest away from any surface water bodies. Estimated from near surface measurements, 39 Temperature (°C) -4 -3 -2 -1 0 70-i Figure 4 TEMPERATURE BOREHOLES: SPRUCE-COVERED SITES Figure 5 TEMPERATURE BOREHOLES: SLIP-OFF SLOPE SITES o the mean annual surface temperature for such sites appears to be on the order of -4.0 to - 4 . 5 ° C ; the mean annual river temperature (unfrozen portion) is close to +4.0°C, and in the lakes possibly +3.2°C, whilst for the bare ground on slip-off slopes the mean annual surface temperature is about - 1 . 0 ° to -1.5°C (See Chapter 5 for more extensive discussion of these differences.) Mean annual water temperatures are based on daily measurements for the period May to October, and an assumed wintertime value of 0.0°C (Table. 3). In winter the unfrozen portions of the lakes are too shallow to permit any thermal stratification, and the water flowing in channels is mixed and cooled to a uniform temperature. Again, based on extrapolation, the following thicknesses have been determined for spruce-covered areas (for locations see Figures 1 and 3, and Plate 1) : Table 4 Permafrost Thicknesses for Spruce-covered Areas Site # Permafrost Thickness (m) 2-1 52.0 2-8 50.0 6-2 65.0 6-3 65.0 6-17 53.0 SL-10 57.0 Tree cores from these sites indicate that the surfaces are not less than 300 to 500 years old; spruce-covered sites are thus areas of l i t t le geomorphic change. In such areas, the thermal effect of surface water bodies is exhibited as warmer mean annual ground temperatures in their proximity (x is distance to channel): 42 Table 3 River- and Lake-Temperature Data Monthly Mean Monthly Mean River Temperatures(°C) Lake Temperatures(°C) 1967* 1968** 1969** 1970 1968** 1969** Jan (O.O)1 (0.0) (0.0) (0.0) (0.0) 1 (0-0) Feb (0.0) (0.0) (0.0) (0.0) (0.0) (0.0) Mar (0.0) (0.0) (0.0) (0.0) (0.0) (0.0) Apr (0.0) (0.0) (0.0) (0.0) (0.0) (0.0) May 0.2 (0.2) 0.2 0.2 (0.2) (0.2) June 8.4 9.2 10.2 9.2 (7.2) 7.0 July 14.2 15.6 14.8 16.33 15.6 14.2 Aug 12.6 14.2 10.5 15.0 12.7 8.1 Sept 7.3 (7.6) 7.9 (7.6) (5.4) 5.4 Oct (1.5) (1.5) 1.52 (1.5) (1.0) (1.0) Nov (0.1) (0.1) (0.1) (0.1) (0.1) (0.1) Dec (0.0) (0.0) (0.0) (0.0) (0.0) (0.0) Year 3.7 4.0 3.8 4.2 3.5 3.0 Values in parentheses are estimates based on incomplete or limited field data, or data from other years. The following temperature data refer to various winter dates: River Lake Water Bottom Water Bottom March 1969 0.0 0.0 0.0 0.0 March 1970 0.05 0.07 0.08 0.08 Dec 1970 0.0 0.0 Estimate based on measurements for October 1-6 only 'The following temperature soundings were made on 24/7/70 (p.m.), and indicate that the river is well mixed to a uniform temperature: #1 #2 Depth(m) Temp(°C) Depth (m) Temp(°C) 1.0 16.7 1.0 16.7 2.0 16.6 2.0 16.7 3.0 16.6 3.0 16.6 4.0 16.7 4.0 16.6 4.3(bottom) 16.8 5.0 16.6 6.0 16.8 6.5 (bottom) 16.8 Data supplied by D. G i l l (pers. comm.) Data supplied by C. P. Lewis (pers. comm.) 43 Table 5 Ground Temperatures Beneath a Cut Bank and a Slip-off Slope Cut Bank Slip-off Slope Depth(m) #6-1 #6-2 #6-5 (x=lm) (x=36m) (x=35m) 6 -2.8°C . -3 .6°C -0.5 9 -2.4 -3.3 0.0 12 -2.0 -3.0 +0.2 15 -1.7 -2.7 +0.4 20 -1.4 -2.4 +0.7 In locations indicative of contemporary geomorphic change, perma-frost is much thinner, and may even be entirely lacking. Ground tempera-tures under the slip-off slope are warmer than those on the cut bank side of the river (Table 5). On slip-off slopes, close to the channel, the following permafrost thicknesses have been determined: Table 6 Permafrost Thicknesses for Slip-off Slopes Site # 2-2-A 2-3 6-4-A 6-4-B 6-4 6-5 Distance to Channel(m) 10 20 5 15 25 35 Permafrost Thickness(m) 2.5 7.0 3.4 5.8 8.5 9.0 Method of Determination Resistivity sounding (see Fig.6) Temperature borehole (see Fig.5) II II it II Resistivity sounding These sites are characterised by bare surfaces (frequently submerged in summer). As one moves away from the river, there is a succession of vegetation from Equisetum through to a "scattered growth of Salix 44 Master Curve Type K-19 (1-20-1) Site 6-5 Master Curve Type K-16 (1-10-2.5) Site 6-4A ~A Thickness of permafrost (second layer) = 1,35 K 7,5 m = 101 m Thickness of permafrost (second layer) Electrode spacing, Um) Electrode (pacing. L(mj Master Curve Type K-22 (1-40-0) Site 6-4-B Master Curve Type K-19 (1-20-1) Site 2-2-A Thickness of permafrost (second layer) * M 5 x 5 m Thickness ol permafrost (second layor) * 0.82 K 3 m * 2.5 m Electrode spacing. L(m) 1 I ' ' " I ' 5 10 Electrode spacing, L(m) Figure 6 RESISTIVITY SOUNDING DATA, FOR SITES ON SLIP-OFF SLOPES (Master Curves from Orellana and Mooney, 1966) 45 alaxensis" (Gill 1971) occupying the slip-off slope.* This successive increase in biomass leads to a concurrent lowering of ground temperatures and the aggradation of permafrost (see Benninghoff 1952, Tyrtikov 1963, Viereck 1970). The pattern of permafrost aggradation is, however, only partly caused by the insulating effect of the developing vegetation. For, as the channel migrates laterally, a part of the surface which it previously occupied is exposed, and the ground there will gradually cool under the influence of lowered mean annual surface temperatures (actually below 0 °C) . As one moves up the slip-off slope, the land surface is progressively older, and consequently the degree of thermal recovery is correspondingly more advanced, and permafrost thicker: Table 7 Variation of Permafrost Thickness with Distance away from River Distance from Temperature Permafrost Site # River (m) at 9 m (°C) Thickness (m) 6-4 25 +0.02 8.5 6-5 35 -0.02 9.0 6-7 55 -0.1 10.0 6-9 75 -0.1 12.0 6-11 100 -0.7 17.5 6-12 135 -1.2 22.5 6-13 170 -1.9 24.5 The boreholes on the slip-off slope show that temperatures continue to increase with depth below the base of permafrost (see Figure 5), indicat-ing that a through-talik does possibly exist beneath the channel. It is also possible, though, that temperatures might decrease at even greater depths, so that only a pseudo-talik exists, as suggested by Efimov The boundary between bare ground and Equisetum is quite diffuse, so they have been amalgamated into a single terrain segment (see p.20). 46 (1964, p. 104). In the present study area, the generalised pattern of permafrost aggradation outlined in Table 7 is actually interrupted by a zone of relatively temporary degradation (see Figure 7). The configuration of permafrost shown in Figure 7 was determined by probing (mostly confined to the top 3m) and temperature data. The former technique can be mis-leading at times; for example, the temperature data show that the frozen ground beneath the talik is very close to 0°C and w i l l therefore feel soft to the probe. Resistivity profiling was carried out across the bar, using the Wenner array, with electrode intervals of 1, 5 and 10m (see Van Nostrand and Cook 1966). Values of apparent r e s i s t i v i t y for two ground layers, calculated by the Barnes layer method (Barnes 1954), have been plotted in Figure 8. At either end of the transect the values for both layers are representative of frozen ground (cf. D. K. MacKay 1969, p. 372). For the upper layer (l-5m), the values of less than 100 ohm-meters in the middle of the transect are indicative of unfrozen ground. The values for the lower layer are higher, 270-540 ohm-meters, and might indicate the presence of a frozen layer, although close to 0°C. Dry, unfrozen ground would also produce high values. The talik in Figure 7 coincides spatially with the zone of max-imum seasonal snow accumulation (see G i l l 1971). Along the sli p - o f f slope, the outer belt of willows (Salix(l)) forms an excellent setting for the development of large seasonal snow d r i f t s . These are formed by the prevailing winds, and the general shape is reproduced each year since the extent and volume of snow in them is largely independent of the amount of snowfall (for example, see Benson 1969). As the Salix moves across the bar in colonising new areas, the snowbank location migrates along with i t . Ground temperatures in i t s lee progressively cool, and 47 6-4 6-5 6-6 6-7 6-8 6-9 I I i I • I 10 20 30 40 50 60 Meters Figure7 DETAILS OF PERMAFROST CONFIGURATION BENEATH A SLIP-OFF SLOPE Figure8 RESISTIVITY PROFILE ACROSS A SLIP-OFF SLOPE 48 permafrost wedges back in - a process similar to that in the river migration. The effect of snow cover on ground temperature is fairly well documented (for example, see Shul'gin 1957; Gold 1958, 1963, 1967; Pearce and Gold 1959; Klyukin 1963; Krinsley 1963) but "Detailed local studies of the influence of snow cover on permafrost... are lacking." ( R . J . E . Brown 1969, p. 34). The temperatures in the permafrost under the slip-off slope are quite close to 0°C, which, combined with the grad-ual release of heat from the underlying sediments (heat which derives from the period when the river occupied this position) , clearly makes i t vulnerable to degradation. It is evident that mean annual surface temp-eratures in this snowbank zone are raised to near 0°C, so that permafrost is "temporarily" degrading there. Thus the snow cover is important as a permafrost controlling factor in this locality. This pattern is exam-ined in the context of heat conduction theory, in section 3 of this chapter. The fuller details of snow cover effects on ground temperatures are discussed in Chapter 5. In between the slip-off slope and the spruce-covered area is a surface of intermediate age, dominated by a Salix-Alnus association. Ground temperatures and permafrost thicknesses are intermediate also, with 15-meter temperatures ranging from -0.1°C (#6-11) to -1.6°C (#2-6) and permafrost thicknesses as follows: Table 8 Permafrost Thicknesses for Areas of Salix-Alnus Site # Permafrost Thickness (m) Distance from back of slip-off slope (m) 2-5 2-6 6-11 6-12 6-13 6-14 29.0 38.0 17.5 22.5 24.5 29.0 3.0 22.0 2.0 37.0 72.0 107.0 4 9 In summary, i t is possible to recognise three concomitant sets of processes which affect the overall configuration of permafrost. Under steady-state conditions, the thermal effect of water bodies depends upon the distance from them; in the case of the shifting channel (transient state) the distance relates to the degree of thermal recovery (i.e. the process of permafrost aggradation). In this latter situation, assoc-iated with the "horizontal gradient" of thermal recovery is a biomass gradient, which acts upon the ground thermal regime in the same direction. The major features of the resultant pattern of permafrost configuration are summarised in Figure 2. Lastly, superimposed on this configuration is the permafrost degradation associated with the snowbank. Ground Temperatures and Heat Conduction Theory Symbols used in this section: T temperature (°C) (T indicates term mean) T g surface temperature T^ temperature of the disturbance (e.g. river temperature) x,y horizontal coordinates (m) z depth (m) (z=0 is the surface, and z is positive downwards) t time since initiation of temperature disturbance (days, years) 2 - 1 2 - 1 a thermal diffusivity (cm sec or m day ) k thermal conductivity (cal cm * sec * °C *) C volumetric heat capacity (cal cm ^ °C *) 9(x,y,z,t) the thermal disturbance produced by T^ on the temperature at any (x,y,z), after any time t (°C) Gg earth's geothermal gradient (°C m *) erfc x = 2 C e U du ~nr J Assumptions. Increased value can be gained from detailed local thermal studies i f i t is possible to demonstrate that the ground temper-ature field displays some consistency with respect to environmental fac-tors . This is now attempted through the framework of simple heat 50 conduction theory. Some assumptions necessary for i t s application here are that: 1. heat transfer takes places by conduction alone (any non-conductive transfer is ignored); 2. the ground is homogeneous with respect to thermal properties, and these properties are not functions of temperature (latent heat effects are thus ignored); 3. the mean annual lake- and river-bottom temperatures can be approximated by their respective mean water temperatures. Albeit scanty data (Table 3), indicate that such an assumpt-ion should be satisfactory. Brewer (1958a) found that lakes were essentially isothermal during the ice-free period. Assumptions (1) and (2) represent a considerable simplification of the real situation. But i t is possible to go ahead, assuming them to be valid, and compute an apparent, gross value for oC, for input into sub-sequent heat conduction models. Before this is done, however, the actual ground materials w i l l be described. Ground materials. As would be expected for a delta environment, the grain-size distributions of the f i f t y samples tested f a l l within f a i r l y narrow limits. Characteristics of some of the samples are pre-sented in Figure 9. The material to a depth of 30 m consists mainly of s i l t and fine sand. The fact that most of the samples are 3-meter in-tegrated sections, inevitably produces some homogenising effect. Data from PB-1, which are for 0.6-meter sections, reveal some more detailed stra t i f i c a t i o n . Total moisture contents, on a dry-weight basis ( w w ), vary from almost 100%, in near surface layers, to 30% at depth. Total car-bon content, as determined by loss on ignition, varied between only 5 and 7% for 30 samples. These data are' similar to those of Johnston and Brown (1965). They describe (p. 105) a typical section as follows: 0 to 100 feet (0 to 30 m) thinly s t r a t i f i e d sandy s i l t , with layers of decomposed organic material throughout. 51 20 40 60 60% 0 20 40% 20 40 60 80 100% 0 H ' 1 • - \ 1 " *4 ' ± 1 I PB-1 Figure 9 MATERIAL CHARACTERISTICS OF SOME SAMPLE BOREHOLES 100 to 180 feet (30 to 55 m) fine to medium sand, with thin layers of organic material >480 feet (> 55 m) very dense s i l t y clay They also found that moisture content decreased with depth. P. J. Williams (1968) analysed some of these same core samples, and stated that: L i t t l e ice segregation was recorded...Moisture contents (with depth) show that l i t t l e migration and accumulation of water had occurred during freezing except in the near-surface layers, where substantial accumulation had occurred (p. 1383). Johnston and Brown (1965) found that visible ice segregation was confined mostly to the upper 10 m. Below this depth they describe the material as solidly frozen, with sandy material being well bonded by ice not visible to the eye. R. J. E. Brown (1956) reported that ground ice in some Delta soils at Aklavik was either cement ice or thin (up to 16 mm) vein-lets. This was the pattern in the present study area, with some wedges also being observed. Thermal properties of some of the f i e l d samples were calculated, assuming a l l the moisture to be ice and a l l the carbon to be organic matter (Table 9). Values for conductivity, k, were calculated using Kersten's (1949) formulae, and volumetric heat capacity, C, from the formula: C = X C + X C + X C w w m m o o (de Vries 1963). Here, X is the volume fraction and w, m and o signify water (ice),mineral and organic respectively. The thermal di f f u s i v i t y , , is given by k/C. Apparent thermal di f f u s i v i t y. The models being employed here assume solely conduction in a homogeneous medium, whose thermal proper-ties are not functions of temperature. In order to be consistent with this view of the problem, i t is considered more appropriate to use an Table 9 Physical and Thermal Properties of Some Soil Samples Borehole Depth Interval(m) Soil Type* Ww% X0% B** (grm cm-^) k (m cal cm - 1 s e c - 1 CT 1) C (m cal cm--*) a (cm2 sec" 1) a (m2 day" 1) SL-1 0-3 3-6 6-9 9-12 12-15 15-18 s i l t s i l t s i l t sandy-silt s i l t s i l t 63.3 46.9 30.0 34.1 35.9 36.7 (6.0) (6.0) (6.0) (6.0) (6.0) (6.0) 1.35 1.38 1.42 1.45 1.49 1.52 8.99 6.98 4.80 5.62 6.21 6.59 681 583 480 520 548 565 0.0132 0.0120 0.0100 0.0108 0.0113 0.0117 0.114 0.104 0.086 0.093 0.098 0.101 SL-9 0-3 3-6 6-9 9-12 12-15 s i l t silt/sand sandy/siIt clayey-silt clayey-silt 39.4 37.7 39.8 33.3 33.7 6.0 6.5 6.0 5.7 5.6 1.35 1.38 1.42 1.45 1.49 5.69 5.66 6.27 5.50 5.85 516 516 545 510 527 0.0110 0.0110 0.0115 0.0108 0.0111 0.095 0.095 0.099 0.093 0.096 SL-10 0-3 3-6 6-9 9-12 12-15 15-18 18-21 21-24 24-27 27-30 clayey-silt s i l t c l a yey-silt sandy-silt sandy-silt silty-sand silty-sand silty-sand sandy-silt s andy-clayey-silt 90.0 40.0 34.0 30.5 32.2 30.6 . 31.8 33.0 33.9 31.0 (6.3) 6.3 (6.3) 6.3 (5.5) 4.9 (5.0) 5.4 (5.5) 6.1 1.35 1.38 1.42 1.45 1.49 1.52 1.55 1.57 1.59 1.61 12.68 5.99 5.40 5.07 5.80 6.73 8.95 8.34 6.92 6.34 857 531 504 490 515 504 523 550 564 548 0.0148 0.0113 0.0107 0.0104 0.0113 0.0134 0.0171 0.0152 0.0123 0.0116 0.128 • 0.098 0.092 0.090 0.098 0.116 0.148 0.131 0.106 0.100 * Grain-size classes are per U.S.D.A. c l a s s i f i c a t i o n . Where only a single class appears this indicates that neither of the other two exceeds 20%. When a class(es) exceeds 20%, but i s not the main one, i t appears as the modifier. ** Values supplied by R.J.E. Brown (pers. comm.) A l l thermal properties pertain to the frozen state 54 apparent, over-all value for oi as input into the models, as opposed to the values calculated above. If an appropriate ground temperature record is available (i.e. observations of T vs. z, for different times), i t is possible to analyse i t , consistent with the above assumptions, and compute the value of oC for which the observations best f i t the theory. It is this apparent, bulk value which would then be used in subsequent analyses. Methods, based on the periodic flow of heat in a homogeneous medium, have been used to infer certain information on ground material properties, from temperature records (e.g. Ingersoll, Zobel and Ingersoll 1954; Carson 1963; van Wijk 1963). The method used here is based on that of Lovering and Goode (1963): The diffusivity of (the ground) controls the wavelength of any heat wave that penetrates the (ground), and the times t i and t2 of measurement of the subsurface-temperature curve determine where the curves will cross at depth for any specific value of c* . The measurement of the half or full wavelength, or of the depth of the crossing point of two subsurface temperature curves, thus provides data for calculating diffusivity. (p.24) The vertical separation of successive crossings of any two curves is always equal to one-half the wavelength (see Figure 10b); i f this can be measured, the diffusivity can be easily calculated. In practice, the small range of actual temperatures at the depths of the second crossing makes its precise determination very difficult (see Figure 10a). An alternative procedure is presented by Lovering and Goode (1963), when two or more temperature-depth curves are available and the times t i and t2 (after t=0) at which they were measured are known. It is thus mandatory to know the date for t=0, i .e . the time in spring when the annual surface temperature wave passes through the mean value. oC is then calculated from, 55 -8 Temperature (°C) -4 -2 Figure 10 EXAMPLES OF T E M P E R A T U R E - D E P T H CURVES USED FOR CALCULATION OF A P P A R E N T DIFFUSIVITY 56 4x2 TT/P 2 , - 1 , cv = c m day (1) [2(t x TT/P + t 2 TT/ P )+nTT]2 where x^ is the depth of the first crossing point, P the period of the wave and n is zero or any integer (Lovering and Goode, p. 42). If the annual temperature cycle is asymmetric, the appropriate half-period should be used. Since the date of t=0 was not accurately known in the present study, a variation of the method was devised. Transposing (1) we have, t.+t. = _\ / f ~ f££ days (2) /a v n l_ Now, i f a tautochrone is also available for some time t^ , we have, t7+t = X c / ^  + nP days (3) J /cv 1 1 2 Subtracting (2) from (3.) leads to, ( xc " X c ) /P .„ (4) t - t = / - days o r > 2 ( xc " X c ) P 2 -1 cv = ; . - m day (5) ( t 3 - t 2 ) 2 " Calculations were carried out on data from two boreholes in different terrain segments, and results are presented in Table 10. The period, P, was taken as 365 days. Only where crossing points could be confidently located were the values used; where tautochrones happen to cross below about 7 m, they do so so obliquely that i t is generally very difficult 2 -1 to fix their crossing point. The overall mean value of 0.063m day 2 -1 compares closely to the value of 0.067 m day calculated by W. G. Brown et al (1964) from their Mackenzie Delta data. The values of a determined in this manner are lower than those Table 9. A possible explanation for this is that latent heat effects 57 Table 10 Calculations for Apparent Diffusivity, using data from boreholes #2-6 and "2-8 Tautochrone Pair (m) Dates Number #2-6 #2-8 18/5/70 + 4/6/70 1 4.90 5.30 18/5 + 15/6. 2 5.15 5.55 18/5 + 12/7 3 5.85 6.25 18/5 + 10/8 4 6.55 6.85 15/6 + 12/7 5 6.50 6.80 15/6 + 10/8 6 7.10 7.40 M t 3 Tautochrone - V By combining #2-6 #2-8 Dates Days Pairs #' s (x' c-x c) am2 day'1 (x' c-x c) 2 am day'1 15/6 - 4/6 11 (2) - (1) 0.25 0 060 0.25 0 060 12/7 - 4/6 38 (3) - CD 0.95 0 073 0.95 0 073 10/8 - 4/6 67 (4) - (1) 1.65 0 070 1.55 0 062 12/7 - 15/6 27 (3) - (2) 0.70 0 078 0.70 0 078 10/8 - 15/6 56 (4) - (2) 1.40 0 073 1 .30 0 062 10/8 - 12/7 29 (4) - (3) 0.70 0 067 0.60 0 050 12/7 - 18/5 55 (5) • (2) 1.35 0 070 1.25 0 060 15/6 - 18/5 28 (5) - (3) 0.65 0 062 0.55 0 045 10/8 - 18/5 84 (6) • (2) 1.95 0 062 1.85 0 056 10/8 - 12/7 29 (6) - (5) 0.60 0 050 0.60 0 050 a = 0.067 a = 0.060 a = to. 008 a = tO.OO'J 58 in the active layer tend to slow down the penetration of isotherms, either during thawing or freezing. Since the above method does not treat these effects ex p l i c i t l y , the reduced rate of penetration is interpreted in terms of a lower diffu s i v i t y . Theory. If the mean surface temperature i s everywhere the same, and is steady with time, the steady mean temperature at any point in the ground i s simply a function of the surface temperature f and the earth's geothermal gradient Gg. If T were below 0°C, permafrost would form and ultimately attain an equilibrium depth, at which the temperature increase due to internal earth heat just offsets the amount by which 0°C exceeds T . (In practice, the equilibrium configuration might not be approached for perhaps thousands of years, depending on the ultimate thickness -see Table 2). An important and intriguing problem, however, both from a sc i e n t i f i c and an engineering viewpoint, is to determine the disturbance of sub-surface temperatures that results when the surface temperature within some f i n i t e region differs from that of the area outside of the region. A solution to this problem for arbitrary-shaped regions (for example, lakes) has been derived by Lachenbruch (1957a) as follows: where T^ is the mean surface temperature within the f i n i t e region. The temperature at any point in the ground is then given by: T(x,y,z,t) = e-(x,y,z,t) + [T(x,y,0,t) + Gg.zJ (7) Here, the f i r s t term represents the sum of the temperature contributions at the common apex of sectors of a circular annulus, of central angle X and inner and outer radii and R^  (Figure 11). The second term represents the normal (undisturbed) temperature profile for the area. 59 Figure 11 METHOD OF DIVIDING A GIVEN S U R F A C E A R E A INTO S E C T O R S OF C IRCLES. For summing the temperatures under the apex of each sector. a) internal location under an area b) external location c) composite areas 60 For a point lying within the f i n i t e region, i s set to zero and ^  i s simply the radius of the body. For t = oo (steady-state) equation (6) reduces to: e (x ,V,z)= (T d -T s ) E 3 6 O \V1+(R,/Z)2 ~ v"l + (R 2/Z) 2/ (8) This is the form used by W. G. Brown et al (1964, p. 150). The basic solution has been employed in more elaborate form in a theory of pingo formation (Mackay 1962). Lachenbruch (1957b) presents an equation suitable for predicting the thermal effect of a strip-shaped disturbance, such as a river, say. Assuming a steady-state condition, the configuration of taliks beneath rivers w i l l depend upon the heat balance of the river, the mean annual ground surface temperature and the geothermal gradient (the.latter two factors determine the "regional" or undisturbed thickness of permafrost). Whether or not the talik penetrates through the permafrost is also related to the width of the river. The time-dependent case also involves consideration of c< and t. For a homogeneous medium, and neglecting the effects of latent heat, an equation describing the thermal disturbance produced by a river, whose temperature is T^, i s : •0(x,z,t) = (T d-T s)|> (pm) - i K ^ - , m)} (9) where the function • ( j . * ) - * . * ( / » . ) + i j f ^ ^ l d , ( 1 0 ) 2 and where m = z /(4at) x = horizontal distance from one side of the strip s = width of strip (river) u = v a r i a b l e of i n t e g r a t i o n (See Lachenbruch 1957b, pp. 1517-1522). Both T^ and f g can be varied ! over discrete time intervals, thus making i t possible to account, in some way, for climatic change, for example. For the steady-state, (10) reduces to: x 'o and (9) becomes simply: (T d - T ) 6(x,z) = " tan 1 (12) Equations (6) and (9) both f a i l to account for the volumetric latent heat, when freezing and thawing are involved. There is no analytical solution to the two-dimensional phase change problem however. The one-dimensional thawing or freezing problem has been treated extensively to the literature (see Muehlbauer and Sunderland 1965); however, there are many problems that are distinctly two- or three-dimensional, and cannot be approximated by a one-dimensional analysis. Equations (6) and (9) do successfully account for the problem geometry, but the neglect of latent heat effects leads to distortion in the shape and rate of penetration of the predicted isotherms. In spite of this i t would s t i l l seem useful to present some calculations based upon these equations, and input values have been chosen that generally cor-respond to conditions occurring in the Mackenzie Delta. In the f i r s t group of examples (Figure 12) computations have been made for the steady-state solution (m=0), for various values of s. The thermal disturbance was calculated from equation (9), and the ground temperature f i e l d from equation (7). It is evident that as the width of the river i s increased, a c r i t i c a l width is reached, beyond which a through-talik w i l l exist beneath the river. As the width is further increased, the proportion of unfrozen ground becomes progressively 62 Horizontal distance (meters) - 1 0 0 - 5 0 0 50 100 Solid lines are 0°C isotherms Figure 12 S T E A D Y - S T A T E P E R M A F R O S T C O N F I G U R A T I O N U N D E R R I V E R S 30, 45, 60, 70, 80 and 100 M E T E R S W I D E 63 Horizontal distance (meters) -100 -50 0 50 1 0 0 1 i i i I 1 1 i i i • • • i • i i • 50 years Figure 13 PERMAFROST REGRESSION, WITH TIME, UNDER A RIVER (100m wide) 64 greater. While the upper surface of permafrost is lowered under the influence of the river, i t is mirrored by a rise in the lower perma-frost surface, since the normal (undisturbed) geothermal effect is augmented by heat flow from the surface source. In Figure 13, results are presented which show the recession of the permafrost table with time, beneath a river 100 m wide, and assuming 2 a thermal diffusivity of 0.060 m /day (a bulk value, believed to be representative of frozen ground in the study area— see p.56). Obviously a higher diffusivity would advance the recession whereas a lower value would slow it down. The computations presented in Figure 13 were made for a river at +4°C, which was assumed to have been instantaneously placed on ground at -4°C, at time-zero. The calculations used for Fig-ures 12 and 13 reveal that in the vicinity of the 100 m wide river, for depths up to 30 m for example, the steady-state configuration is virtually attained within 500 years (deviation of 0 . 1 - 0 . 2 ° C ) . For depths up to 60 m, this takes 750-1000 years. Some further calculations were made to illustrate the effect of lake #2 (Figure 1) on the ground temperatures at site #6-3* at various times after the instantaneous introduction of the lake into the land-scape (Table 11). Equation (6) was used to compute 0 for various values of t,with o(.= 0.06 m day" and 0^-T.J = 7 .4°C; the lake outline was digitised, and al l calculations were carried out by computer. Table 11 shows, for example, that after 500 years, the temperature effect is within, at most, 0.2°C of the steady-state solution; for depths up to about 20 m, this difference is only 0.1°C or less: * S i t e 6-3 i s 40 m from the shore. 65 Table 11 Theoretical Thermal Effect (°C) of Lake #2 on Ground Temperatures at Various Depths at Site #6-3, as a Function of Time Time (years) 50 100 200 300 500 750 1000 Steady-state 5 0. 08 0.12 0.14 0.15 0.17 0.17 0.18 0.20 r—\ e 10 0. 16 0.23 0.28 0.31 0.33 0.35 0.36 0.40 15 0. 23 0.33 0.40 0.44 0.47 0.50 0.51 0.60 ept: 20 0. 27 0.40 0.50 0.54 0.60 0.64 0.66 0.74 Q 25 0. 30 0.45 0.58 0.64 0.70 0.74 0.77 0.87 30 0. 31 0.48 0.64 0.70 0.78 0.83 0.86 0.99 3. Present Application of Heat Conduction Theory. Steady-State Solution. This is the simplest application of the heat conduction model, involving only the geometry of the problem. Use of this solution (equation(8)) implies the following assumptions, in addition to those listed on p.50: i) The mean annual ground surface and water temperatures have not changed over time; i i ) The distribution of land and water has, likewise, not changed. Sample calculations have shown that, for depths up to 30 m, the steady-state configuration is very closely approached within 500 years. Even for this period of time, though, the two above assumptions cannot be con-sidered altogether valid. The second assumption is certainly not valid in the case of the shifting river channel, where quite rapid geomorpho-logical change is taking place. Also, most lakes in the area show some evidence of morphologic change, either by sedimentation, wave action or thermal erosion. In spite of these shortcomings, i t is thought that this 66 simple model might provide a useful first approximation of the ground temperature field. Through the use of equation (8), the total thermal effect, 9, of a l l the water bodies in the area on the ground temperatures at any point, and at any depth, can be assessed. (See also W. G. Brown et al 1964). The predicted temperature for any (x,y,z) can then be determined from equation (6). Lake and river outlines were converted into digital (co-ordinate) form, and a computer program written to calculate the 9 term (see Appendix 2 for a listing). The base map was constructed from the 1967 air photograph, which was-taken during the spring flood. Out-lines of water bodies were then reduced, on the basis of field data, by excluding areas not submerged during the rest of the year. (Use of the outlines straight off the air photograph would lead to some over-estimate of the 9 term). The computer program can accommodate outlines of com-pletely arbitrary shape, and the specified point (x,y,z) can be anywhere, either inside or outside a water body. Distinction was maintained between lakes and rivers; from field data, values of 3 .2° and 4.0°C were taken to be representative of lake- and river-mean annual temperatures. Small lakes known to freeze through in winter were arbitrarily assigned a value of 0°C. Ground surface temperatures were estimated from near-surface measurements. A value for Gg was calculated from the data of W. G. Brown et al (1964), who worked in the Delta just 50 km south-east of the present study area. They computed the 9 term for some (x,y,z), and by knowing al l the other parameters, solved equation (8) for Gg. However, they assumed a water temperature of 33°F ( 0 . 6 ° C ) , which is probably too low; this yielded a value of 3.4°C/100 m for Gg, which is rather high. Their 67 data has been reworked here, using 3.6°C for f w ; this gives an average value of 2.5°C/100 m for Gg. An average temperature gradient of about 2.3°C/100 m has been measured in a deep borehole some 35 km north-west of the study area (Jessop 1970). Although the two sites are certainly different, the deep borehole result is taken as confirmation of the general validity of the 2.5° value. The model was f i r s t applied to boreholes 6-1, 6-2 and 6-3, on the cut bank side of the river. A value for T of -4.2°C for spruce-covered sites was estimated from borehole #2-8. Such sites are the most stable, as indicated by the presence of trees up to 500 years old, and s should be the best suited to the model. Observed and predicted temper-atures are presented in Table 12, and agreement is very close. The slightly larger predicted values for #6-1 are at least partly due to an over-estimate of the river effect—the river has, of course, not been steady in i t s present position for such a long period of time. For each of these boreholes, the total thermal contribution of a l l water bodies i generally on the order of twice as great as the earth's geothermal grad-ient. The thickness of permafrost in the vici n i t y of boreholes 6-2 and 6-3 is estimated at about 65 m, which correlates well with a seismic reflection at 66 m for this locality. Under the influence of the earth* geothermal gradient alone, the 30-meter temperature at #6-3 would be about -3.4°C, and permafrost would be some 170 m thick. On the basis of the close agreement above, temperatures were predicted for other points along this transect. The transect is 300 m long; with points spaced every 10 m, 5 minutes of computer time were required on a Xerox Sigma 9, to compute the ground temperature f i e l d . The output from this program was read directly into a computer mapping 68 Table 12 Observed ( T ^ ) and Predicted (Tp r e) Temperatures, Cut Bank Section Temperature Contribution (°C) Depth (m) Lakes Rivers Gg Total T pre ^obs 6 0.07 1.22 0.15 1.44 -2.8 -2.8 9 0.10 1.64 0.23 1.97 -2.2 -2.4 12 0.14 1.95 0.30 2.39 -1.8 -2.0 15 0.17 2.16 0.38 2.71 -1.5 -1.7 20 0.24 2.38 0.50 3.12 -1.1 -1.4 25 0.29. 2.49 0.63 3.43 -0.8 -30 0.34 2.57 0.75 3.66 -0.5 -40 0.44 2.59 1.00 4.03 -0.2 -50 0.54 2.54 1.25 4.33 +0.1 -6 0.11 0.25 0.15 0.51 -3.7 -3.6 9 0.16 0.36 0.23 0.75 -3.4 -3.3 12 0.23 0.48 0.30 1.01 -3.2 -3.0 15 0.29 0.61 0.38 1.28 -2.9 -2.7 20 0.36 0.76 0.50 1.62 -2.6 -2.4 25 0.45 0.91 0.63 1.99 -2.2 -2.1 30 0.52 1.05 0.75 2.32 -1.9 -1.8 40 0.67 1.26 1.00 2.93 -1.3 -50 0.79 1.40 1.25 3.44 -0.8 -60 0.90 1.51 1.50 3.91 -0.3 -70 1.00 1.61 1.75 4.36 +0.2 -6 0.25 0.12 0.15 0.52 -3.7 -3.8 9 0.37 0.17 0.23 0.77 -3.4 -3.5 12 0.48 0.23 0.30 0.01 -3.2 -3.2 15 0.67 0.29 0.38 1.34 -2.9 -2.9 20 0.75 0.39 0.50 1.64 -2.6 -2.5 25 0.89 0.47 0.63 1.99 -2.2 -2.2 30 1.01 0.55 0.75 2.31 -1.9 -1.9 40 1.19 0.71 1.00 2.90 -1.3 -50 1.31 0.84 1.25 3.40 -0.8 -60 1.39 0.95 1.50 3.84 -0.3 -70 1.46 1.03 1.75 4.24 0.0 -Mean annual surface temperature = 4.2°C For lakes, therefore, (Tj - T g) = 7.4°C For rivers, (T, - T ) = 8.2°C d s 6 9 program (SYMAP), which then generated maps of ground isotherms (Figure 1 4 ) . Permafrost plunges steeply at the lake shore, and a through-talik exists beneath the lake, as indicated by increasing temperatures beyond a depth of 60 m. The temperatures under the lake are remarkably uniform, with a variation from 3.2°C at the surface to only 3.6°C at a depth of 70 m. These results are consistent with the findings of W. G. Brown, et al (1964). The thawing effect of the lake is confined to the ground lying beneath i t ; permafrost is present, though much thinner, even beneath the narrow peninsula. The thermal effect of the lake extends into the sur-rounding area; at site #6-3 (40 m away from the shore), for example, the 30-meter temperature is 0.9°C warmer because of the lake. Even at site #6-1 (110 m away), there is a warming effect of 0.3°C produced at a depth of 30 m. The same method was applied to sites on the other side of the river, but, as expected, agreement was less satisfactory. In a l l cases, the predicted temperatures were too cold, and permafrost thicknesses were thus over-estimated (Table 13). At site #2-6, for example, the observed temperature gradient is 0.12°C/m, whereas the predicted rate is only 0.06°C/m. A major thermal contribution is thus being under-estimated by the model. Agreement is "best" close to the river; for example, at site #6-5, the observed and predicted 20-meter temperatures are 0.7°C and 0 .0 °C. The further from the river, the worse the results; at site #6-12, the observed and predicted 30-meter temperatures are 0.3°C and-1.5°C, and at #6-14, 0.0°C and -2 .3 °C . This model is based on the assumption that the conditions at present have existed unchanged for a very long period of time, but i t is known that sites in the lee of river migration have become progressively colder with time. Thus, at site #6-12 T has not 70 a) Ground Temperatures b) Pormalrott Figure 14 GROUND TEMPERATURES AND PERMAFROST DISTRIBUTION ALONG A CUT BANK TRANSECT (SYMAP) 71 always been as cold as the -2.6°C used here; rather, in the recent past i t was warmer than i t now is (see Figure 16). The ongoing cooling trend is illustrated in the shape of the temperature-depth curve (compare Figures 4 and 5). Having once established the appropriate values of mean annual lake, river and ground surface temperatures and the geothermal gradient, the entire mean annual ground temperature regime can be calculated using equations (7) and (8). For stable sites such predictions should be quite accurate. As a final application of this model, mean temperatures have been calculated under a traverse through a stable area, for which no ground temperatures are available (see Figure 1). The calculated annual isotherms are shown in Figure 15. A value of -4.2°C was used for the ground surface temperature, 3.2°C for both the lakes and 4.0°C for the river. The maximum permafrost thickness along the traverse is 95 m; the maximum thickness in the vicinity of the traverse is 102 m. These values are in excellent agreement with the data of Johnston and Brown (1964). Permafrost beneath the isthmus reaches only to 60 m. The permafrost shows the characteristically steep plunge at the edge of the river and lake #3. Under the small lake, however, although the boundary plunges in i t ia l ly , the thermal effect here is great enough only to form an "hour-glass shaped" talik. The upper permafrost surface is much depressed, while the lower one is raised up (see also the 0.5°C isotherm), with only a narrow chimney actually penetrating the permafrost. If lake #3 was not so close, there would be no through-talik beneath the small lake; the temperature at 50 and 60 m is only 0 .1 °C. Hand borings to depths of 1.8 to 3.4 m, made from the ice surface in a small lake nearby (lake #4), in February 73 1968 (C. P. Lewis and D. G i l l , pers. comm.), indicate that the permafrost boundary falls away steeply at the shoreline. Transient-State: Simple Model. When the steady-state model was applied to sites on the slip-off slope side of the river, agreement was not very satisfactory. As previously mentioned though, since the river is undergoing lateral migration, i t was, in the somewhat recent past, much closer to such boreholes than it is now. The steady-state model thus under-estimates the river thermal effect. A correction for the transient term was attempted. This was done first using a simple step-function model, using data from transect 2. This simple transient model was subsequently refined, and applied to conditions along transect 6. The back of the slip-off slope is marked by a fossil cut bank (Plate 3). Assuming that this delineates some " i n i t i a l " position of the channel, the steady-state temperature effect was computed for the channel occupying this position, using equation (9) with m = 0 (t = ° ° ) . For site #2-6 (T = -3 .0 °C , T, -T = 4.0 -(-3.0) = 7.0°C) this works out to s d s be 1.26°C at a depth of 15 m (x = 22 m, from the fossil cut bank); with this contribution the predicted temperature is then -1 .1 °C , which is in fact 0.5°C warmer than that now observed (Table 13). In other words, since the river began to shift, the ground at this location has undergone about 0.5°C of cooling, according to these calculations. As a first approximation, the channel can be assumed to have shifted to its present position (a distance of 75 m) in a single step, some time t^ years ago, being "replaced" by a bar 75 m wide. Surface conditions on the bar are not homogeneous, and the mean temperature varies spatially from near 0°C to about -1 .5 °C . A weighted overall mean of -0.5°C is used here. The problem, then, is to calculate how long ago a step-change 74 2-6 ( V - 3 2-8 Table 13 Observed and Predicted Temperatures, with Transient C o r r e c t i o n , f o r Boreholes on a S l i p - O f f Slope TEMPERATURE CONTRIBUTION (°C) Depth (m) 2-S (f s =-3.0°C) ,0°C) .2°C) Gg S h i f t i n g Channel* ( i ) ( i i ) ( i i i ) Total Other Rivers T o t a l pre obs S h i f t i n g Channel** (1) (2) (3) 1 + 2 + 3 (4) 3 0 .08 +2 .15 -1 .31 • 0 .01 *0.85 0 .04 0. ,97 -2 .0 -1, .8 0.06 6 0 .15 +2 .71 -1 .59 +0 .02 + 1.14 0, .09 1, ,38 -1 .6 -1 .6 0.12 9 0 .23 + 2 .90 -1 .65 +0 .03 + 1.28 0, .13 1. 64 -1 .4 -1. .3 0.18 12 0 .30 + 2 .98 -1. .64 + 0, 04 + 1 .38 0. . 18 1. 86 -1 .1 -1, .0 0.24 15 0 .38 + 3 .01 -1, .59 • 0 .05 + 1.47 0 .23 2. .08 -0 .9 -0 .8 0.30 20 0 .50 + 3 .02 -1, .49 • 0. .06 + 1.59 0, .31 2. 40 -0 .6 -• 0.40 30 0 .75 + 2 .96 -1, .26 +0 .08 + 1. 78 0. .45 2. ,98 0 .0 -- 0.57 3 0 .08 +0 .30 -0, .13 +0, .00 +0.17 0 .05 0. ,30 -2 .7 -2. .8 0.05 6 0, .15 +0 .58 -0. ,26 + 0 .01 + 0.33 0, ,11 0. ,59 -2 .4 -2, .5 0.09 9 0, .23 +0. .84 -0, .37 +0. .01 +0.48 0, .17 0. 88 -2, . 1 -2. .2 0.14 12 0. .30 + 1. ,06 -0, ,46 + 0, .02 • 0.62 0. ,22 1. 14 -1, .9 -1. .9 0.18 15 0. .38 + 1. .26 -0, .52 +0, .02 +0.76 0, ,29 1. 43 -1 .6 -1, .6 0.23 20 0. 50 + 1. ,51 -0, ,60 • 0, ,03 +0.94 0. .37 1. 81 -1, .2 -• 0.30 30 0. .75 + 1. ,84 -0. ,64 +0, ,04 + 1.24 0. ,55 2. 54 -0, .5 -- 0.43 40 1. .00 +2. ,00 -0. ,59 + 0. ,04 + 1.45 0. ,70 3. 15 0, .2 -- 0.56 3 0. .08 + 0. .06 -0, .00 0, .00 +0.06 0. .17 0. 31 -3. .9 -4. .0 0.02 6 0. 15 +0. 11 -0. ,01 0. ,00 +0.10 0. ,34 0. 59 -3, .6 -3. .7 0.05 9 0. 23 + 0. 16 -0. .01 0. ,00 +0.15 0. 51 0. 89 -3. ,3 -3. .3 0.07 12 0. 30 + 0. .22 -0. ,01 0, .00 +0.21 0. ,66 1. 17 -3. .0 -2. .8 0.09 15 0. 38 + 0. 27 -0. ,02 0. ,00 +0.25 0. .83 1. 46 -2. 7 -2. ,5 0.12 20 0. 50 +0. 35 -0. 02 0. ,00 +0.33 1. 05 1. 88 -2. .3 -- 0.16 30 0. 75 +0. SI -0. ,03 0, .00 +0.48 1. .42 2. 65 -1, .5 -- 0.24 40 1. 00 +0. 66 -0. ,03 0, ,00 +0.63 1. 70 3. 33 -0, .9 -- 0.32 50 1. 25 + 0. 79 -0, 03 0. ,00 +0.76 1. 89 3. 90 -0, .3 -- 0.39 60 1. SO +0. 90 -0. ,03 0, ,00 +0.87 2. ,02 4. 39 0. .2 -- 0.46 3 0. .08 • 4. .27 -4, .20 0, .03 + 0.10 0, .03 0.21 -0. .3 -0.0 0. .06 6 0. .15 +4. ,07 -3, .90 0. .05 + 0.22 0, .05 0.42 -0. 1 -0.0 o. . 13 9 0. .23 + 3. ,87 -3, .61 0. ,07 +0.33 0. ,07 0.63 0. 1 -0.1 0. . 19 12 0. .30 + 3, .69 -3, .35 0, .10 + 0.44 0. .10 0.84 0. ,3 -0.2 0, .25 15 0. ,38 + 3. 51 -3, .10 0, ,12 +0.53 0. .12 1.03 0. ,5 -0.2 0, .31 20 0. .50 + 3. ,27 -2. ,72 0. ,15 + 0.70 0. 15 1.35 0. ,9 - - 0. .41 30 0. .75 +2. 88 -2. ,10 0. ,19 + 0.97 0. 23 1.95 1. ,5 - - 0. .55 * This i s the channel c o n t r i b u t i o n , with the t r a n s i e n t c o r r e c t i o n : ( i ) = steady-state c o n t r i b u t i o n form the channel i n i t s former p o s i t i o n ( i i ) = the recovery i n temperature due to the presence of the r i v e r bar ( t j assumed = 100 years) ( i i i ) = the c o n t r i b u t i o n from the channel i n i t s present p o s i t i o n ( f o r t j = 100 years) * This represents the steady-state c o n t r i b u t i o n from the channel i n i t s present p o s i t i o n , and was the value used i n the steady-state model. Comparison of values under (2) and (4) i n d i c a t e the e r r o r involved i n the steady-state mode 1. 75 would have had to occur to produce the observed recovery of temperature at site #2-6. Equation (9) was solved for t^, with the bar replacing the river as the strip-shaped disturbance. Thus, - f = -4.5°C (the bar is 4.5°C colder than the river which i t replaced); s = 75 m; 0 = 0 .5 °C; x = 22 m, and z = 15 m. Now, i f a state of equilibrium is dis-c turbed, the rate at which a new equilibrium is established is controlled 2 -1 by the thermal diffusivity of the ground. With a = 0.05 m day (a value somewhat lower than that for frozen ground, since the area of the bar was ini t ia l ly unfrozen, when beneath the river), t^ turns out to be 110 years; with a = 0.06, is 93 years. Measurements from aerial photographs taken in 1935, 1950 and 1967 indicate that the cut bank opposite retreated about 35 m during these 32 years, i .e . 1.1 m year Between 1935 and 1950,the retreat was about 17 m, and between 1950 and 1967, about 18 m. Measurements over nearly three summers (1969-1971) from some 40 stakes along the cut bank section opposite transect #2, give an average retreat of about 2.2 m (s.d.=-0.9 m). Consequently, a "predicted" retreat of 75 m in something like 100 years certainly seems to be realistic. One final contribution to the ground temperature has to be con-sidered, that due to the channel occupying its present position for about the past 100 years. This is calculated from equation (9) with t = 100 years, f d - T = 7.0°C, and s = 160 m (width of river). For site #2-6, x = (22+75) = 97 m, and 9 is found to be very small for a l l z (Table 13). This i s , in fact, why this borehole was used to solve for t, through equation (9); the problem was then able to be considered simply as a non-linear equation with one unknown. 2 Since the field observation period does not span 3 full ice-free seasons, but only about 2h, the current average rate of retreat is possibly closer to 2.2/2.5, or about 0.9 m year~^~ . The transient correction was applied to the other boreholes along transect #2; equation (9) was solved for 9, for specified (x,z)'s, using 2 - 1 0.06 m day , t = 93 years, and with values for s and T^ as used above. There was a resultant improvement in agreement between observed and predicted values, over that of the steady-state model (Table 13). However, for the borehole actually on the bar itself , #2-4, the predicted temperature pattern does not adequately resemble that observed. The surface temperature of such sites has undergone marked changes during the period of river migration* subsequent vegetation succession and snowbank migration. Thus, the use of a constant T for any particular site does not simulate its thermal history realistically. Transient-state: Refined Model. In reality the river migration is a continuous process. An attempt is now made to approach the real situation more closely than did the preceding simple method, by treating the migration as a series of small, finite steps. From the viewpoint of the thermal history, the migration of the channel can be simulated as a temperature-wave disturbance travelling 3 across the surface (Figure 16). This wave is not symmetrical, however, since the aggrading surface in the rear of the wave is subject to a sequential development of surface conditions--i.e. the succession of vegetation. The shape and amplitude of the wave was formed according to measured ground temperature data, as shown in Figure 16. The wave is moved across the surface, from some in i t ia l position to its present position, at a rate, v, thought to approximate the average rate of shift over a long period of time (400-500 years). The in i t ia l position was taken as the older of two fossil cut banks (see Plate 3); between this and the present position is another cut bank, indicating that the 3 This specific view of the problem arose out of discussion with C. T. Hwang. 77 Lake 2 © © © River © © (13) (15) Temperature boreholes Transect 6 (jl) Lake 3 0 meters 100 i i I =•7 Present position shift t = 0 (x, s) Shoreline moves from x = ««> to x - x, at t - 0 Diagrammatic example of river shifting in equal steps of s Figure 16 T E M P E R A T U R E WAVE SIMULATING RIVER SHIFTING 78 shifting has not been monotonic. There has been an average rate of s h i f t -ing of about 1.1 m year -* over the past 30 years. It was decided to use a lower, "apparent" rate of shift in the model, however, which would in -corporate some unknown lag time involved in the formation of the second cut bank, thereby hopefully reducing the shifting process to an equiv- . alent monotonic form. If the river is assumed to have been shifting at a constant rate of 0.5 m year the time between the i n i t i a l and present positions would be 460 years. The thermal history could, for example, be computed on the basis of 10-meter steps, i.e. corresponding to 20-year intervals. In order to reproduce the thermal history mathematically, assump-tions have to be made regarding the thermal regime which existed when the channel was in i t s i n i t i a l position. The i n i t i a l condition for this model was taken to be the steady-state solution with the channel in i t s i n i t i a l position, prior to migration. Lachenbruch (1957b, p. 1521) gives an equation for 9 in the case of an ocean which has transgressed, or regressed, by a number of stages of movement. For a shifting river, i f 3 stages C t Q (=0), tx , t 2 ) are involved for example (see Figure 16), the equation would be, (13) 79 2 Here, the notation m(t-tp means the value of m=z /4a t for t=(t-t^), etc. The movement from x=°°to x=x^ at time t Q(=0) is counted as stage 1. In equation (13), the f i r s t group of 3 terms represents the warming in -fluence of the river (i.e. permafrost degradation), whereas the second group of 2 terms accounts for the thermal recovery behind the migrating river (i.e. permafrost aggradation). Latent heat effects are ignored. Now, i f n stages of movement are involved, equation (13) becomes, 6(x,z,t) = ( t d - f s ) j [ < ( i r i Mt^- i>{ V .mct ^ j - (vvj[H~ 'm(t-t1)) - * v ~ — .-ct-vjj + X [ * ( ^ ^ c t - t . ) ) - ^ ( ^ ^ jm(t-t.))J for t>t (14) n-i v ' Equation (13) assumes that f i s the same before and after the river has passed by. Now, as already mentioned, this i s not the case. However, this can be handled in the same way as for a climatic change--viz. i f ( T d - f s ) = for t < t j , and some new ( f d - f g ) = A 2 for t ^ t j , the result, for a stationary strip i s , 6(x,z,t) = kx ,m(t))- </> (^~- ,m(t)jj for t>t, ( 1 5 ) l (see Lachenbruch 1957b, p. 1521). Further, one can see that i f details of some climatic change are also known, this can be easily incorporated. Finally, the effect of a number of stages of shoreline movement, combined with that of a number of surface temperature changes, can be 80 obtained by combining equations (14) and (15) . The second group of terms in (14) is expanded to incorporate the effects of a varying f . A com-puter program was written to handle the solution (see Appendix 3 for a listing). Some of these solutions will now be discussed. The case with v = 0.5 m year * will serve to illustrate some of the computational details. The total extent of the wave is 350 m; 230 m is the distance the river has shifted, and this has taken 460 years. Thus, there is a total of 35 10-meter strips to represent the wave (Figure 17). The strip between 230 to 220 m corresponds to a surface temperature drop of 4 .0 °C ; from 220 back to 190 m, each strip corresponds to (1.2/3) = 0 .4 °C; and from 190 back to 0 m, each 10 m spans a temper-ature drop of (3.0/19) = 0.16°C (Figure 17). The problem consists of evaluating the temperature effect of each of these 10-meter strips at al l (x,z)'s in the cross-sectional space, using the appropriate values of f s and t. As an example, the thermal history of the strip between 140 and 150 m is indicated in Figure 17--remember that 10 m corresponds to 20 years, for v = 0.5 m year * . For the first 60 years, f = -4 .2 °C , as the river approaches; for the next 240 years, T = 4 .0 °C, as the river wave "passes by". Thereafter, the surface temperature declines, in 20-year steps, to the present -1 .8 °C ; in this way, the changing thermal regime related to the vegetation succession is accounted for. The present temperature field reflects the sum total of a l l these stages. The pro-cedure is repeated for a l l the strips. Before the predicted temperatures can be compared to observed values, one final effect has to be included—that of the snowbank zone on the slip-off slope (see p.46). This can be incorporated as a minor wave following the river disturbance, with the same speed v (Figure 17). F i g u r e 1 7 DIAGRAM TO ILLUSTRATE SAMPLE SOLUTION OF TRANSIENT MODEL 00 82 The shape of this wave was formed in accordance with temperature measure-ments from snowbank profile #6 (see Figure 3); its amplitude is about 1.0°C, and surface temperatures in this zone are close to 0°C. Figure 18b presents the computed present-day permafrost config-uration in the vicinity of the migrating river, using v = 0.5 m year * 2 - 1 2 - 1 and oc = 21.9 m year (0.06 m day ). Observed and predicted temper-atures are shown for the borehole locations. The in i t ia l condition, prior to migration, is also shown partly (Figure 18a). The final computed temperatures also reflect the addition of the thermal contribution of a l l other water bodies in the area. The overall pattern computed by the model is generally consistent with the observed configuration; i t is also similar to that described in other field studies (see Pewe' 1965, J. R. Williams 1970). Some of the details of the solution, however, are not perfect. The permafrost history can be described in general terms as follows. In the in i t i a l position, a curtain-shaped through-talik exists beneath the river, with the permafrost boundaries plunging steeply down-wards. As the river migrates across the land surface, this causes the talik to migrate also. In Figure 18b, the isotherms beneath the river and in the lee of its migration slant away from the surface. This is due to the lag, with depth, in the penetration of the temperature dis-turbance, as i t moves across the surface. The lag in talik formation is shown by the bulge in the isotherms beneath the cut bank (cf. the perma-frost boundaries in Figure 18a). One notes a remarkable uniformity of temperature, at depth, beneath the river itself . Following the river disturbance, surface temperatures on the slip-off slope gradually decrease, and permafrost "wedges" back in again. This configuration is 83 Figure 18 PERMAFROST HISTORY UNDER A SHIFTING CHANNEL 84 a function of the decreasing surface temperatures away from the river, and the lag in the temperature recovery following disturbance. Temper-atures on the cut bank side of the river are colder than those under the slip-off slope. On the cut bank side, agreement between observed and predicted values is very close; the maximum deviation is 0 .4 °C , and agreement is typically within 0 . 1 ° to 0 .3 °C. The predicted values are generally slightly colder, except close to the river itself . Deviations (T , -T ) 6 ' ' r v obs pre' increase negatively with depth, and the predicted permafrost thickness of 80-90 m compares to the 60-70 m value of the steady-state model (p.68). On the slip-off slope side, the thermal regime is again quite faithfully reproduced, in the zone within 100 m of the river. Here, agree-ment is typically within 0 . 2 ° to 0 .5 °C, with predicted values generally colder and permafrost thicknesses overestimated. At site #6-5, for ex-ample, the predicted thickness of 13 m compares to the measured value of 10 m. With the snowbank effect included, a zone of permafrost degrada-tion is produced under the slip-off slope (shown in detail in Figure 19), which is very similar to that observed in the field (see Figure 7). In this vicinity the overall pattern of isotherms is disrupted, with deeper, warmer isotherms being drawn up towards the surface. This is the charac-teristic configuration around a talik (cf. the isotherms beneath the river in Figure 18b). As the distance from the river increases, however, the agreement progressively deteriorates with deviations becoming greater than -1°C. At #6-12, for example, about 140 m from the river, the dev-iations range up to -1 .4 °C , and the predicted thickness of 50 m compares to the measured value of 22.5 m. It is in this zone that the model is least satisfactory. Figure 19 PREDICTED MEAN ANNUAL GROUND TEMPERATURES IN THE VICINITY OF THE SNOWBANK ZONE, SLIP-OFF S L O P E 00 tn 86 What could account for the errors apparent in the model? Agree-ment is good in surface layers, with deviations becoming larger at depth. It is unlikely, therefore, that the present surface boundary conditions are much in error, but there is the unknown factor of climatic change. It is possible that the value for Gg might be too small, although this error is unlikely to be large. For example, though, i f i t were to be 3°C/100 m (a somewhat high value), this would only partly offset the trend of larger negative deviations with depth. It is possible that some aspect(s) of the migration history has not been adequately reproduced in the model. This is a complex problem and cannot be readily evaluated. If the river did pause at some stage, however, this would presumably cause warmer temperatures in that vicinity. The probable explanation of the errors, though, is the exclusion of the latent heat term in the present solution. If i t were included, temperatures beneath the slip-off slope would not adjust so quickly to the surface cooling, and would therefore be warmer. To illustrate the effects of the latent heat term, some sample calculations have been made, for the case of one-dimensional freezing, using one solution which ignores this term (see Ingersoll et al 1954, Ch. 7) and one which includes i t (Neumann's Solution). Details of the problem are shown in Table 14, together with the respective solutions for the depth of freezing and temperatures at 20 and 40 m. The penetra-tion of the freezing isotherm is greatly retarded in the second solution, and ground temperatures are consequently warmer. It is to be assumed, therefore, that inclusion of latent heat in the equations would improve the predicted values. This is a complex mathematical problem however. Finally, mention should be made of the possibility of heat trans-fer by groundwater flow along taliks. This could conceivably involve a considerable amount of heat. Table 14 Sample Calculations to Illustrate Effects of Latent Heat Term on Depth of Freezing and Ground Temperature Calculations Input Data Solution (1) For a homogeneous medium, = erf Soil Water content Organic content Dry density I n i t i a l (uniform) temperature T Q Step change at surface T s Time since step change t Solution (2) = sandy-silt_ = 0.40 gm gm_ = 0.05 gm gm_ = 1.42 gm cm = 4.0°C = -3.0°C = 50 years For the depth of freezing, set T and solve for z. 0°C, For T , input z and solve. The equations were solved for values of a of 0.0046 cm2 s e c - 1 (0.04 m2 day - 1), 0.0058 (0.05), and 0.0069 (0.06). Results z, depth of freezing T at z = 20 m T at z = 40 m Depth of freezing z = aVt~, where a i s a constant which is the root of the transcendental equation, exp(-a'/4au) erf (a/2 v/TTTj) j o h. Jll T a exp(-a'/4af) erfc(a/2/5TT) C u T s The subscripts f and u refer to frozen and unfrozen; L i s the volumetric latent heat, a l l other variables are as previously defined. The equation was solved via an iterative procedure. Input values (all c.g.s.): k f = 0.00627 C f = 0.545 af = 0.0115 k u = 0.00306 C u = 0.799 a u = 0.00383 a=0.04 21.6m -0.2°C +1.9°C L = 45.2 (assume a l l water freezes at 0 C) Solution (1) Solution (2) 10.3 m +1.1°C +2.7°C 0.05 24.2 -0.5 +1.6 0.06 26.5 -0.7 + 1.2 88 The thermal effect of the river on the surrounding ground temperatures depends not only on the strength of the source, but also upon the length of time available to the thermal processes. The latter is a function of the rate of migration. The effect of varying the speed of migration is illustrated in Figure 20. As v is increased to 1 m year \ temperatures on the cut bank side (point #400) tend to be just slightly cooler, while those under the slip-off slope (point #100) are a l i t t le warmer. For slower migration rates, the river will have been in close proximity to the present cut bank for a longer period, and thus the warming effect will be consequently greater. For the slip-off slope, faster migration rates will mean there has been less time for temperature recovery (i.e. cooling). The ground around the river shows the greatest effects of a changing v (point #'s 220, 300, 360). If the river migrates more rapidly, there is less time for the warming wave to penetrate to depth. Because of the increasing lag in penetration with depth, the effects of varying v are more pronounced at greater depths (cf. Table 2). In a model using a constant rate of migration, a value of about 0.5 m year 1 gives the best overall results. There seems to be no way to establish the plausibility of this overall value, using vegetation data at least. Further field information is necessary to date certain feat-ures, which might provide more information about the actual migration history. 4. Summary In spite of the few larger deviations between observed and pre-dicted temperatures, the results obtained from the models are interpreted as confirmation of the general validity of the hypotheses developed in the present study. Any models, however, can only be ultimately confirmed Figure20 EFFECT OF RIVER SHIFTING RATE ON MAGNITUDE OF THERMAL DISTURBANCE 90 by obtaining data from greater depths (60-80 m). Mean annual surface temperatures, including those for water bodies, are important input parameters in these models. Once their values are established, they can be used together with a knowledge of the geothermal gradient, to calculate the ground temperature field from the equations presented. In view of the results obtained for the stable (spruce-covered) sites, i t is concluded that the boundary values used must be fairly representative. Apart from the good agreement between observed and predicted temperatures per se, the temperature gradients at each bore-hole location also agree well. Observed temperature gradients are about three times greater than provided for by Gg alone; tempera-ture gradients induced by the water bodies in the area have been shown to account for the difference. For the spruce-covered site close to the shifting channel (#6-1), use of the steady-state model did not appear to introduce any large errors. For sites where surface boundary conditions have obviously been changing, the steady-state model is not satisfactory. A quite simple, single-step transient model was shown, however, to produce very reasonable results. A fossil cut bank was taken as delineating an ini t ia l position. The rate of channel shift "suggested" by this model is close to the actual rate deduced from aerial photographs (1935-1967). Prediction of the thermal regime beneath the bar itself was improved upon using a refined model. The use of a temperature wave to simulate changing thermal conditions associated with the channel migration permitted a more realistic simulation, and produced generally satisfactory results. Beneath the bar, the predicted regime duplicated the observed pattern well; inclusion of the thermal wave associated with snowbank migration indeed produced a zone of permafrost degradation as observed in the field. The errors in the model, at boreholes distant from the channel, are believed to be due to the failure to include the latent heat term in the equations. Al l the calculations carried out indicate that through-taliks exist beneath the channel and the larger lakes. Chapter 5 VARIATIONS IN MICROCLIMATE 1. Introduction In Chapter 4, the variations in surface temperature regime were considered simply as prescribed boundary conditions. Now, these variations are described, as they relate to variations in microclimate; these derive from differences in site characteristics. Ground temperature observations in the layer above the depth of zero annual amplitude show that significant differences in thermal regime exist under various types of vegetation. The mean annual sur-face temperature varies from near 0°C to -4 ° or -4.5°C over the study area, whereas the mean annual air temperature at Aklavik is -9.1°C (1931-1960). This shows that caution should be used in estimating permafrost temperatures on the basis of air temperature data. There is a general decrease in ground temperatures with in-creasing biomass. Vegetation has a direct influence on permafrost by determining the quantity of heat that enters and leaves the ground. The effects of aerial climate on ground climate are conditioned by • the nature of the surface boundary conditions, since the latter determine the magnitude of the individual component processes of the surface energy regime. As vegetation develops, as in a successional sequence for example, i t has a changing effect on the conditions of heat and moisture exchange between the air and the ground. However, because of the complex interaction between vegetation, terrain and 92 93 microclimate, i t is sometimes d i f f i c u l t to resolve the effects of vegetation per se. The interactions between vegetation and perma-frost have been variously studied (see for example, Benninghoff 1952, 1966; Drury 1956; Tyrtikov 1963; R.J.E. Brown 1965, 1966; Running 1969; Viereck 1970; G i l l 1971). Various terrain segments have been identified in the study area, and although there are variations in thermal regime within each segment, the differences between segments are more significant. This is demonstrated by an analysis of variance conducted on active layer depths (Table 15). The results indicate that the units do indeed have some meaning in terms of variations in thermal regime, since active layer development represents the integrated effects of both summer and winter regimes. Brief descriptions of five sites used in most of the micro-climatic studies (between-site and around-site scales) are given in Table 16; four of the. sites are shown in Plate 5. The following discussion is organised into three sections: differences in annual thermal regime, variations in summer micro-climate (including active layer regime), and winter differences. 2. Annual Thermal Regime Ground temperature observations were carried our irregularly over the study period (1969-1971), being concentrated in the summer months. Regular, intermediate temperature values have been estimated for each site using Fourier synthesis. The observed values for each depth were fi t t e d to a compound Fourier series using UBC FCF*, the procedure continuing until the average residual (JQ^S - T p r e ) w a s This program permits Fourier curve f i t t i n g on unequally-space data points. 94 Table 15 Analysis of Variance - Active Layer Depths in the Five Terrain Segments (July 1970) SOURCE OF VARIATION DEGREE OF FREEDOM SUM OF SQUARES MEAN SQUARE F Active layer depths 4 136926.133 34231.533 1404.771** Error 145 3533.367 24.368 Total 149 140459.500 ** Exceeds the five percent level of significance Mean Active Layer Depths in Five Terrain Segments Ranked and Differentiated by the Newman-Keuls Test SITE MEAN ACTIVE LAYER DEPTH (cms) NUMBER OF MEASUREMENTS 5: Picea 30.8 30 4: Salix-Alnus 62.6 30 3: Salix(2) 99.2 30 2: Salix(l) 103.3 30 1: Bare ground 110.6 30 A l l differences are significant at the five percent level 95 T a b l e 16 C h a r a c t e r i s t i c s o f F i v e M i c r o c l i m a t i c S i t e s Site Vegetation Soil Bare ground-Equisetum (Frequently submerged in summer) E q . f l u v i a t i l e (about 10% cover*) 0-10cm: S a n d y - s i l t , k«=0.0017** 10-2Scm: S i l t y - s a n d , k«0.0024 S a l i x (1) (Rarely inundated i n summer) Dense growth of S.alaxensis (av. diameter 1-1.5cm, av. height 1.5-1.8m). Abundant ground cover of Eq.arvense*. 0-10cm: S a n d y - s i l t , k=0.0012 10-25cm: S a n d y - s i l t , k=0.0012 Salix( 2 ) (Usually flooded only i n spring) More scattered growth of S.alax- ensis (av. diameter 4-6cm, av. height 3-4m). More dense ground cover o f Eq.arvense, and other spp.* 0-10cm: S i l t , k-0.0014 10-25cm: S i l t , k=0.0015 4. Salix-Alnus (Only o c c a s i o n a l l y inundated, by spring flood) Dense growth of S a l i x spp. and Alnus c r i s p a * . up to 2.5-3m high. Ground cover o f Rubus a r c t i c u s , Pyrola g r a n d i f l o r a , and feather mosses (Prepano~ cladus uncinatus, Tomenthypnum n i t e n s ) * 0-10cm: Moss and peat, with 2-3cm of s i l t , k=0.0001-0.0006 10-25cm: Mainly s i l t , k=0.0023 S, Picea (Rarely inundated by spring flood) Mature canopy of P.glauca, up to 20m high, with a dense under-st o r y of Alnus c r i s p a and S a l i x spp. Ground cover s i m i l a r to (4), but a l s o Hylocomium splendens*. 0-10cm: Moss and peat, k=0.0001-0.0006 10-25cm: S i l t with organic l a y e r s , k=0.0009 * See G i l l (1971) * These are sample values o n l y , and are estimates based on the p r e v a i l i n g s o i l moisture conditions at the time of sampling. * Estimated from R.J.E.Brown and G.P.Williams (1972) d) Picea 97 reduced below 0.1°C. (This was generally not possible for the 50 cm depth, where the average residual was about 0 .3 °C) . For depths greater than 1.5 m, the average residual was usually less than 0.05°C. No attempt has been made to place any interpretation on the fitted series. Once a f i t had been satisfactorily achieved, intermediate values were generated. The predicted temperature regime is confined by the phase and amplitude characteristics in the field observations, and some departures from reality have probably been introduced for the upper 1.5 m. Temperature data are listed in Appendix 4. As the annual surface temperature wave passes through the ground, its amplitude diminishes and its phase is progressively re-tarded. Measurable (0.1°C) seasonal temperature fluctuations extend down to about 12 m at the study sites. This depth of zero annual amplitude is related to the ground thermal properties and the surface amplitude. In the following discussion the ground layer down to 12 m will be considered. Significant differences in annual ground temperature patterns occur among the five sites; minor differences at each site occurred between the two years, as a result of macroclimatic variations. For each of the five sites, ground temperatures for the period September 1969 to April 1971, at depths down to 12 m, are shown by isotherms in Figure 21. Air temperature and snow cover data for Inuvik are also shown. In summer, ground temperatures follow the trend of air temperatures quite closely, but in winter the correlation is much weaker. It seems that snow cover must be primarily respon-sible for maintaining ground surface temperatures 5° to 10°C warmer than the average air temperature. In fact, ground temperatures during the second winter were everywhere warmer than in 1969-1970, even though Figure 21 GROUND TEMPERATURE ISOTHERMS AT FIVE MICRO-CLIMATIC SITES (September 1969 - February 1971) 99 average air temperatures were 2° to 9°C colder. At a l l sites, snow depths were greater in 1970 to 1971, and moreover, snow was on the ground by the end of September (see Figure 21). The effects of snow cover on ground temperatures are discussed more fully in Section 4 • Factors other than those discussed in Chapter 4 are responsible for the differences displayed in Figure 21. The temperature regimes at sites 4 and 5 are very similar, the only real difference being that the latter is colder by 1°C or so. The regime at site 1 partly re-sembles these, except that the penetration of isotherms is more limited, due to latent heat effects at the 7 - to 9-meter depth. The regimes at sites 2 and 3 are distinctly different from the others, particularly in winter. The deep snow accumulations at these sites cause a virtual absence of the winter cooling wave in the ground. Also, temperatures are close to 0°C and latent heat effects dampen temperature wave propagation. Near the ground surface, seasonal temperature fluctuations are greatest at site 1 (17.7°C at 50 cm). Because of the lack of vegetation there, ground temperatures are warm in summer; values up to 13.9°c at 25 cm and 9.2°C at 50 cm were measured in July 1970. In winter, because of the relatively greater exposure, snow accumulation is less than at other sites, and the 50-cm temperature in March 1970 was -8 .5 °C . In contrast, sites 2 and 3 are much warmer in winter, due to the greater insulation afforded by snow drifts. At site 2, which lies in the zone of maximum snow accumulation, the 50-cm temp^  erature in March 1970 was -2 .3 °C ; at site 3, the corresponding value was -4 .2 °C . The presence of this deep snow cover does not really re-tard spring warming either, since the snowbank remnants are flushed 100 away by the spring flood. The presence of vegetation at sites 2 and 3 leads to lower summer temperatures than at site 1; the 50-cm temperature in July 1970 reached 7.4°C at site 2, and 7.2°C at site 3. Compared to site 1, over the whole year, the reduced winter cool-ing at sites 2 and 3 more than compensates for their slightly cooler summer temperatures, and their mean annual temperatures are higher. At sites 4 and 5 ground temperatures are colder, and this is probably related to the presence of moss and peat in the surface ground layer. According to R.J.E. Brown (1966) dry (summer) peat has a low thermal conductivity, thereby inhibiting summer warming; saturated frozen peat, however, has a higher conductivity, and this reduces its in-sulating effect during the cold season. At site 4, the temperature maximum at 50 cm was only 3.7°C (August 1970). The winter minimum in March 1970, was -9 .3 °C . The tree canopy at site 5 helps to maintain lower mean ground temperatures there by restricting summer warming: in March 1970 the 50-cm temperature was -10 .6 °C, and i t warmed to only +1.6°C by August. A comparison of 50-cm temperatures at various seasons should help reveal something about the causes of differences between sites: Site 1 2 3 4 5 Date 8/70 8.6 6.5 6.3 3.2 1.6 12/70 -3.3 -0.4 -1.1 -5.5 -6.0 3/71 -7.7 -1.3 -2.9 -8.7 -9.8 6/71 4.9 3.3 3.0 0.6 -0.9 Temperatures at sites 4 and 5 remain roughly parallel year-round; the lesser vegetation cover at 4 presumably leads to greater summer warm-ing and a higher mean temperature. Compared to these two sites, site 1 is almost as cold in winter (1.0°C warmer than site 4, and 2.3°C 101 warmer than 5). In summer, however, the differences are much greater (5.4°C warmer than 4, and 7.0°C warmer than 5), and i t is this which accounts more for the higher mean value at site 1. Site 1 is about 2°C warmer than sites 2 and 3 in summer, but in winter site 2 is about 6.5°C warmer than site 1, and site 3 is about 5°C warmer than 1. By June, these winter differences are overcome by the homogenising effect of the spring flood. When comparing sites 2 and 3 to sites 4 and 5, the differences are again greater during winter. The foregoing cer-tainly indicates that i t is the winter regime which i s the most im-portant in maintaining sites 2 and 3 at the highest mean temperatures of any of the sites. The differences observed at the 50-cm depth can be mostly followed through at the 3-meter depth. Site 5 is s t i l l the coldest, ranging between -2.0° to -6.8°C (1969-1970). This is followed by site 4 (-1.2° to -5.7°C), site 1 (-0.4° to -2.8°C), site 3 (0.0°C to -0.2°C) and lastly site 2 (+1.1° to -0.2°C). The very small range at site 3 results from the damped winter wave, and latent heat effects where the ground is continually close to 0°C. The very warm temperature at site 2 in October 1969 is probably related to the snow depth which accumulated during the previous winter (1968-1969). In the winter of 1969-1970, snow depths and insulation were less, and the 3-meter temp-erature in October 1970 reached only 0.0°C. Following the snowier winter of 1970-1971, the 3-meter temperature had already reached 0°C by July 1971. The reduced temperature range at site 1 may also be due to latent heat effects in the. moist ground above 1.5 m; the 1.5-meter temperature hovered around 0°C during the summer, but i t never did actually thaw. 102 The ground layer above about 12 m acts as a heat reservoir, absorbing part of the excess heat in summer and releasing it to the air in winter. The heat flux density at the ground surface determines the quantity of heat entering and leaving the ground; it is thereby the most important component in building the thermal regime of the ground. Calculations have been made of average daily surface heat flux 2 for sites 1, 2, 4 and 5, (Figure 22) using the temperature-integral method (see Carson and Moses 1963, Scott 1964). The method of calcu-lation is described in Appendix 5. The major vacillations in the surface heat flux regime are associated with the periods of thawing and freezing in the active layer. Latent heat effects involve large quantities of energy, and most of the ground-conductive transfer takes place in this period June to November. Site 1 experiences the greatest energy exchanges, and site 5 the smallest, with sites 2 and 4 being intermediate. These values are consistent in terms of the surface conditions occurring at each site, although varia-tions in ground thermal properties will also cause some differences. Heat flux values during in i t ia l thawing and freezing periods are quite high, and may be explained by the very steep temperature gradients which develop in the surface layer during the penetration of the 0 ° C isotherm. Measured values during July and August compare favourably with the calculated ones (see below, under section 3). Figure 22 shows that site 2 cools more slowly in autumn; the top 2 to 3 m are virtually iso-thermal, near 0°C, and the cooling wave cannot penetrate nearly so quickly as in the other sites (see Figure 21). In winter, the heat flow out of 2 Calculations were not carried out for site 3, because of uncertainties in delimiting freezing and thawing layers. Similar, but less serious problems were encountered for sites 1 and 2. The results for site 3 should be similar to those of site 2. 103 100-1 1970 1971 Figure 22 C A L C U L A T E D V A L U E S O F A V E R A G E DAILY S U R F A C E HEAT F L U X AT F O U R MICROCLIMATIC S I T E S (April 1970 - April 1971) 104 the ground is almost zero at site 2, where snow accumulation is greatest. Outflow is greatest at site 5, and slightly less at site 4; this may be due to the greater snow accumulation at the latter. Outflow at site 1 is less than sites 4 and 5 - remember, though, that these values are based upon exchanges down to 12 m, and at site 1 the winter cooling wave does not penetrate effectively beyond 5 m (see Figure 21). Possibly cooling is offset by the inflow of heat, at depth, from the nearby river. (Heat flow values for the surface layer itself are discussed in section 4). In the discussion so far, only between-site differences along the successional transect have been discussed. Mention was made in Chapter 4 of the talik beneath part of the slip-off slope; sampling revealed this zone to be larger at the downstream end of the bar. There is thus a longitudinal gradient in ground temperatures, along the slip-off slope. These variations are discussed more fully in section 4 of this Chapter, since they seem to be primarily related to variations in snow accumulation. Differences in the thermal regimes between sites could result from differences in microclimatic regime in summer; differences in winter snow cover resulting in differential insulation; differences in ground and surface properties; etc. These factors are of course integrated over the annual picture; however, some of them will now be discussed separately insofar as i t helps explain the differences between sites. 3. Summer Microclimate The five main sites discussed above were instrumented for more detailed investigations during July and August, 1970. Even though this is a short period of time, enough information was collected to yield con-clusive results. The major effort was directed towards continuous re-cording of air and active-layer temperatures at the five sites, with more 105 limited measurements of net radiation and ground heat flux. Air temperatures. An analysis of variance revealed no significant differences in mean daily air temperatures between the five sites (Table 17a). However, the mean values appear qualitatively consistent with respect to the variations in energy regimes. Site 1 is the warmest, followed by sites 2 and 4 together, and lastly sites 3 and 5 which are both treed.' An analysis of sunny days only (categorised on the basis of incoming solar radiation), showed greater differences between the sites but these were s t i l l not significant (Table 17b). As expected, tempera-tures are homogenised on cloudy days. It is felt that a major problem in comparing air temperature regimes is due to the small extent of the terrain segments, so that there are undoubtedly advection effects between them. Surface regime. Surface temperatures were measured with thermistor beads, camouflaged by dipping them in epoxy resin and coating them with in situ material, and then pressing them into the ground surface. An analysis of mean daily surface temperatures revealed some significant differences between sites (Table 18). The two treed sites, 3 and 5, were significantly colder than the other sites, with the spruce-covered site the coldest overall. Sites 2 and 4, both with ta l l shrub vegetation, were significantly warmer than the treed sites, but colder than the bare site 1. The mean diurnal regimes are shown in Figure 23. Differences in the sur-face temperature regimes spring from spatial variations in energy balance components. The diurnal regimes fall into two distinct groups: sites 1, 2 and 3 are broadly similar, and quite different from sites 4 and 5. The variations within each of these two groups are related to the individual radiation regimes, and are discussed below. The presence of these two distinct groups is a result of profound differences in ground surface Table 17a Analysis of Variance - Mean Daily A i r Temperatures at Five Microclimatic Sites ( a l l days, July-August 1970) SOURCE OF VARIATION DEGREE OF FREEDOM SUM OF SQUARES MEAN SQUARE F Sites 4 18.042 4.511 0.7979 Within 160 904.526 5.653 Total 169 922.568 Mean Daily Air Temperatures ( a l l days) SITE MEAN DAILY AIR TEMPERATURE C°C) NUMBER OF MEASUREMENTS 5 Picea 13.1 33 4 Sal ix- Alnus 13.8 33 3 Salix (2) 13.2 33 Sal i x (1) 13.8 33 1 Bare j round Equisetum 13.8 33 F -test i s not s i g n i f i c a n t Table 17b Analysis of Variance - Mean Daily A i r Temperatures at Five Microclimatic Sites (sunny days, July-August 1970) SOURCE OF VARIATION DEGREE OF FREEDOM SUM OF SQUARES MEAN SQUARE F Sites 4 16.006 4.001 0.8474 Within 160 424.969 4.722 Total 164 440.975 Mean Daily A i r Temperatures (sunny days) SITE MEAN DAILY A IF TEMPERATURE (°C) NUMBER OF MEASUREMENTS 5 Picea 13.8 19 4 Salix-Alnus 14.6 19 3 Salix (2) 13.8 19 2 Salix (1) 14.6 19 1 Bare ground Equisetum 14.6 19 F -test i s not sig n i f i c a n t 107 Table 18 Analysis of Variance - Mean Daily Surface Temperatures at Five Microclimatic Sites (July-August, 1970) SOURCE OF VARIATION DEGREE OF FREEDOM SUM OF SQUARES MEAN SQUARE F Sites 4 242.503 60.626 29.257** Within 160 331.545 2.072 Total 164 574.048 * * Exceeds the five percent level of significance Mean Daily Surface Temperatures Ranked and Differentiated by the N-K Test SITE MEAN SURFACE TEMPERATURE(°C) NUMBER OF MEASUREMENTS 5: Picea 10.7 33 3: Salix(2) .11.4 33 4: Salix-Alnus 12.3 33 2: Salix(l) 12.9 33 1: Bare ground 14.2 33 5 3 4 2 1 Any two sites underscored by the same line are not significantly different at the five percent level of significance Figure 23 MEAN DIURNAL SURFACE TEMPERATURE REGIMES AT s FIVE MICROCLIMATIC SITES (July-August, 1970) 109 materials (see Table 16): i) Sites 1, 2 and 3 have a similar mineral soi l , with some variation in l i tter amounts, i i ) Sites 4 and 5 have surface layers of moss and peat over-lying silty soi l . The very low thermal conductivity of peat is well known and is due to its low density and fibrous structure. R. J. E. Brown and G. P. Williams (1972) write: The thermal conductivity of unfrozen peat at high moist-ure contents is in the range of the lowest reported values for mineral soils . . . The thermal conductivity of dry sphagnum is probably an order of magnitude lower than the lowest values for mineral soils (p. 5). At sites 4 and 5, therefore, the surface has a high thermal resistance; this promotes high surface temperatures during the day, since heat is unable to easily penetrate into the ground. The maximum surface tem-perature recorded at site 4 was 26.1°C (on 29/7/70), compared to a maximum of 23.3°C at site 1. Because l i t t le heat is accumulated in the ground during the day, there is l i t t le available to offset surface heat losses at night, and the surface temperature consequently falls as i t satisfies heat losses by radiation. The mean temperature gradient be-tween the surface and the 10-cm depth at site 4 is between -0 .09 ° to -0.1°C cm-* during the middle of the day, and whereas the corresponding value at site 1 is only about -0.04°C cm - 1 , the ground heat flux is in fact greater there (see below). This clearly indicates high thermal resistance in the surface layer at site 4. As a consequence of these effects, the diurnal temperature range is greatest at sites 4 and 5. The latter, being tree-covered, has the smaller range. At sites 1, 2 and 3, ground heat flux values are greater than at the other sites and heat accumulated in the upper layers during 110 the day is released at night, helping offset the cooling of the surface. Heat flux values are discussed below under subsurface regimes. The influence of spatial variations in net radiation amounts on the pattern of surface temperature regimes is indicated by the greater spread of temperature values during the daytime (Figure 23). At night, 3 when radiation levels are very low, the range of values is much reduced, and temperatures fal l neatly into the two groups, with sites 4 and 5 being significantly colder than the others (see Table 19a for an analysis of variance of minimum daily temperatures). Because only three radiometers were available to monitor five sites, i t was decided to keep one at site 1 as a control and move the other two around, so that a l l combinations of the remaining sites were sampled. It is felt that a more extensive sam-pling program would not have added substantially to the overall results. Measurements were made at a height of 1 m. Data are given in Appendix 6. Analysing the regimes in two groups, net radiation values are greatest for site 1, with smaller totals observed at sites 2 and 3 re-spectively (see Figure 24). On the average, the net radiation at 2 was 86% of that at 1, and at site 3 only 54% of that at 1. This progressive reduction in radiation totals, due to increased vegetation cover, is reflected in lower daytime surface temperatures--site 1 is warmer than site 2 which is warmer than 3 (Figure 23). Night-time cooling is reduced at sites 2 and 3, presumably because of the presence of vegetation. For the other group (sites 4 and 5) the same relationships are present; the tree cover at site 5 leads to low radiation income (Figure 24), and surface temperatures are colder than at site 4. The asymmetry in the 3 Although the theoretical night-length is short at this time of the year, i t is more prolonged in the study area since the sun falls below the local topographic horizon (Caribou Hills) in the early morning hours. Table 19a Analysis of Variance - Minimum Daily Surface Temperatures at Five Microclimatic Sites (July - August, 1970) SOURCE OF VARIATION DEGREE OF FREEDOM SUM OF SQUARES MEAN SQUARE F Sites 4 400.974 100.244 34.696** Within 165 476.721 2.889 Total 169 877.695 ** Exceeds the five percent level of significance Mean Daily Minimum Surface Temperatures Ranked and Differentiated by the N-K Test SITE MEAN MINIMUM SURFACE TEMPERATURE (°C) NUMBER OF MEASUREMENTS 4: Salix-Alnus 5: Picea S a l i x (2) S a l i x (1) Bare ground Equisetum 6.8 7.0 9.8 10.1 10.2 34 34 34 34 34 Any two sites underscored by the sane line are not sig n i f i c a n t l y different at the five percent level of significance Table 19b Analysis of Variance - Maximum Daily Surface Temperatures at Five Microclimatic Sites (July-August, 1970) SOURCE OF DEGREE OF SUM OF MEAN VARIATION FREEDOM SQUARES SQUARE F Sites 4 3074.038 768.509 43.844** Within 165 438.205 17.528 Total 169 3512.242 ** Exceeds the five percent level of significance Mean Daily Maximum Surface Temperatures Ranked and Differentiated by the N-K Test SITE MEAN MAXIMUM SURFACE TEMPERATURE (°C) NUMBER OF MEASUREMENTS 3: Salix (2) 13.2 34 5: Picea 16.9 •54 2: Salix (1) 16.9 34 1: Bare ground-Equisetum 18.9 34 4: Salix-Alnus 19.6 34 3 5 2 1 4 Any two sites underscored bv the same line are not signi f i c a n t l y different at the five percent level of significance Solar Radiation 600 -, 400 a •o 200 - i 22 23 24 25 26 27 28 29 30 31 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 July August Net Radiation 400-, 4 22 23 24 25 26 27 28 29 30 31 1 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 July August Q Site 1 | Site 2 | Site 3 § Site 4 | Site 5~ No data Figure 24 DAILY RADIATION TOTALS FOR FIVE MICROCLIMATIC SITES (July-August, 1970) 113 temperature curve for site 5 is due to sun flecking. When comparing surface temperatures between the two groups, the radiation differences are partly offset by the effects due to surface materials. Net radiation totals are lowest for site 5 (21% of that for site 1) but daytime surface temperatures are higher there than at site 3, where net radiation is more than twice as much (Figure 24). These two sites have the lowest average radiation totals, and also the lowest daytime surface temperatures. Site 4, which has similar net radiation to site 2, (79% of that for site 1 vs. 86%) nevertheless has higher daytime temperatures--as high, in fact, as site 1 (see Table 19b for an analysis of variance of maximum daily temp-eratures) . On balance, however, the lower night-time temperatures at site 4 offset the higher daytime values, and the mean daily temperature is lower there than at site 2. Similarly, site 5 is colder than site 3. One problem in discussing contrasts in net radiation income between sites is that of the representativeness of single measurements. Because of equipment limitations, simple measures had to be employed to assess around-site variability. Lull and Reigner (1967) found only small differences in longwave radiation between plots, and that 89% to 94% of the variation in daily net radiation totals was attributable to variations in solar radiation. Since the visible portion of the spectrum is the major component of solar radiation, measurements with a camera exposure meter should permit a valid assessment of radiation variability. Visible light was measured at 10 randomly selected points around each of sites 2, 3, 4 and 5 at various times during a perfectly sunny day. Each complete scan was easily accomplished in 10 minutes. An analysis of variance was performed, considering the data as a stratified random sample (Table 20). At al l four vegetated sites, incident light values were significantly lower then at site 1. Only sites 2 and 4 were not significantly different 114 Table 20 Analysis of Variance - Incident Light Values around Five Microclimatic Sites (July 1970) SOURCE OF VARIATION DEGREE OF FREEDOM SUM OF SQUARES MEAN SQUARE F Sites 4 249.144 62.286 64.694** Within 295 284.018 0.963 Total 299 533.163 * * Exceeds the five percent level of significance Mean Incident Light Values Ranked and Differentiated by the N-K Test SITE MEAN LIGHT VALUES* NUMBER OF MEASUREMENTS 5: Picea 12.42 60 3: Salix(2) 13.36 60 4: Salix-Alnus 14.04 60 2: Salix(l) 14.07 60 1: Bare ground 15.19 60 5 3 4 2 1 * Units are EV values Any two sites underscored by the same line are not significantly different at the five percent level of significance from each other, and the measured net radiation totals were also very similar at these two sites. The net radiation data are wholly consistent with the pattern of incident light values, indicating that there are significant differences in net radiation economy between sites (see also Gi l l 1971). In summary, observed differences in net radiation totals are responsible for the differences in surface temperature regimes between sites 1, 2 and 3. For the same reason, site 4 is warmer than site 5. At the two latter sites, surface material with low thermal conductivity promotes higher daytime surface temperatures than are consistent with net radiation values alone. Thus, during the day, site 5 is warmer than site 3, and 4 is warmer than 2. At night, however, temperatures are significantly lower at sites 4 and 5, and, in fact, this aspect of their regimes is the more important since, on the daily average, site 4 is colder than site 2, and 5 is colder than 3. Subsurface regime. Within each of the two groups, the pattern of surface temperature values is reflected in subsurface temperatures. Thus, at the 10-cm depth for example, site 1 is significantly warmer than 2, which, in turn, is warmer than 3 (Table 21). Similarly, site 4 is warmer than 5. The mean diurnal 10-cm regimes are shown in Figure 25. The low surface conductivity at sites 4 and 5 means that the temperature wave is quickly damped out, and ground temperatures are much colder, with reduced diurnal ranges. At sites 1, 2 and 3, the mean daily 10-cm temp-eratures are about 1°C lower than the respective surface values; at sites 4 and 5, however, the reduction is about 6°C. The mean diurnal range of surface temperature at site 4 is 10.7°C, but i t is only 2.2°C at 10 cm. In comparing sites 3 and 4, the influence of surface- and ground-thermal properties is evident. Whereas the surface temperature at site 4 is significantly higher than at site 3, this relationship is 116 Table 21 Analysis of Variance - Mean Daily 10-cm Temperatures at Five Microclimatic Sites (July-August 1970) SOURCE OF VARIATION DEGREE OF FREEDOM SUM OF SQUARES MEAN SQUARE F Sites 4 1550.362 387.591 413.487** Within 160 149.979 0.937 Total 164 1700.341 **Exceeds the five percent level of significance Mean 10-cm Temperatures Ranked and Differentiated by the N-K Test SITE MEAN 10-cm NUMBER OF TEMPERATURE(°C) MEASUREMENTS 5: Picea 4.8 33 4: Salix-Alnus 6.8 33 3: Salix(2) 10.6 33 2: Salix(l) 11.6 33 1: Bare ground 13.0 33 A l l differences are significant at the five percent level 12 16 2 0 2 4 Hours (Local Time) ure 25 MEAN DIURNAL 10cm. REGIMES AT FIVE MICROCLIMATIC SITES (July-August, 1970) 118 reversed at the 10-cm depth., where site 4 is significantly colder (Table 21). Measurements were made of ground heat flux, which is the major energy component of the ground thermal regime. Only two recording sys-tems were available; one was kept at site 1 whilst the second was moved around the other four sites. Although this provided only about 8 days' of data at each site (some occasional data loss did occur), the values do form a consistent picture. Daily heat flux totals are listed in Appendix 6. Heat flux densities were generally small values (less than 0.1 ly min 1 ), and this made data reduction quite difficult. On average, values at site 1 are about 8% of net radiation there; ratios at the other sites are about 7% at 2, 5.5% at 3, 4.3% at 4, and 6.5% at 5. Actual average values, by site, are given in Table 22. At sites 1, 2 and 3, the pattern of G values more or less paral-lels the Rn values. Ground thermal properties are similar at these three sites (see Table 16), and subsurface temperatures mirror closely the surface regimes. In other words, the variations in subsurface regime on the slip-off slope are determined principally by variations in net radiation. This is supported by the values for daily maximum and mini-mum 10-cm temperatures (Table 23). Differences are greater during the day than at night, indicating that radiation differences are important in terms of subsurface regime. In contrast to this, at sites 4 and 5 i t must be the extremely small ground heat flux values that are responsible for the low ground temperatures there. These small heat fluxes are a result of the low conductivity of the organic material in the surface layer. R.J.E. Brown (1965), in a study at Norman Wells, N.W.T., found there, to be a general decrease in temperature in the active layer with increased combined moss and peat thickness. Hopkins et al (1955), from 119 Table 22 Average Daily Net Radiation (R n) and Ground Heat Flux (G) at Five Microclimatic Sites (July-August, 1970)* Site Pairs 1 2 1 3 1 4 1 5 No. Days 9 9 6 6 6 6 7 7 R„ (ly day-1) 218. 9 187.1 336.5 179.0 215. 1 172.9 207. 2 47.8 G (ly d a y l ) 16. 9 13.1 28.9 9.9 17. 9 7.5 16. 3 3.1 G/RJI (%) 7. 7 7.0 8.6 5.5 8. 3 4.3 7. 9 6.5 R/Rl (%)** 85.5 - 53.2 80.4 23.1 G/Gx (%)** 77.5 - 34.2 41.9 19.0 *Paired observations were made between site 1 and the other sites in turn. **The ratio of the value at the particular site (2,3,4 or 5) to the corresponding value for site 1. Table 23 Mean Daily Maximum and Minimum 10-cm Temperatures at Sites 1, 2 and 3 (July-August 1970) Maximum Minimum 1 14.7°C 11.2 2 12.8 10.4 3 11.1 10.0 120 the Kenai Lowland, Alaska, state that: Known occurrences of permafrost are restricted to black spruce islands, where a dense forest cover, a thick insulating mat of moss, and... peat soils favour its preservation (p. 133). As a further investigation of the influence of the surface organic layer in the present study area, ground temperatures were measured at two sites, 1 m apart, in the spruce-covered area. Temperature cables were originally emplaced in August 1969, and measurements through until June 1970 showed the two sites to be very similar. In June, 10 cm of organic material was removed at one of the sites, where the thermistors were re-positioned to conform to the new ground surface. Temperatures were then recorded for a six-week period, and there was a marked difference between the two sites. The mean diurnal 10-cm regimes are shown in Figure 26. The disturbed site was about 3°C warmer, with the difference being greater during the day. The diurnal range was much greater at the disturbed site with its predominantly mineral soil (2 .0 °C, compared to 0.4°C at the other site), indicating a much greater ground heat flux term. According to R.J.E. Brown and G. P. Williams (1972): Because peat soils have low thermal conductivities and relatively high volumetric heat capacities their thermal diffusivities, ranging from 0.0005 to 0.0015 cm /sec, are low compared with those for mineral soils (0.002 to 0.016 cm^/sec) (p. 6). Thus the effectiveness with which diurnal waves penetrate peat is much less than that for inorganic soils. Returning to the five main sites, the pattern of temperatures recorded at the 10-cm depth carries through at the 25-cm depth (Table 24). Al l differences are significant, although there seems to be the beginning of some overlap between sites 2 and 3. An assessment of around-site variability pf subsurface, regime 121 Figure 26 M E A N DIURNAL 10cm. T E M P E R A T U R E R E G I M E S AT T W O S I T E S IN T H E Picea S E G M E N T (Ju ly -Augus t , 1970) 122 Table 24 Analysis of Variance - Mean Daily 25-cm Temperatures at Five Microclimatic Sites (July-August, 1970) SOURCE OF VARIATION DEGREE OF FREEDOM SUM OF SQUARES MEAN SQUARE F Sites 4 2571.177 642.794 269.679** Within 160 81.002 0.506 Total 164 2652.179 * * Exceeds the five percent level of significance Mean Daily 25-cm Temperatures Ranked and Differentiated by the N-K Test SITE MEAN 25-cm NUMBER OF TEMPERATURE(°C) MEASUREMENTS 5: Picea 0.7 33 4: Salix-Alnus 4.1 33 3: Salix(2) 9.2 33 2: Salix(l) 9.6 33 1: Bare ground 11.2 33 Al l differences are significant at the five percent level 123 was attempted by recording 10-cm temperatures at seven randomly-selected locations around each of the five microclimatic sites. Recording was carried out over two 48-hour periods: sites 1, 2 and 3 together, and sites 1, 4 and 5 together. The data were treated as time-stratified random samples; analyses of variance revealed significant differences in ground thermal regime between sites (Table 25). Only in the case of sites 2 and 3 does there seem to be any overlap. This is not so sur-prising, since these two terrain segments are the smallest in extent (see also the similarity in active layer depths in Table 15). 4. Winter Conditions Snow cover is the decisive factor affecting ground climate in the winter season. In fact, on a longer time scale, snow cover seems to be instrumental in the formation of a talik beneath part of the slip-off slope, as described in Chapter 4. It is widely accepted that snow is a leading factor in protecting the ground from cold penetration. For example, the use of snow to amel-iorate ground temperatures is widely practised in the northeast U.S.S.R., in agriculture and open-pit mining (see Klyukin 1963). Gold (1967), from observations at an Ottawa site, found that: Snow cover maintained the average surface temperature about 10°C warmer than the lowest value of the monthly average air temperature (p. 208). Ives (1961) noted a good correlation between vegetation, snow accumulation and the distribution of permafrost, in Labrador-Ungava. For the same region, Annersten (1964) writes: It is concluded that the snow cover must be a permafrost controlling factor in the area. Variations in snow cover cause temperature variations in the soil far greater than those resulting from vegetation cover (p. 115). Table 25a Analysis of Variance - Half-Hourly 10-cm Temperatures at Three Microclimatic Sites: 1,4,5 (August 23-24, 1970) SOURCE OF VARIATION DEGREES OF FREEDOM SUM OF SQUARES MEAN SQUARE F Sites 2 1317S.498 6587.749 855.828** Within 1320 14 84.987 1.125 Total 1322 14660.485 **E.xceeds the five percent level of significance Mean 10-cm Temperatures at 1,4,5 Ranked and Differentiated by the N-K Test SITE MEAN 10-CM TEMPERATURE (°C) NUMBER OF MEASUREMENTS 5: Picea 4: Sali.x-Alnus 1: Bare ground 5.0 6.1 12.2 441 441 441 All differences are significant at the five percent level Table 25b Analysis of Variance - Half-Hourly 10-cm Temperatures at Three Microclimatic Sites: 1,2,3 (August 25-26, 1970) SOURCE OF VARIATION DEGREES OF FREEDOM SUM OF SQUARES MEAN' SQUARE F Sites 2 310.030 155.015 390.815** Within 1152 456.936 0.397 Total 1154 766.966 "Exceeds the five percent level of significance Mean 10-cm Temperatures at 1,2,3 Ranked and Differentiated by the N-K Test SITE MEAN 10-CM TEMPERATURE (°C) NUMBER OF MEASUREMENTS 3: Salix (2) S.6 385 2: Salix (1) S.S 385 1: Bare ground 9.S 385 A l l differences are significant at the five percent level 125 One can identify a twofold influence on the ground thermal regime due to the presence of a snow cover (Gold 1963): 1) It interposes a layer with low thermal conductivity between the air and the ground, and thus protects the latter against cooling (and warming). The insulating effect of snow is greatest for lowest densities since the thermal conductivity of snow is a function of grain-to-grain contacts (i.e., density). (Other processes of heat transfer are not con-sidered here, but see, for example, Yen 1963). 2) It increases the effective depth, below the surface, of points within the ground (i.e., a point 1 m in the ground, and beneath 1 m of snow, "sees" the surface 2 m above i t ) . This affects the phase and amplitude of the propagation of temperature waves through the ground. Among the consequent effects of the above are that winter cooling waves may be damped out within the snow, and have l i t t l e effect on the regime of the underlying ground. The annual amplitude at the ground surface is reduced; Gold (1963) showed that the snow cover induced a Fourier com-ponent with a period of a half-year into the annual regime. In winter, ground temperatures at snowy sites are higher than at sites with no snow, assuming they were at the same temperature in autumn. Many studies have shown that a snow cover protects the s o i l from rapid temperature changes, and maintains higher ground temperatures (for example, Bay et al 1952; Crawford 1952; Potter 1956; Beckel 1957; Gold 1958, 1963, 1967; Annersten . 1964, 1966). Gold (1963) showed, at an Ottawa site, that snow cover was the main factor in maintaining the mean annual ground temperature from 1.25° to 3.25°C higher than the air temp-erature. Where the winter season i s longer, this effect should be greater. 126 One can assume that wherever the snow cover is persistent during the cooling period, then the average ground temperature must be higher than otherwise—not only in winter, but as the annual mean. Brown (1969) has discussed the importance of snow cover in the distribution of permafrost in the discontinuous zone, emphasising the importance of phenology: A heavy fal l and accumulation of snow in the autumn inhibits frost penetration and the formation of permafrost. On the other hand, a thick snow cover that persists on the ground in spring will delay thawing (p. 35). Clearly, at any location the relationship between the accumulation and i ablation periods will determine the net effect of snow cover on the ground thermal regime. In discussing the influence of snow cover on ground thermal regime, the important parameters are therefore thickness, density and phenology. In the study area, the snow phenology at particular sites is complicated by drifting. A regular snow sampling program set up for the winter of 1970-1971 unfortunately was not followed through, so that the following discussion is necessarily based on more limited data. It is believed, however, that the results are s t i l l conclusive. It should be pointed out that the snow cover of the Mackenzie Delta is important in inhibiting the thickening of lake and river ice, and may therefore prevent relatively shallow lakes from freezing to the bottom. This is important in terms of their effect on permafrost dis-tribution. Sampling of snow depths, on various occasions, revealed signif-icant variations in snow accumulation between the terrain segments. An analysis of variance conducted on data for March 1971 (Table 26a) showed that mean snow depths for six sites, including the river channel, were Table 26a Analysis of Variance - Snow Depths in Six Terrain Segments (March 1971) SOURCE OF VARIATION DEGREE OF FREEDOM SUM OF SQUARES MEAN SQUARE F Sites S 97324.167 19464.833 289.074** Within 114 7676.200 67.335 Total 119 105000.367 **Exceeds the five percent level of significance Mean Snow Depths Ranked and Differentiated by the N-K Test SITE MEAN SNOW DEPTH (CM) COEFF. OF VARIATION NUMBER OF MEASUREMENTS 6: Channel Ice 29 29.9% 20 1: Bare ground 41 22.4 20 5: Picea 59 11.3 20 3: Salix (2) 75 3.0 20 4: Salix-Alnus 80 8.5 20 2: Salix (1) 116 10.6 20 6 1 5 3 • . 1 2 Any two s i t e s underscored by the same l i n e are not s i g n i f i c a n t l y d i f f e r e n t at the f i v e percent l e v e l Table 26b Analysis of Variance - Snow Depths i n Three Terrain Segments (December 1970) SOURCE OF VARIATION DEGREE OF FREEDOM SUM OF SQUARES MEAN SQUARE F Sites 2 39302.578 19651.289 149.240** Within 42 5530.400 131.676 Total 44 44832.978 "Exceeds the five percent level of significance Mean Snow Depths Ranked and Differentiated by the N-K Test SITE MEAN SNOW DEPTH (CM) COEFF. OF VARIATION NUMBER OF MEASUREMENTS 1: Bare ground 26 46.0% 15 3: Salix (2) 50 4.4 15 2: Salix (1) 98 16.0 15 Al l differences are significant at the five percent level 128 significantly different. Snow sampling in December 1970 showed that this spatial pattern was well established by then (Table 26b). On the slip-off slope exposure is the major factor determining the pattern; at the other two sites the differences are related to the vegetation cover - snow depths are less and the variation greater in the spruce-covered area, presumably because of snow retained in the crowns of trees. On the slip-off slope the interactions between snow accumulation, vegetation and ex-posure are well illustrated. The channels of the Mackenzie Delta provide excellent settings for the development of snow drifts. Drifting in these open areas is ubiquitous, and in the form of longitudinal accumulations behind vegetation barriers. Benson (1969) studied similar drifts in Alaska and found that: The drifting snow which characterises the Arctic slope is complex in detail, but has a useful degree of regularity . . . In this work we have assumed that the complex drift patterns are reproduced in shape each year and that variations are restricted primarily to the quantity. The basic assumption has proved valid . . . During 1962-1967 the sizes and shapes of the drifts observed in the Meade River test area were very similar (p. 15). The drift pattern in the present study area is related to the prevailing winds, and is thus reproduced in a general form each year. Snow amounts were considerably less in 1969-1970, for example, but the same spatial pattern was in evidence: Table 27 Snow Depths in Five Terrain Segments (March 1970) 1 2 3 4 5 Mean Depth 38.1 86.5 45.9 47.2 42.3 (cm) Coefficient of 44.4 22.0 3.5 6.4 9.5 Variation % The pattern has also been observed in previous years (see Gi l l 1971). 1 2 9 Areas where vegetation is completely lacking are also those which are the most exposed. Such sites'have l i t t l e snow cover with the greatest variation (Table 26a); exceptions are where there are special local features such as wave-cut bluffs (see Figure 30). In some places along the bar, for example near the point, exposure is extreme and snow may be completely absent (Plate 6). The snowdrift area is associated with the outer line of willows, which simply traps the snow which has been blown off the channel (the mean depth on the latter was 29 cm in March 1971) and the bare ground (mean depth of 41 cm). In the drift area snow depths up to 170 cm were measured. This distinctive accumulation pattern is shown in Plate 7. Behind the.drift area the snow cover is remarkably uniform (Table 26a). Transverse sampling at various locations along the bar revealed the drift to be deeper and more extensive in a downstream direction (see below). The complete sampling program was repeated on another bar, and the patterns described above were wholly duplicated, although amounts in the drift area were higher, because of greater exposure and fetch. In conjunction with the snow sampling program, various temperature measurements were also carried out. Because the major variations in snow accumulation occur on the slip-off slope, efforts were concentrated there. In March 1970, temperatures at the snow-ground interface were measured at numerous locations on the slip-off slope; results from 38 locations, are plotted in Figure 27. Temperatures are warmer under deeper snow cover; the exponential nature of the curve has been noted previously by Annersten (1964). In terms of ground surface temperature, variations in snow depth are most crit ical at shallow snow depths. The exponential distribution is consistent with the simple heat conduction model of temp-erature propagation in a homogeneous medium (see Annersten 1964, pp.109-110). 130 Plate 6 Plate 7 Snowbank Zone on a Slip-Off Slope 131 100 80 60-E o CL Hi a i o 40-20 -25 o o o o oo o o o o o o o o o -20 -15 Temperature (°C) — i — -10 Figure27 EFFECT OF SNOW DEPTH ON THE TEMPERATURE AT THE GROUND SURFACE (March 1970) 132 The scatter in Figure 27 could be due to variations in snow density (see below), or snow cover mobility - i . e . , because snow depths change with time, the temperature measured on a single occasion at any location may not "correspond" to the actual prevailing snow depth. At the time of the observations in Figure 27, the air temperature was about -24°C; the ground surface temperature varied from -24°C beneath 4 cm of snow to about -5°C beneath 100 cm of snow. The greatest difference observed in surface temp-eratures in summer was only about 10°C. This seems to indicate that.on the slip-off slope spatial variations in thermal regime are more signif-icant in winter than in summer. The insulating effect of the snow cover depends on its density, as well as its depth. Snow density was measured at a number of locations, and the salient feature of the snow in the study area is its quite low density-generally less than 0.25 gm cm"! Trabant et al (1969) observed the same thing in Alaska, and attributed the low values to depth hoar resulting from prolonged exposure to steep snow-temperature gradients, with l i t t le wind action. In the present study area, the more exposed, windy sites have somewhat denser snow (Table 28). The low densities en-hance the snow's value as an insulator. Values for thermal conductivity have been estimated from Abels' formula (see Mellor 1964, p. 70), which is suitable.for the range of densities encountered (Table 28). Along transect 1, the higher values over the bare ground are due to the greater wind action around the point bar itself . Values drop in the more sheltered snowdrift area (Salix (1)), although some wind action is s t i l l present. Behind the snowbank i t is very sheltered, and densities are very low. The thermal conductivity of the underlying frozen ground would be in the order of 0.0035 c.g.s.; this illustrates the quality of the snow as an insulator. Downstream from the point itself , the bare ground is less exposed 133 Table 28 Snow cover characteristics along two transects across a slip-off slope Transect 1 0-25 cm 25-50 cm 50-100 cm Point Snow(cm) Y* k** Y k Y k 1 23 .31 .65 _ _ Bare 2 40 .36 . .88 .33 .74 Ground 3 4 .33 .74 - -4 23 .33 .74 - -Snowb ank J ' 5 70 .27 .50 .28 .53 I t 6 110 .20 .27 .32 .70 .30 .53 r 7 64 .14 .13 .25 .43 Salix(2) 8 1 9 44 48 .13 .13 .11 .11 .27 .26 .50 .46 0-25 Point Snow(cm) Y * 1 50 .22 Bare 2 77 .19 Ground 3 20 .17 4 37 .19 Snowbank \ 5 98 .18 1 I 6 115 .21 7 68 .13 Salix (.2)-. 8 49 .13 9 45 .14 3 * Density (gm cm ) * * Thermal conductivity (c.g.s.xlO ) 3 25-50 cm 50-100 cm k** Y k Y k .33. .33 .74 .25 .29 .57 .20 .23 .36 .25 .27 .50 1 .22 .30 .53 .31 .65 .30 .24 .39 .30 .53 .11 .23 .36 .11 .24 .39 .13 .23 .36 134 and average densities are lower (Table 28). Thus sites on the point itself suffer from less snow, and of a higher density (see Plate 6) . At the sites away from the slip-off slope snow densities are similar to those behind the snowbank (Table 28). It is recognised that the ground temperatures in winter depend to some extent on the heat balance of the previous summer. The winter snow cover affects how much heat flows upward through the surface in winter. In order to study the effects of differential snow accumulation on the ground thermal regime, therefore, permanent temperature cables had to be installed. This was done in the form of transects across the slip-off slope, with thermistors at a 1.0 or 1.5-meter depth (see Figure 3). The data from transect 2 is discussed first . In August 1970, the 1-meter temperatures along transect 2 ranged from 4.0°C (in the bare ground segment) to 2.1°C (Salix (1) site). Figure 28 is an attempt to show, diagrammatically, the temperature trajectory from this time to July 1971, for the ten locations along the transect. Sites 1 to 4 are on the bare ground, in front of the drift area; sites 5 to 8 are in the drift area itself ; sites 9 and 10 are in the Salix (2) zone behind the drift area. During the freeze-up period in October the range in values is greatly reduced (-0 .1 ° to - 0 . 2 ° C ) , a result of the zero curtain phenomenon. Two sites, 6 and 7, showed only slight cooling in September; these sites are in the snowbank area, and there was an unusually heavy snowfall in September 1970, perhaps resulting in an early accumula-tion at these sites. By December, temperature values were beginning to diverge again, and by the following March the range of values had reached a maximum ( 4 . 6 ° C ) ; the snow cover had introduced a highly variable surface condition. At this time, the coldest site was in the bare ground segment (-4.8°C) and the warmest (-0.2°C) beneath 110 to 130 cm of snow in the 135 Figure 28 TEMPORAL VARIATION OF ONE-METER TEMPERATURES AT TEN SITES ACROSS A SLIP-OFF SLOPE (August 1970-July 1971) 140-1 120 100 I 80 60 40 20 -5 A 7 10 10 • * 8 if* -4 • August 1970 • December 1970 A March 1971 6.V ' 0 1 Temperature (°C) Figure 29 ONE-METER TEMPERATURES PLOTTED AGAINST SNOW DEPTH AT TEN LOCATIONS ACROSS A SLIP-OFF SLOPE 136 snowbank zone. In the previous winter, with thinner snow covers at the exposed sites, the range in 1-meter temperatures in,March 1970 was from - 0 . 6 ° to -6 .4 °C . Since snow cover remnants are flushed away by the spring flood, there is very l i t t l e retardation of spring warming at the sites in the snowbank zone. Figure 28 shows, for example, that by late July 1971, the sites on the bare ground were only 1.5° to 1.8°C warmer than those of the snowbank zone. In Figure 29, the 1-meter temperatures along transect 2 have been plotted against respective snow depths, for three different times. In late-August, with no snow, the range of values was 2°C. Temperatures in December were fairly uniform along the transect; the differences existing in August having been subsequently eradicated through differential cooling. Sites 1, 2 and 3, where snow depths were least, had cooled more than sites 5, 6, 7 and 8, where snow depths were already a lot greater. In March there was a quite distinct pattern--the sites with the least snow were now considerably colder than those under the deep snow in the drift area. At the latter sites there was no measurable cooling between December to March. This must be a result of the very limited heat outflow, and probably also because of the fact that the ground at these sites is close to 0°C to considerable depth, so that there is a prolonged zero curtain effect. The rate of heat outflow from the top 1-meter layer has been calculated for the three microclimatic sites on the slip-off slope, using the temperature-integral method (Table 29). These data illustrate con-vincingly the effect that a deep snow cover has in reducing the winter outflow of heat from the ground. The heat flux values at the snowbank site are extremely small throughout the period; those at the Salix (2) site, although twice as great are s t i l l , nevertheless, quite small. At the bare ground site, where snow depths were least, heat flux values are Table 29 Outward Heat Flow (ly day 1 ) from the Top one-meter Ground Layer at Three Sites on a Slip-Off Slope December 1970-March 1971 Ground S a l i x ^ S a l i x ^ 1/12/70 - 15/12/70 -1.9 -0.4 -0.8 15/12/70 - 31/12.70 -1.7 -0.1 -0.6 1/1/71 - 15/1.71 -2.0 -0.4 -0.9 15/1/71 - 31/1/71 -1.8 -0.2 -0.7 1/2/71 - 15/2/71 -1.9 -0.4 -0.8 15/2/71 - 28/2/71 -2.0 -0.3 -0.8 1/3.71 - 15/3.71 -1.0 -0.2 -0.5 138 altogether higher. Snow depths at this site were, however, s t i l l between 30 to 40 cm; at those sites on the bare ground where snow depths were less, heat flux values would have been even higher. The foregoing indicates that, on the slip-off slope, winter cooling is more important in producing spatial variations in ground thermal regime than summer heating. Temperature data, from each of the ten sites at 3-meter intervals along transect #2, for the two-year period 1969-1971, are summarised in Table 30 (temperatures are at 1 m depth) : Table 30 Temperature data from a transect through the snowbank zone, slip-off slope (sites 3 m apart). Annual Mean(°C) 1 -1. Bare 2 .2 -1. ground 3 ,3 -1.0 4 -1. , 1 1 5 1 -0 Snowbank Zone 6 7 8 .4 +0.3 +0.4 +0. 1 .2 Salix(2) 9 10 -0.2 -0.4 Maximum 3, .9 4. ,0 3.8 2, .6 2 .2 2.1 2.5 2. .3 3.5 4.0 Minimum -5. .7 -6. .4 -5.8 -5. .3 -1, .5 -0.6 -0.7 -1, .5 -2.3 -2.5 There is a narrow zone where the mean annual temperature is raised above 0°C and a talik is formed there. The warmer sites are so because of higher minimum (winter) temperatures, thus clearly indicating the essential role of the snowbank in the talik-forming process. The thermal processes involved in this were discussed in Chapter 4. Maycock and Matthews (1966) describe a situation where it is possible that a permanently unfrozen layer exists beneath willow thickets which collect a very deep snow cover in winter (p.135). Potter (1956) described a situation where the snow cover was sufficient not only to affect the rate of frost penetration, but also to facilitate thawing of the frozen ground from below. During a sampling program of active layer depths on the slip-off slope, i t was discovered that the talik was wider at the downstream end. 139 The distribution of frozen ground along a number of transects (on a second s l i p - o f f slope—see Figure 3) was determined by over two hundred 4 hand borings in August 1970. A l l borings were made to a depth of 3m, using a hand d r i l l . The results from three of the transects are shown in Figure 30, together with the snow cover data for March 1971. The complicity of the snowbank in the pattern of talik variation is clearly indicated; both the talik and the snowbank are more extensive in the downstream direction. There i s then a wider zone of warmer ground temperatures at the downstream end, as shown in Table 31. As was shown for transect 2, the zone of warmer temperatures correlates with the zone of reduced winter cooling; spatial variations in summer regime are not so important. The maximum and minimum temperature data in Table 31 further substantiate this explanation. The warming effect due to the snowbank can be followed through to greater depths than 1.5 m. For example, the mean annual temperatures at various points along transect 5 are as follows: Bare Ground Snowbank Zone Salix(2) 5-1 5-2 5-3 5-4 Distance (m) 10 5 5 n 3 -0.8 -0.1 +0.1 -0.7 D ^ h 6 -0.5 -0.0 - -0.5 U n J 9 -0.1 -0.1 - -0.2 The sites in the snowbank zone are warmer at least to depths of 6 m. By 9 m the differences have been eradicated, and the ground is frozen a l l the way across the slope. The unfrozen zone associated with the snowbank thus forms a "basin", or pseudo-talik. Data from transect 7 reveal a Frozen, in this context, means solidly frozen. 140 Willows start I Transect 5 Willows 0 - 2 -4 Transect 5-A Willows Transect 7 See Figure 3 for location of Transects Figure 30 DETAILS OF PERMAFROST CONFIGURATION ALONG VARIOUS TRANSECTS A C R O S S A SL IP-OFF SLOPE 141 Table 31 Temperature data from snowbank transects 5 and 7 (All temperatures are at a depth of 1.5 m) Transect 5 Site No. Distance (m) Temp. (°C): Mean Annual Maximum Minimum 2 3 2.5 2.5 Snowbank Zone 4 5 6 •1.8 -0.8 -0.2 -0.1 0.6 1.1 1.3 0.2 -7.6 -2.7 -0.8 -0.4 2.5 2.5 -0.1 0.0 -0.1 7 8 2.5 2.5 10 0.3 1.9 0.0 0.6 2.6 0.0 .0.3 1.9 -0.1 -0.9 -1.4 -0.2 -0.3 -2.2 -3.3 Transect 7 I Snowbank Zone j Site No. 1 2 3 4 5 6 7 8 9 10 Distance (m) 5 2.5 2.5 2.5 2.5 2.5 2.5 5 5 Temp. (°C): Mean Annual -2. .2 -0. .2 0. ,8 1. .1 1. .3 1, .0 0, .9 1. .0 0. .9 Maximum 0. ,0 0. .0 3. .1 4. .7 5, .0 4. .7 4. ,9 4. .8 3. 8 Minimum -8. ; i -0. .3 - o . ,2 0. .0 0, .1 0. .0 0, .0 0. .0 0. ,0 142 similar pattern, but with a wider unfrozen zone: J Snowbank Zone | 7-2 7-3 7-4 7-5 Distance (m) 10 10 10 Depth 3 -0.3 +0.1 +0.1 -0.3 6 -0.1 -0.1 0.0 -0.1 9 -0.2 -0.2 -0.2 -0.2 A fi n a l stage in the analysis of talik variation might be to account for the differential snow accumulation along the s l i p - o f f slope. The fetch to the north-west (a prevailing wind direction) is greater at the downstream end, which might account for some of the difference. However, on the other s l i p - o f f slope, where this difference in exposure is not really present, a similar differential snow accumulation is s t i l l found to some extent. The Salix(l) band of willows is narrower at the upstream end, although i t seems that this would not be important once the d r i f t has been initiated. Finally, there are differences in topography; the outer slope is steeper at the upstream end (Figure 30), and i t may be that more of the snow there is blown along rather than across the slope, and does not end up in the snowbank zone. Finally, the similarity between the snowbank effect and that due to unfrozen water bodies should be noted. The presence of unfrozen water beneath lake and river ice, maintains bottom temperatures near 0°C throughout the winter. This reduction in winter cooling leads to warmer mean annual temperatures, and the net effect i s thus analogous to that of the snowbank. 143 5. Summary Variations in ground temperature regime that are due to changes in surface conditions can occur over very short distances. Vegetation cover affects the ground thermal regime through controls exercised on the surface energy balance. For example, significant differences in net radiation were found to exist between major terrain segments. On the slip-off slope in summer, radiation differences pro-duce significant differences in surface temperature regime. Because of similarities in ground thermal properties, these differences carry through to the subsurface regimes. At the other sites, where ground materials are markedly different, low ground temperatures are a result of small ground heat fluxes. The importance of the insulating surface organic layer in producing low temperatures was demonstrated by a controlled experiment. The organic layer is undoubtedly responsible for maintaining permafrost close to the surface (see also Viereck 1970). The direct effect of a vegetation cover should be to lower ground temperatures; Stearns (1966) has written: Vegetation is one of the most important environmental factors contributing to the presence or absence of permafrost. It provides an insulating cover over the soi l , which tends to pre-serve existing permafrost (p. 26). On an annual basis this seems to apply to the differences between sites 1, 4 and 5. However, in general, i t is not altogether valid--the effects are not quite so simple as stated, particularly because in winter, snow cover imposes a newly-varying surface condition. Where differences in surface conditions affect the accumulation and retention of snow, marked differences in ground thermal regime occur (see also Beckel 1957; Annersten 1964). In the analysis of the effects of surface cover, i t was concluded that variations in snow accumulation 144 were a major controlling factor. On the annual basis, snow cover variations cause temperature variations on the slip-off slope greater than those resulting from vegetation differences per se. Permafrost can only be maintained where the mean annual surface temperature is below 0°C. Beneath part of the slip-off slope a talik has formed as a result of the insulating effects of very deep snow, the latter being instrumental in raising the mean annual surface temperature above 0°C. In this zone the vegetation is thus most important in its role of snow accumulator. 145 Chapter 6 CONCLUSIONS Although climate is basic to the formation of permafrost, this study has demonstrated that local factors are responsible for wide variation in permafrost conditions over a small area. Variations in ground thermal regime due to changes in surface conditions can occur over very short distances. About 50% of the area is covered by water bodies; over the remainder, vegetation shows a sequential distribution. Actively forming sections near river channels are bare of vegetation, willow and alder grow away from the rivers, and the inactive parts of the floodplain are populated by spruce. There is thus a variety of microclimates. The combined thermal influence of the large number of surface water bodies manifests i tself in thinner permafrost than observed on the nearby tundra (see Jessop 1970). Further, the permafrost of the Mackenzie Delta must be of a highly perforated nature, since permafrost is absent beneath the larger lakes and channels. It is estimated that in the absence of water bodies, permafrost would be about three-times thicker in the Delta. In addition to spatial variations, geomorphic and biological evidence shows that surface conditions are also changing with time. The study area contains a landform assemblage that is typical of the Delta environment. A major distributary undergoing lateral migration, is actively cutting into a frozen, mature, spruce-covered surface on 146 the outside bends of meanders, with consequent degradation of permafrost. New alluvium is deposited on slip-off slopes, and permafrost forms there ab init io . The progressive reduction in ground temperatures in the lee of river migration is partly related to the process of thermal recovery following the river disturbance, and partly a result of the insulating effect, of the developing vegetation. Superimposed on these two trends, however, is the permafrost degradation associated with the snowbank. The consistency of this interpretation of ground temperature variations was demonstrated through the framework of simple heat conduction theory. More specifically, the major conclusions of the study are as follows: 1) Temperature borehole data indicate that permafrost thicknesses on the order of 60-80 m are broadly representative for mature, spruce-covered areas. The greatest thicknesses are at sites most distant from water bodies; calculations show that the maximum thickness in the area is about 100 m (p.71), a value in good agreement with the data of Johnston and Brown (1964). 2) Permafrost is much thinner (less than 10 m) in areas of recently deposited alluvium. Values were determined from temperature boreholes and resistivity sounding. On the slip-off slope, temperatures de-crease and permafrost thickens with distance from the river. Perma-frost may be completely absent in places on the slip-off slope, with snow cover being the important factor (see below). 3) Observed temperature gradients are about three-times greater than provided for by the earth's geothermal gradient alone. The combined thermal effect of the water bodies in the area was shown to account for the difference. In the absence of this effect, permafrost would be about 170 m thick at spruce-covered sites. 147 4) The mean annual air temperature in this area is -9° to -10°C. Estimated mean annual ground surface temperatures range from +4.0°C (river bottom), +3.2°C (lakes), - 1 . 0 ° to -1.5°C (bare ground on slip-off slope), -3 .0°C (willow/alder association), to -4.2°C (spruce forest). Borehole temperatures at 15 m range from about +0.4°C to -3 .5 °C . 5) Through the framework of heat conduction theory, a consistent explanation of permafrost distribution in terms of local environmental factors was developed, and served to confirm the general validity of the hypotheses advanced in the present study. The calculated variations in permafrost distribution compare well with field measurements, and, in a qualitative sense, with that reported in the literature (Benninghoff 1952, W. G. Brown et al 1964, Pewe" 1965). The models further provide a means for predicting variations in the ground temperature field. 6) The heat conduction models can only be ultimately confirmed by obtaining ground temperature data from depths up to 60-80 m. 7) Application of the steady-state model to sites in stable areas yielded predicted results which are in excellent agreement with field observations. This indicates that, with a knowledge of mean annual ground-surface and water temperatures, and the earth's geothermal gradient, the ground temperature field can be reliably calculated using equations (7) and (8) (pp.59-60). A computer program was written for this purpose, and a listing is given in Appendix 2. Outlines of water bodies must be specified in digitised form, and the program can accom-modate any arbitrary shape. 8) For areas of geomorphic change, the steady-state model is not satisfactory. A simple, single-step transient model yielded a predicted river shifting rate in close agreement with that determined from actual measurements (p. 75). This model resulted in improved agreement between 148 observed and calculated ground temperatures behind the slip-off slope. 9) A further transient model was developed, using a temperature wave to simulate the river migration, and i t yielded satisfactory results. A listing of the computer program, based on equations (14) and (15) (p. 79), is given in Appendix 3. Using appropriate values for thermal diffusivity, shifting rate, and the temperature wave, i t yields satisfactory prediction of the thermal disturbance due to channel shifting. The deterioration in predicted values at distances away from the channel is thought to result from the failure to include the latent heat term in the equations. This cannot be incorporated in any simple way. 10) Al l the calculations carried out indicate that through-taliks exist beneath the river channel and the larger lakes. 11) Significant differences in seasonal regimes exist under the various types of vegetation. There is a general decrease in ground temperatures with increasing biomass. The importance of radiation differences between sites, in producing variations in ground thermal regime, was demonstrated It was concluded, however, that the presence of a surface organic layer at some sites is more instrumental in maintaining lower ground tempera-tures there. Removal of 10 cm of organic material at one site led to an increase of 3°C in the summer daily mean 10-cm temperature. 12) On the slip-off slope, variations in snow accumulation produce ground temperature variations greater than those resulting from the vegetation cover per se; vegetation here is more important in its role of snow accumulator. It is concluded that snow cover is a permafrost-controlling factor in this locality. Beneath the snowbank zone a talik has formed as a result of the insulating effects of deep snow. The longitudinal variation in this unfrozen zone was shown to be related to the extent of the snowbank itself . APPENDIXES 1 4 9 150 APPENDIX 1 Glossary of Terms Active layer Depth of zero annual amplitude Frost table Geothermal gradient The top layer of ground subject to seasonal freezing and thawing The depth to which seasonal temperature fluctuations extend into the ground. Beneath this, temperatures remain constant year-round The surface which represents the level, at any time in spring and summer, to which thawing of the seasonally frozen ground has penetrated (Stearns 1966) The increase of temperature with depth in the earth, due to the heat received from sources within the earth Pereletok Permafrost table Talik Through-talik Pseudo-talik Terrain segment Zero curtain effect A frozen layer at the base of the active layer which remains unthawed for one or two summers (Stearns 1966) The surface which represents the upper limit of permafrost An unfrozen portion within the body of perma-frost. It usually implies thawed ground that was probably permafrost at some time (Stearns 1966) A thawed zone that perforates the permafrost A thawed zone that does not perforate the perma-frost. The permafrost table is locally depressed, while an upward indentation is formed in the base of permafrost A portion of the surface area which can be characterised by a degree of homogeneity in its physical composition (nature of surface cover, topographic position) During autumn freezing of the active layer, latent heat of fusion is released, thereby impeding penetration of the freezing front. This causes temperatures below the frost line to remain near 0°C for quite some time, maybe many weeks—this is the period of zero curtain 151 APPENDIX 2 Computer program to compute steady-state thermal effect of water bodies C THIS PROGRAM COMPUTES DISTANCES AL0N3 RAYS FROM ANY BASE POINT C TO A SPECIFIED LA<E OR RIVER OUTLINE (OUTLINE IN DIGITISED FORM J £ US-ING THESE DIST-ANCE S—A-S—I-NP-U-t*—IT—T-HEJS-CO.MPJJ.TES_THE—T HERMA1 C EFFECT OF THE WATER BODY ON THE GROUND TEMPERATURES (AT ANY C DEPTHS} AT THAT BASE POINT C REF • LACHENBRUCH*-.1957! - U « S t G » S » - BULLETIN..* 1052-B C THE PROCEDURE IS REPEATED FOR ALL WATER BODIES IN THE AREA C AND THE TOTAL EFFECT SUMMED C A NY—NUMBER—-0 E-&ASE-P-G UiXS_CAN_B E A C C OHM 0 D AJ.EO IN A_5-LNQ L E-RLLN C C IN THE PROGRAM BELOW* THE OUTLINES ARE IN INCHES* WHILST THE C OUTPUT IS CONVERTED TO METERS AND <MS . _. . C DISTINCTION IS MAINTAINED BETWEEN LAKES AND RIVERS C IC-1 (LAKE) C- I-C*2 (R-UVXR4 : :  C C THE PROGRAM* AS LISTED* USES A LIBRARY ROUTINE (SOLVD) TO C SOLVE-A-PAIR OF SIMULTANEOUS EQUATIONS." T H E VARIABLES A* DET* TEST C ARE REQUIRED BY THIS PROGRAM C S.EAL_kAJ3S.DJ DOUBLE PRECISION A* DET* TEST DIMENSION A(2*3)*B(2*2)*Z(2*2)*T(10*10) IMENSION-R1(500)*R2(500)*X(200-)*Y(20.0)ARV1(50)*JRV2(50) ... M O N SSTEMP(20)*DTHETA(20)*D(20)#TTEF1(20)*TTEF2(20) COMMON RVl*RV2*Rl*R2*ID I F F * I S A M E * I L A K E * K C C : c ..... READ IN INPUT DATA c C IF- IAR-0* . LAKE- AREAS - ARE CALCULATEDF-IF IAR-1* THEY.ARE NOT. . . C KD-NUMBER OF DEPTHS FOR WHICH THE TEMPERATURE EFFECT IS TO BE C CALCULATED C -LABD-A«XHE—A-NGLE U-fcUDEGREES ) BY_kH-IC-H—T-HE—R A X S _ A R E _ I N C R E M EN I E D . C SCALE»SCALE OF BASE MAP (RATIO FORM) R E A D ( 5 * 1 0 ) I A R * K D * L A M B D A * S C A L E 1 0 F O R M A T ! I I * I 2 * F 2 » 0 * F 6 » 0 ) S C - S C A L E / 3 9 . 3 7 0 1 C D U J - T H E D E P T H S F O R W H I C H T HE T E M P E R A T U R E E F F E C T I S C A L C U L A T E D READ-15+-1-14 ( D L K - U X - « ^ » J C D J 1 1 F 0 R M A T ( 2 C F 3 » 0 ) C R E A D I N T H E B A S E P O I N T « I » D « ' C O O R D I N A T E S ) — 1 R E A D t - 5 j - 1 3 j - E N D - a 3 Q O ) I DM2^-XQJLYJQ : 1 3 F O R M A T ( I 3 / 2 F 1 0 . 5 ) R E W I N D 8 A N G L E — « _ L A j a B D A./-3. 6-QJ R A D L A M - L A M B D A * . 0 1 7 4 5 I T 0 T - 1 8 0 . 0 / L A M B D A W R I T E ( 6* 1 0 2 0 ) I D N 2 . J X 0 J J * 0 — 1 0 2 0 F O R M A T ! 1 H 1 / 2 5 X * » * * 3 E 0 T H E R M A L F U N C T I O N I S T E A D Y - S T A T E ) t S I T E S « J I 3 * U X * ' t X 0 » » j F 6 . 2 * • Y 0 » ' i F 6 . 2 * » ) * * • ) W R l X £ - ( 4 4 - 1 0 3 . 0 ) I D-t-JCLi . X P-U.iCDJ . 1 0 3 0 F O R M A T ( / / I O X J i Z ' 1 1 5 X * 1 0 I F 5 • l » 5 X ) ) D O 1 1 1 K - l ' K D T T E F 1 ( K ) " 0 • 0 „ . . 1 1 1 T T E F 2 ( K ) " 0 . 0 2 K I - 1 ic.au Mi«fl I N K - O I N U M - 1 J l - 0 __ . K C - 5 0 0 C D I G I T I S E D O U T L I N E S A R E R E A D I N F R O M U N I T 8 C E N D O F A N Y O U T L I N E I N D I C A T E D B Y Qj_Q QJJQ C ..... R E A D I N L A K E O U T L I N E 3 I L - I K I - 1 ) * 7 + l I U « I L * 6 . -R E A D ( 8 , 1 2 * E N D - 8 5 0 ) I D N 1 * l Z » < X ( I ) * Y ( I ) » I - I L * I U > 1 2 F 0 R M A T ( I 3 i I l < l * F 5 « 2 > D O h J ^ I L ^ D J : I F ( X ( J ) » N E « 0 . 0 ) 3 0 T O 4 I F ( Y ( J ) . E Q . O . O ) QO T O 5 - -~ »t C O N T I N U E ...... - .- - --I C D U N T o I C O U N T + 7 K I - K I + 1 G O _ i o _ a 5 I C O U N T = I C O U N T + ( J - I L ) ..... Z E R O O U T A R R A Y S D O 6. J B I J K D -6 S S T E M P I J I - O . D O 8 J » 1 J K C R.U.J-L*-OJ 8 R 2 ( J > » 0 « K C - 0 Y 1 » Y ( 1 ) _ X 1 « X ~ ( 1 ) Y 2 « Y I 2 ) X 2 = X - t - 2 - ) — F I N D S L O P E OF B A S E L I N E .... . - C H E C K — T - O — S E E - - I F - T H E — S L O P E - - I S — I-NF-1N I T E — 1 V E O X l - X O I F I V E C I ' E Q . O . O ) G O T O 2 0 S L O R £ 4 » 4 - T 4 - " 0 W - W V 4 C 1 D I V » S Q R T ( l . t > S L O P E l * S L 0 P E l ) C 0 N » Y 0 - X 0 * S L 0 P E 1 C Y » 1 . -Q O T O 2 2 2 0 C Y " 0 . S L O P i E J f l * C O N - X O V E C 1 - Y 1 - Y 0 2 2 C O N T I N U E R V 1 ( 1 ) » S Q R T ( ( Y l - Y 0 ) * ¥ 2 + ( X l - X 0 ) * * 2 > I D I F F - 0 I S A M £ " - 1 : ..... C H E C K FOR T A N G E N T C O N D I T I O N ..... S I G N 1 » Y 2 * C Y - S L O P E 1 * X 2 - C O N S I G N 2 - Y I I C O U N T ) * C Y - S L O P E l * X l I C O U N T ) - C O N -I F < S I Q N 1 1 3 0 * 3 2 * 3 4 3 0 I F ( S I G N 2 ) 3 6 * 3 8 * 3 8 3 2 IF-i-S I Gisi2-l38-i-36.jj-3 8 : 3 4 I F ( S I G N 2 ) 3 8 * 3 8 * 3 6 3 6 I S A M E - I S A M E + 1 R V 1 ( I S A M E ) » R V 1 ( 1 ) C C . . . . . F I N D O T H E R I N T E R S E C T I O N P O I N T ( S ) 3-8-CO NXIiNU E DO 1 0 0 > 2 J I C Q U N T X I » X ( I ) Y I - Y J I > -X I P « X ( I - l ) Y I P = Y ( I - l ) S- I G N « Y I » C Y - S L O P E H r X l - C O N . S I G N - S I G N / D I V C • • • • • T E S T F O R C H A N G E O F S I G N IF-LS.I&N) 4 0 * 6 0 * 5 0 4 0 J 2 » l I F ( J 1 . E Q « J 2 ) GO TO 1 0 0 I F - U - U S Q t Q ) GO TO 10.0 GO T O 5 4 5 0 J 2 - 2 1 F { J 1 . E Q « J 2 ) - G O — T O - 1 0 0 I F I J L E Q ' O ) GO To 1 0 0 C • • • • • S E T UP T H E TWO E Q U A T I O N S AND F I N D I N T E R S E C T 5 4 A < 1 * 1 U C Y A ( 1 * 2 ) - - S L 0 P E 1 A t 1 * 3 ) > C 0 N . C • • C H E C K T 0 S E E. I F T H E . S L O P E . .IS I N F I N I T E • X T - X I - X I P I F ( X T » E Q » C « 0 ) GO TO 5 6 SLO-P-E2a-( Y I - Y I P L ^ X I -A ( 2 J 1 ) a 1 • A ( 2 * 2 ) - - S L 0 P E 2 A ( 2 * 3 ) « Y I - S L 0 P E 2 * X L . . . _ Q O T O 5 8 5 6 A t 2 * 1 ) « 0 « _Al2i2J.-lj '. -A ( 2 * 3 ) » X I 5 8 C A L L S O L V D l A * 2 * 2 * 3 * 0 . 0 D 0 * D E T * T E S T ) - Q O T O 7 0 -6 0 Z ( 1 * 1 ) - Y l Z ( 2 * l 1 - X I . . j _ t» C H E C K F O R T A N G E N T C O N D I T I O N » • » • • I F A T A N G E N T * R V A L U E I S I G N O R E D S I G N 1 - Y I P * C Y - S L O P E 1 * X I P - C O N I F ( I . E Q « I C O U N T ) GO T O 6 2 S I G N 2 - Y ( 1 + 1 > # C Y - S L 0 P E 1 * X ( I + l ) - C O N G O T O 6 3 6 2 _ S I G N 2 - i - Y - l A C X ? - £ L 0 P E 1 » X 1 - C O N 6 3 I F t S I G N l 1 6 * * 6 5 * 6 6 6 4 I F ( S I G N 2 > 1 0 0 * 7 0 > 7 0 6 5 I F ( S I G N 2 ) 7 0 * 1 0 0 * 7 0 6 6 I F ( S I G N 2 « G T » 0 . 0 > G O T O 1 0 0 7 0 Z ( 1 * 1 ) » A ( 1 * 3 ) Z - L 2 * - U « A - t 2 * 3 - ) V E C 2 « Z ( 2 * 1 ) - X 0 R - S Q R T ( ( Z < l * l ) - Y 0 ) * * 2 + V E C 2 » V E C 2 ) C t ^ j j _ t _ C H E C K T O S F E I F T H I S V E C T O R I S I N T H E S A J l E _ J ) I R E C T l O N A S T H E B A S E V E C T O R I F ( V E C 2 » E Q « 0 . Q ) V E C 2 « Z ( 1 * 1 ) - Y 0 V-SIGN«VE-C1^V-£C2 I F ( V S I G N . G T » 0 . 0 ) GO T O 8 0 I D I F F - I D I F F + 1 R V 2 ( I D I F F ) « R - - - -G O T O 1 0 0 8 0 I S A M E - I S A M E + 1 R_V 111S A MEJ J LR 1 0 0 J 1 - J 2 C IS THE BASE POINT WITHIN THE LA<E OUTLINE? C IF IDIFF IS > Oi AND ODD* THE BASE.POINT IS INSIDE C THE LAKE • • • • • INOEX"MOD(IDIFFJ 2 ) 1 COUNT--1 CO-UN** 4 X(ICOUNT)»X1 Y(ICOUNT)»Yl C - - -C C O M P U T E I N T E R S E C T I O N S F O R O T H E R R A Y S C -C C . . . . . F I N D A N G L E O F B A S E L I N E C T H E T A B A T A N - ( S L O P E D ISUM-i K - i C C • • • • • C H E C K W H E T H E R T H E L A S T RAY I N T E R S E C T E D T H E L A K E • • • • • 2 0 0 I F ( I N U M ' E Q . O ) GO TO 2 1 0 I F ! I N D E X . G T » 0 ) G 0 T O . 2 0 4 C A L L E X S O R T GO TO 2 0 5 2 0 4 CALL I N S O R T 2 0 5 C O N T I N U E C F I N D NEW S L O P E AND E Q U A T I O N FOR S U C C E S S I V E R A Y S I N R - 0 I F ( I L A K E « E Q « 1 ) GO TO 2 3 5 £ . . . . . I S T H I S T H E F I R S T OR S F C O N O G R O U P OF R A Y S . » • « . I F I I N K . E Q . O ) GO TO 2 2 0 I K - - 1 I-IVUM--0 GO TO 2 3 0 C I F T H E P R E V I O U S RAY WAS T H E L A S T TO I N T E R S E C T T H E L A K E _ c GO.T.O_.THE...AEXJ P A ST_.QE_ T.H E . C 0 MPU.TAT 1 0 N. 210 IF(INK.EG'1) Q0 TO 555 I K = -< ... INK-1 . . . _ 30 TO 230 220 IK-1 1 NUM*0 230 ISUM-ISUM+1 IFIISUM»QT.ITDT) SO TO 555 - T H E T A » T H L T A + ( RADLAM*FLOATdK) ) 00 TO 236 235 ISUM»ISUM+1 IF4-ISUM-«-G-T-t-I-T0T ) 30 TO 555 THETA»THETA+RADLAM CHECK TO SEE I F THE SLOPE IS INFINITE -236- I F ( ABS ( SIN ( T H E T A .L) • E Q .1* L_Q OL_T 0_2 40 , SLOPE-TANITHETA) DIV-SQRTIl.+SLOPE*SLOPE) CQN*Y-C--XC.*SLC-P.E CY«1» GO TO 250 _240--CY»0. SLOPE»-li CON-XO R5£L-Z.Q NIINJJ E S E T VALUE OF J l . » . » • SIGN"Y1*CY-X1*SL0PE-C0N SIGN-SIGN/DIV : IF(SIGN»GT.O.) GO TO 260 J l - 1 GO—T0_2-7_Q 260 Jl-2 270 CONTINUE THDEG»THETA/0.01745 - . FIND INTERSECTS FOR EACH NEW RAY DO 500 I»2*1C0UNT XI"X( I ) y-i-g-Y 11) XlP«X<i-i) YIP"Y( 1-1 ) S L S MnJLI J L C X ^ X I » S L 0 P E <L0jj SIGN-SIGN/DIV C TEST F O R CHANGE OF SIGN • IFISIGN)300*340J31-0 300 J2»l IF(Jl.EQ'O) GO To 400 I-F4-J2-*EQJLJI ) GO TO 500 :  GO TO 320 310 J2«2 1F(Jl•EQ•0) GO To 400 IF(J2.EQ«J1) GO TO 500 C SET UP THE TWO EQUATIONS AND FIND INTERSECT £ CHECK TO SEE IF THE SLOPE IS INFINITE >n'J 320 XT=XI-XIP IF(XT.EQ»0»O) GO TO 325 SL0PE2-(YI-YIP)/XT- , — . A(2il)•!• A(2J2)»-SL0PE2 Al-2 J-3-LB-Y >SL0PE2»XI GO TO 330 325 A(2J1)-0. A(2J2)B1* Ai2i3)>XI 330 A(ii 1)-CY A l l J_2_li»3UiJP_E :  A(li3)»C0N C A L L SOLVDIA,2J2•3>0•ODO,DET>TEST> GO TO 350 340 INUM-I Z ( 1 # 1 ) - Y I ZX2.#.1.1«XL J2«0 CHECK FOR TAN3ENT CONDITION • - - - IF A TANGENT* R VALUE.IS IGNORED -SIGNl-YlP*CY-SLOpE*XlP-CON SIGN2«Y ( I + l )*CY-SLOPE*X( I-+1 )-CON -I-P-J-SIG M->342>344>34 6 342 IFlSIGN2)400>350,350 34* IF(SIGN2)350*400,350 SIGN2-»-QT-J-0 t 0 ) GO T-O—4&Q 350 Z( If 1)-A(1*3) Z(2*l)-A(2*3) R»SQ5T-UZX1<-L) - YO ) *+ 2 + ( ? ( 2* 1) -XO ) »»g ) 358 IF( INR.EQ.1) GO TO 360 VEC1«Z(2*1)-X0 IF(VEC1.EQ.0»0) VEC1-Z(lil)-Y0 RV1(1)-R ISAME«1 INR*1 : . : . INUM-1 GO TO 400 -360-VEC2«Z.(2ill-XQ IF(VEC2»EQ»0.0) VEC2-Z11*1)-YO VSIGN-VEC1/VEC2 ^.tJ_I_CHE-CK TO SEE IF THIS VECTOR IS IN Tii£_SAflE-QXRECTIQM AS THE BASE VECTOR ••••• IF(VSIGN.GT'O.O) GO TO 370 IDIFF-IDIFF + I -RV2IIDIFF1-R GO TO *00 3-7JD_ISAME»ISAMEAl : RV1(ISAME)-R 400 Ji«J2 500 CONTINUE . K = K + 1 GO TO 200 555-CON.T.INUE . ICQUNT-ICOUNT-1 C C CONVERT.. DISTANCES TO REAL. UNITS • • • •. DO 600 J-liKC Rl(J)«Rl(J)*SC 600 R2iJJ-PR21JJJLSC C C COMPUTE THE AREA OF THE WATER BODY IF(IAR*EQ*1) QQ TO 680 C0NST»SCALE*2.54E-5 C0NST»C0NST*C0NST S-UM<U : Xi«X(l) Yl-YI1) X -SXARXaX i YSTART-Y1 DO 620 J«2JJ ICOUNT IF-UC-UL) t N E » O t ) QQ TO 61Q IF(Y(J)«EQ«0.) QO TO 630 610 SUM«SUM+(Yl-Y(J))*<X1+X(Jl) _._ X1 - X I J\ 620 Y1»Y(J) 630 SUM«SUM+(Y1-YSTART)*(Xl+XSTART) SUM"ABS< SUM»QJ_5J AREA»SUM*CONST 680 CONTINUE "c ..... COMPUTE THEF FUNCTION FOR"EACH DEP T H C DO 710—tO»l+KP DK»1»0/D(K) DO 700 J-l/KC RAT 101"1•/(SQRT(1••(RI(J)*DK)**?)_.) RATI02»1«/(SQRT(1» + (R2(J)*DK)**2) ) SSTD-RATI01-RATI02 700 SSTEMPt K ) «SSTEMP ( < ) + SSTD 7 1 0 C O N T I N U E DO 7 2 0 K » 1 * K D 7 2 0 - S S T E M P ( K ) » S S T E M P ( X ) • A N G L E . - _.. ~ C A S S I G N V A L U E S TO A P P R O P R I A T E S U B - T O T A L I F ( I C » E Q » 2 > GO To 7 3 0 D.0_225_-K"1J.XD 7 2 5 T T E F 1 ( < ) » T T E F 1 ( K ) + S S T E M P ( K ) GO TO 770 7 3 0 - C O N T I N U E - - -DO 7 3 5 K»l*KD 7 3 5 T T E F 2 ( K ) " T T E F 2 ( K ) + S S T E M P ( K ) 7J74^0I^-I-NUE 3 0 0 W R I T E I 6* 1 0 4 0 ) I D N 1 * I S S T E M P ( < ) t K - l * < D ) 1 0 4 0 F O R M A T ( / / 5 X * 1 F < L A K E 5 • * 1 3 * ' ) « t 7 X * 1 0 ( F 7 . 6 * 3 X ) / ) I F ( I A R . E Q » 0 J W R I T E ( 6* 1 0 1 0 ) A R E A 1 0 1 0 F O R M A T { / 2 X J ' A R E A • ' * F 5 . 2 * ' SQ K M S ' ) C GO TO T H E N E X T L A K E GO TO 2 8 5 0 W R I T E ( 6 * 1045) 1045 F O R M A T ( / / 2 X i W R I T E ( 6 * 1 0 4 4 ) ( T T E F ( K ) t K " l * K D ) 3JJMf_F-0RMAJ4-U<0*-2-4-XJ-1UXF7 . 6 J 3X-L) C GO TO T H E N E X T B A S E P O I N T GO TO 1 9 0 0 W R I T E I 6 * 1 0 6 0 ) - . . . 1 0 6 0 F 0 R M A T ( / / / * 4 0 X i T H I S IS T H E L A S T B A S E P O I N T C STOP : ENO S U B R O U T I N E I N S O R T D I M E N S I O N R V 1 ( 5 0 ) i R V 2 ( 5 0 ) i R l ( 5 0 0 ) , R 2 ( 5 0 0 ) C 0 M MON__R V L l i - R V 2 jRljJiZjJIlllFlJJLSAhEu ILk&Z.iJUL I L A K E - 1 I F ( I S A M E ' E Q ' 1 ) QO TO 1 2 5 C A L L S S 0 R T ( R V 1 J I S A M E ) _. M - I S A M E - 1 DO 1 0 I = 1 * M * 2 K C » K C * 1 R 2 ( K C ) » R V 1 ( I ) 1 0 R I 1 K O - R V 1 ( I + l ) 1 2 - K C » K C + i — R i l K O - C O R 2 ( K C ) » R V 1 ( I S A M E ) I S.A ME«.Q I F I I D I F F » Q T » 0 ) 3 0 TO 1 5 R E T U R N -15- I F ( I D I F F J E Q ' - 1 ) — Q O — T - 0 - 2 2 C A L L S S 0 R T ( R V 2 J I D I F F ) M - I D I F F - 1 0.0-2 0_X MU-IU-Z K C - K C + 1 R 2 ( K C ) » R V 2 ( I ) 2 0 - R l ( K C ) - R V . 2 1 I t l - l 2 2 K C » K C * 1 R 1 (KC ) " 0 • 0 R . 2 1 K C l . R V g t I D I F F ) I D I F F - 0 R E T U R N END-SUBROUTINE EXSORT D I M E N S I O N R V 1 ( 5 0 ) * R V 2 { 5 0 ) J R 1 ( 5 0 0 ) J R 2 ( 5 0 0 > C 0 M mO N-R-V-l *R V-2 * R - 1 ^ 2^-DXFF_*4 - S J ^ £ J _ I L A X £ J-K-C ILAKE«0 5 C A L L S S O R T ( R V l i l s A M E ) M-ISAME-1 DO 10 I"1*M*2 KC=KC+1 R24-KC-U-RY-U-I-) 10 RI ( K O - R V l ( 1 + 1 ) ISAME-O — - I F {IDIFF...i QT»0 ) S0 TO 1 5 RETURN 15 C A L L S S 0 R T ( R V 2 i l D l F F ) M «I-D-IF F-*-l DO 20 > 1 * M * 2 KC"KC+1 R2(KC)«RV2( I-) 20 R 1 ( < C ) « R V 2 ( I + 1 ) I D I F F - 0 RETURN END SUBROUTINE SSORT t ARRAY* N) D I M E N S I O N A R R A Y ( 5 0 ) NN*N«1 DO 10 I»1*N 00 13 J " 1 * N N 1F ( A R R A V- ( J ) • G E-.-A R R A Y-l-J • 11-)- G O — T -0-13 T 1 « A R R A Y ( J ) A R R A Y ! J ) " A R R A Y ( J + l ) A RRA-Y-tJ*U-*-Hl _ 13 CONTINUE 10 CONTINUE RETURN ... . END 165 APPENDIX 3 Computer program to compute thermal effect of a shifting river T H I S P ROGRAM C O M P U T E S T H E GROUND T H E R M A L E F F E C T O F A S T R I P - S H A P E D D I S T U R B A N C E ON T HE S U R F A C E ( E • G • A R I V E R ) .1N—TH I S V E R S I O N * T-HE.-R LY.£R_lS_ALLfl W E 0_TO_MI.GSA.TE-. A CR OSS_T.HE._SUREA.C E AND T H E T H E R M A L D I S T U R B A N C E I S C A L C U L A T E D A C C O R D I N G L Y . T H E S H I F T I N G R I V E R I S S I M U L A T E D BY A T E M P E R A T U R E WAVE* W H I C H I S F O R M U L A T E D TO I N C L U D E T H E E F F E C T S O F V E 3 E T A T I O N S U C C E S S I O N * T H E FORM O F T H E WAVE I S S P E C I F I E D BY T H E A R R A Y "A* • A C O M P A N I O N A R R A Y " T I M E " P R O V I D E S I N F O R M A T I O N ON T H E R A T E AT W H I C H T H E T A I L O F X H E-W A V E - C H A N G E-S_W.IXR_THE_V.EG E T AJ.IO N _ S U C.CES S I A N J . . . 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(/); in ui u CJ to o cn a. _ UJ in T LL »— in —• ru 1^ •» —• x X ~* sc -— o X -x i X o rt O O •rt n <u x mi x •» »-« «-« _ «U — _ —j — I »-! O lil < U l 4 »-• rr n o d o _ o ore* : J *o o oi o : ru ru a. o o i — z in ui o SUBROUTINE WARM(XSIJTIMi) COMMON TSHIFT IF- IX S1 A Q ELi.120 _ 0 S Q__a__.Q TlMl»9999i0+XSi*(TSHIFT/10»0) RETURN 10 IFtXSl.QE.240.0) 30 TO 20 . TIM1-12«0*TSHIFT RETURN 20-T-I Ml ».(XSHIT_T-*l-L»-OJ_-l .XSi-___tOL)j__^.I__/J.a » RETURN END 170 APPENDIX 4 Monthly ground temperatures at five microclimatic sites (1/9/69 - 1/7/71) 171 Site 1 (Bare ground) Depth (m) 0.5 1.5 3.0 6.0 9.0 12.0 1/9/69 6.0 -0.2 -0.5 -0.4 0.1 0.2 1/10/69 0.5 -0.1 -0.5 -0.3 0.1 0.2 1/11/69 -1.1 -0.7 -0.4 -0.2 0.1 0.1 1/12/69 -2.7 -1.3 -0.4 -0.2 0.1 0.1 1/1/70 -4.3 -2.2 -0.6 -0.2 0.1 0.1 1/2/70 -6.1 -3.4 -1.0 -0.4 0.1 0.1 1/3/70 -7.9 -4.0 -1.3 -0.5 0.1 0.1 1/4/70 -7.2 -4.5 -1.9 -0.6 0.1 0.1 1/5/70 -4.6 -3.8 -2.5 -0.7 0.1 0.1 1/6/70 -1.6 -2.2 -2.5 -0.8 0.1 0.1 1/7/70 3.1 -0.8 -1.8 -0.8 0.1 0.1 1/8/70 7.8 -0.3 -1.0 -0.6 0.0 0.1 1/9/70 8.0 -0.1 -0.8 -0.5 0.0 0.2 1/10/70 0.3 -0.1 -0.7 -0.5 0.0 0.2 1/11/70 -1.6 -0.5 -0.6 -0.5 0.0 0.2 1/12/70 -3.0 -0.9 -0.5 -0.5 0.0 0.2 1/1/71 -4.4 -1.5 -0.5 -0.5 0.0 0.2 1/2/71 -5.9 -2.1 -0.6 -0.5 0.1 0.1 1/3/71 -7.3 -2.8 -0.6 -0.5 0.1 0.1 1/4/71 -5.7 -2.6 -0.9 -0.5 0.1 0.1 1/5/71 -3.0 -2.1 -1.4 -0.6 0.1 0.2 1/6/71 -0.2 -1.5 -1.8 -0.7 0.1 0.2 1/7/71 5.0 -0.9 -1.3 -0.8 0.1 0.2 Site 2 (Salix (1)) Depth (m) 0.5 1.5 3.0 6.0 9.0 12.0 1/9/69 5.1 2.4 0.6 0.0 0.0 0.0 1/10/69 0.8 1.7 1.0 0.0 0.0 0.0 1/11/69 -0.1 1.2 1.1 0.0 0.0 0.0 1/12/69 -0.7 0.6 1.0 0.0 0.0 0.0 1/1/70 -1.2 0.2 0.8 0.0 0.0 0.0 1/2/70 -1.7 -0.1 0.5 0.1 0.0 0.0 1/3/70. -2.1 -0.4 0.1 0.1 0.0 0.0 1/4/70 -2.1 -0.6 -0.1 0.0 0.0 0.0 1/5/70 -1.7 -0.6 -0.1 0.0 -0.1 . 0.0 1/6/70 -0.9 -0.6 -0.2 -0.1 -0.1 0.0 1/7/70 4.8 -0.3 -0.2 -0.1 0.0 0.0 1/8/70 6.1 -0.1 -0.1 0.0 0.0 0.0 1/9/70 6.1 -0.0 -0.1 0.0 0.0 0.0 1/10/70 1.5 -0.0 -0.1 0.0 0.0 0.0 1/11/70 0.0 -0.1 -0.1 0.0 0.0 0.0 1/12/70 -0.4 -0.1 -0.1 0.0 0.0 0.0 1/1/71 -0.6 -0.1 -0.1 0.0 0.0 0.0 1/2/71 -0.9 -0.1 -0.1 0.0 0.0 0.0 1/3/71 -1.2 -0.1 -0.2 0.0 0.0 0.0 1/4/71 -1.0 -0.1 -0.2 0.0 0.0 0.0 1/5/71 -0.5 -0.1 -0.1 0.0 0.0 0.0 1/6/71 0.0 -0.1 -0.1 0.0 0.0 0.0 1/7/71 3.5 -0.1 -0.1 0.0 0.0 0.0 Site 3 (Salix(2)) 1/9/69 1/10/69 1/11/69 1/12/69 1/1/70 1/2/70 1/3/70 1/4/70 1/5/70 1/6/70 1/7/70 1/8/70 1/9/70 1/10/70 1/11/70 1/12/70 1/1/71 1/2/71 1/3/71 1/4/71 1/5/71 1/6/71 1/7/71 0.5 1.5 4.1 -0.2 0.3 -0.2 0.5 -0.2 1.1 -0.2 1.9 -0.3 2.8 -0.5 3.8 -0.6 3.7 -0.7 3.0 -0.9 1.5 -0.9 4.0 -0.7 5.3 -0.4 5.9 -0.3 1.2 -0.2 0.2 -0.2 0.7 -0.2 1.3 -0.2 2.0 -0.3 2.7 -0.3 2.4 -0.4 1.6 -0.4 0.9 -0.4 3.3 -0.4 Depth (m) 3.0 6.0 0.0 -0.2 0.0 -0.2 0.0 -0.1 0.0 -0.1 0.0 -0.1 0.0 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -0.1 0.0 -0.1 0.0 -0.1 -0.1 0.0 -0.1 9.0 12.0 -0.2 -0.2 -0.2 -0.2 -0.2 -0.2 -0.2 -0.2 -0.2 -0.2 -0.2 -0.2 -0.2 -0.2 -0.2 -0.2 -0.2 -0.2 -0.2 -0.2 -0.2 -0.1 -0.2 -0.1 -0.2 -0.1 -0.2 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 -0.2 -0.1 -0.2 -0.1 174 Site 4 (Salix-Alnus) Depth (m) 0.5 1.5 3.0 6.0 9.0 12.0 15.0 1/9/69 1.1 -0.7 -1.7 -2.5 -2.3 -1.7 -1.4 1/10/69 0.1 -0.3 -1.3 -2.3 -2.2 -1.8 -1.4 1/11/69 -2.5 -0.8 -1.3 -2.2 -2.2 -1.7 -1.4 1/12/69 -5.0 -1.4 -1.2 -2.2 -2.1 -1.7 -1.4 1/1/70 -6.8 -2.8 -1.9 -2.1 -2.0 -1.7 -1.4 1/2/70 -7.9 -4.6 -3.1 -2.1 -2.0 -1.7 -1.4 1/3/70 -9.0 -6.4 -4.3 -2.2 -1.9 -1.7 -1.4 1/4/70 -8.6 -6.9 -5.0 -2.4 -2.0 -1.7 -1.4 1/5/70 -7.0 -6.5 -5.5 -3.0 -2.1 -1.7 -1.4 1/6/70 -3.5 -4.8 -5.3 -3.5 -2.2 -1.7 -1.4 1/7/70 -0.1 -2.4 -3.8 -3.6 -2.3 -1.7 -1.4 1/8/70 3.2 -1.3 -2.6 -3.2 -2.4 -1.8 -1.4 1/9/70 3.5 -0.9 -2.2 -2.8 -2.5 -1.8 -1.4 1/10/70 1.0 -1.1 -2.0 -2.6 -2.5 -1.8 -1.5 1/11/70 -1.5 -1.3 -1.7 -2.4 -2.4 -1.8 -1.5 1/12/70 -3.9 -1.6 -1.4 -2.2 -2.3 -1.8 -1.5 1/1/71 -5.8 -2.3 -1.7 -2.0 -2.2 -1.8 -1.5 1/2/71 -7.0 -3.6 -2.4 -1.7 -2.1 -1.8 -1.5 1/3/71 -8.2 -5.0 -3.1 -1.8 -2.1 -1.8 -1.5 1/4/71 -6.9 -5.7 -3.6 -1.9 -2.0 -1.8 -1.5 1/5/71 -4.6 -4.6 -3.9 -2.4 -2.1 -1.8 -1.5 1/6/71 -2.1 -3.7 -4.3 -2.9 -2.1 -1.8 -1.5 1/7/71 1.3 -2.0 -3.8 -3.1 -2.2 -1.8 -1.5 175 Site 5 (Picea) Depth (m) 0.5 1.5 3.0 6.0 9.0 12.0 15.0 1/9/69 0.5 -1.4 -2.6 -3.7 -3.5 -2.7 -2.5 1/10/69 -0.2 -1.1 -2.2 -3.4 -3.3 -2.7 -2.5 1/11/69 -2.8 -1.7 -2.1 -3.2 -3.2 -2.7 -2.4 1/12/69 -5.8 -2.4 -2.1 -3.0 -3.1 -2.7 -2.4 1/1/70 -7.6 -3.9 -2.8 -3.0 -3.0 -2.7 -2.4 1/2/70 -8.9 -6.0 -4.4 -3.3 -2.9 -2.7 -2.4 1/3/70 -10.2 -7.9 -5.8 -3.6 -2.8 -2.7 -2.4 1/4/70 -9.9 -8.4 -6.5 -4.0 -3.0 -2.7 -2.4 1/5/70 -8.3 -7.8 -6.8 -4.4 -3.1 -2.7 -2.4 1/6/70 -4.4 -6.2 -6.5 -4.8 -3.3 -2.7 -2.4 1/7/70 -1.1 -3.4 -4.8 -4.9 -3.4 -2.7 -2.4 1/8/70 0.8 -2.1 -3.7 -4.5 -3.5 -2.7 -2.4 1/9/70 1.6 -1.6 -3.1 -4.1 -3.7 -2.8 -2.4 1/10/70 -0.5 -2.0 -2.8 -3.8 -3.6 -2.8 -2.5 1/11/70 -2.7 -2.4 -2.4 -3.5 -3.4 -2.8 -2.5 1/12/70 -4.8 -2.7 -2.2 -3.2 -3.2 -2.8 -2.5 1/1/71 -6.6 -3.6 -2.4 -3.0 -3.1 -2.8 -2.5 1/2/71 -8.0 -5.2 -3.5 -3.1 -3.0 -2.8 -2.5 1/3/71 -9.4 -6.7 -4.7 -3.2 -3.0 -2.8 -2.5 1/4/71 -8.0 -6.8 -5.3 -3.4 -3.0 -2.8 -2.5 1/5/71 -5.2 -5.6 -5.5 -3.8 -3.1 -2.8 -2.5 1/6/71 -2.4 -4.6 -5.4 -4.2 -3.2 -2.8 -2.5 1/7/71 -0.3 -2.9 -4.7 -4.5 -3.4 -2.8 -2.5 176 APPENDIX 5 Calculation of Surface Heat Flux Values, using the Temperature-Integral Method The change in ground heat storage AQ, over some time interval At, can be calculated from the temperature distribution in the ground at the beginning and end of the period, and a knowledge of the ground heat capacity (or capacities) C, from the formula: AQ = / (CAT) dz (1) o where z increases with depth to Z q , the depth at which AT is zero. If the depth-variation of C is known, then, z i z 2 AQ = / C AT dz + / C AT dz (etc.) (2) Now, the change in heat storage must be equal to the difference in the heat flowing into the ground layer and that flowing out.* Therefore, AQ - QQ - Qz (3) o The surface heat flux density is then given by (Scott 1964) %,t = A Q / A t + Q z Q , t (4) Now, i f any freezing or thawing takes place during the interval At, equations (1) and (2) must include the latent heat term *(L.AX) (Scott 1964). Here, L is the volumetric latent heat, AX the thickness of the layer frozen or thawed; the plus sign is used when thawing occurs and the minus sign for freezing. Heat flowing into a layer is designated positive, and that flowing out negative. 177 For layered ground, the final equation becomes, Q Q j t = [E o° C . A T . A Z t L.AX] /At + Qz t (5) If the thermal conductivity at z is known, then, ' o o APPENDIX 6 l Net Radiation and Ground Heat Flux Data (ly day" ) at Five Microclimatic Sites (July-August 1970) Site 1 Site 2 Site 3 Site 4 Site 5 G Rn G R n G R n G R n i G R n 22/7 201.5 18.1 97.6 _ _ 23/7 294.5 25.0 137.8 7. 8 24/7 367.4 35.6 169.5 8. 8 25/7 336.0 27.2 146.1 26/7 293.3 21.7 165.2 9. 7 27/7 300.6 27.1 184.2 11. 2 28/7 382.0 31.7 198.5 10. 0 261. 1 29/7 381.8 34.0 219.0 12. 1 268. 8 30/7 115.1 9.4 92.2 104. 6 5 .3 31/7 246.9 20.8 147.6 184. 4 7 .9 1/8 136.1 11.7 117.7 121. 3 5 .9 2/8 231.1 15.6 178.0 180. 7 7 .4 3/8 119.3 — 107.2 106. 3 4 .3 4/8 248.1 21.3 218.6 206. 4 9 .0 5/8 313.1 28.8 272.2 239. 7 9 .5 6/8 197.1 16.4 .171.3 173. 6 _ . 7/8 277.8 25.1 232. 7 58.4 8/8 228.4 16.8 189. 8 48.1 9/8 222.6 15.3 180. 4 50.9 10/8 70.3 7.4 72. 2 22.4 11/8 76.9 -- 25.2 12/8 156.6 11.5 37.9 13/8 289.2 23.4 64.0 14/8 205.5 14.6 181.3 12. 0 52.6 15/8 290.3 20.6 236.0 14. 8 60.4 16/8 225.3 16.0 200.9 16. 5 43.1 17/8 211.3 14.3 -- 11. 5 46.2 18/8 265.0 20.2 230.1 14. 5 168.3 19/8 122.0 10.3 120.4 10. 7 107.8 20/8 262.3 19.7 223.8 12. 9 167.4 21/8 169.4 15.2 144.9 10. 1 131.5 22/8 -- 20.9 -- 11. 3 4.0 3.5 2.9 1.2 1.6 2.8 3.9 BIBLIOGRAPHY Anisimova, N. 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