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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 o f Georgia, 1968  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF Doctor o f Philosophy i n the Department of GEOGRAPHY  We accept t h i s thesis as conforming to the required standard  THE UNIVERSITY OF BRITISH COLUMBIA October  1973  In  presenting  this  an a d v a n c e d d e g r e e the I  Library  further  for  agree  in  at  University  the  make  that  it  partial  freely  permission for  this  representatives.  for  It  financial  is  gain  Department  Date  of  of  Columbia,  British for  extensive by  the  Columbia  shall  not  the  requirements  reference copying of  Head o f  understood that  written permission.  The U n i v e r s i t y o f B r i t i s h V a n c o u v e r 8, Canada  fulfilment  available  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 h i s of  shall  thesis  I agree and  be a l l o w e d  that  Study.  this  thesis  my D e p a r t m e n t  copying or  for  or  publication  without  my  ABSTRACT  Variations in ground temperature regime and permafrost distribution 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 permafrost 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. ii  Measurements of ground  temperatures, snow depths and ice cover were made in winter. Permafrost is generally perforated in nature, being absent beneath 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 consistent explanation of permafrost distribution in terms of local environmental 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 t h i s research and i n the preparation of t h i s t h e s i s , I have received help and encouragement from many sources. to thank my wife Pauline, who  acted very capably as f i e l d assistant, lab  assistant, reviewer and factotum, and who needed encouragement.  Foremost I wish  gave me continuous and much  Thanks also to Dr. J . R. Mackay, who  the i n i t i a l ideas from which this study developed, and who  suggested provided  continued and superior help and support during the fieldwork and i n the writing of the thesis. who  Grateful appreciation i s extended to Peter Lewis,  f i r s t introduced me to the area, and f o r his valued help i n the f i e l d  and i n discussion. work:  Thanks also to the people who helped me with f i e l d  Gerry A l l e n , Ian Chapman, Dave Dickins, B l a i r F i t z h a r r i s , Ronald  Good, Albert O l i v e r , and O l i v e r O l i v e r .  In Inuvik, I was most fortunate  to receive help and h o s p i t a l i t y from J u l i a n I n g l i s . The f i e l d work for t h i s study was  supported by the Geological  Survey of Canada and by research grants from the Department of Indian A f f a i r s and Northern Development and the National Research Council to Dr. J . R. Mackay, Department of Geography, University of B r i t i s h Columbia.  I would also l i k e to thank the Inuvik Research Laboratory,  p a r t i c u l a r l y John Ostrick, for the help that they provided.  Imperial  O i l Ltd., through G. Rempel, generously provided travel f a c i l i t i e s on occasions, and Gulf O i l cooperated i n d r i l l i n g a number of boreholes. Thanks also to D. K. MacKay, f o r 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. E l l i s also provided comments.  Dr. R.  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  1.  Introduction  2.  Background to the Present Study . 1. 2. 3. 4. 5.  3.  g  1  Permafrost i n the Mackenzie Delta The Thermal Effect of Water Bodies Permafrost Configuration and River Migration The Study Area The Present Study  . .  7 10 15 16 23  Experimental Design and Measurement 1. Areal Scale 2. Between-Site Scale 3. Around-Site Scale  4.  30 34 38  The D i s t r i b u t i o n o f Permafrost: Observed and Predicted 1. Major Features of Permafrost D i s t r i b u t i o n i n the Study Area 2. Ground Temperatures and Heat Conduction Theory . 3. Present Application o f Heat Conduction Theory . . 4. Summary  5.  39 49 65 88  Variations i n Microclimate 1. 2. 3. 4. 5.  6.  a  Introduction Annual Thermal Regime Summer Microclimate Winter Conditions Summary  92 93 104 123 142  Conclusions  144  Appendices 1. Glossary o f terms 2. Computer program f o r steady-state thermal effect o f water bodies 3. Computer program f o r thermal effect o f a shifting river 4. Monthly ground temperatures at five microclimatic s i t e s (1/9/69 - 1/7/71) . 5. Calculation o f surface heat f l u x values, using the temperature-integral method 6. Net radiation and ground heat flux data at f i v e microclimatic s i t e s (July-August 1970) . . . Bibliography  150 151 165 170 176 178 179  vi  e  LIST OF TABLES Table 1. 2.  Page Summary o f Climate Data f o r Selected Stations, N.W.T.  .  9  as a Function o f Time(t) and Thermal D i f f u s i v i t y ( a ) .  27  Depth of Penetration of a Temperature Disturbance  3.  River- and Lake-Temperature Data  42  4.  Permafrost Thicknesses for Spruce-Covered Areas . . . .  41  5.  Ground Temperatures Beneath a Cut Bank and a S l i p - O f f Slope  43  6.  Permafrost Thicknesses f o r S l i p - O f f Slopes  7.  Variation of Permafrost Thickness with Distance Away from River  . . . . . .  . . .  43  45  8.  Permafrost Thicknesses for Areas of Salix-Alnus . . . .  9.  Physical and Thermal Properties of Some S o i l Samples Calculations for Apparent D i f f u s i v i t y , using data from Boreholes #2-6 and #2-8 Theoretical Thermal Effect (°C) o f Lake #2 on Ground Temperatures at Various Depths at Site #6-3, as a Function o f Time Observed and Predicted Temperatures, Cut Bank Section .  65 68  Observed and Predicted Temperatures, with Transient Correction, f o r Boreholes on a S l i p - O f f Slope . . . .  74  Sample Calculations to I l l u s t r a t e Effects of Latent Heat Term on Depth of Freezing and Ground Temperature Calculations  87  Analysis of Variance - Active Layer Depths i n Five Terrain Segments (July 1970)  94  Characteristics of Five Microclimatic s i t e s  95  10. 11.  12. 13. 14.  15.  16.  vii  48  53 57  Table 17.  18. 19.  20. 21. 22. 23.  Page Analysis of Variance - Mean Daily A i r Temperatures at Five Microclimatic S i t e s : a) A l l days (July-August 1970) b) Sunny days (July-August 1970)  106  Analysis of Variance - Mean Daily Surface Temperatures at Five Microclimatic Sites (July-August 1970) . .  107  Analysis o f Variance: a) Minimum Daily Surface Temperature b) Maximum Daily Surface Temperature at Five Microclimatic Sites (July-August  1970) ". .  Ill  Analysis of Variance - Incident Light Values around Five Microclimatic Sites (July 1970)  114  Analysis of Variance - Mean Daily 10-cm Temperatures at Five Microclimatic Sites (July-August 1970) . .  116  Average Daily Net Radiation and Ground Heat Flux at Five Microclimatic Sites (July-August 1970)  119  . .  Mean Daily Maximum and Minimum 10-cm Temperatures at Sites 1, 2 and 3 (July-August 1970) . . . . . . . .  119  Analysis of Variance - Mean Daily 25-cm Temperatures at Five Microclimatic Sites (July-August 1970) . .  122  Analysis of Variance - Half-Hourly 10-cm Temperatures: a) at Three Microclimatic S i t e s : 1, 4, 5 (August 23-24, 1970) b) at Three Microclimatic S i t e s : 1, 2, 3 (August 25-26, 1970)  124  Analysis of Variance - Snow Depths: a) i n S i x Terrain Segments (March 1971) b) i n Three Terrain Segments (December 1970)  . .  127  27.  Snow Depths i n Five Terrain Segments (March 1970)  . .  128  28.  Snow Cover Characteristics Along Two Transects a S l i p - O f f Slope  24. 25.  26.  29.  30. 31.  Across 133  Outward Heat Flow From the Top-One-Meter Ground Layer at Sites on a S l i p - O f f Slope (December 1970 to March 1971)  137  Temperature Data from a Transect Zone, S l i p - O f f Slope  138  Through the Snowbank  Temperature Data from Snowbank Transects  viii  5 and 7 . . .  141  LIST OF FIGURES Figure 1.  2.  Page The Study Area - Location and Salient Surface Features  8  Diagrammatic Cross Section Through a S h i f t i n g Channel Area  19  3.  Temperature Borehole Network on a S l i p - O f f Slope . . . .  35  4.  Temperature Boreholes:  S l i p - O f f Slope Sites  40  5.  Temperature Boreholes:  Spruce-Covered Sites  40  6.  R e s i s t i v i t y Sounding Data, for Sites on S l i p - O f f Slopes 7. ' Details o f Permafrost Configuration Beneath a  44  S l i p - O f f Slope  47  8.  R e s i s t i v i t y P r o f i l e Across a S l i p - O f f Slope  9.  Material Characteristics of Some Sample Boreholes  10. 11.  12. 13. 14.  47 ...  Examples of Temperature--Depth Curves used f o r Calculation o f Apparent D i f f u s i v i t y Method o f Dividing a Given Surface Area into Sectors of C i r c l e s . (For summing the temperatures under the apex of each sector)  51  55  59  Steady-State Permafrost Configuration Under Rivers 30, 45, 60, 70, 80 and 100 meters Wide . .  62  Permafrost Regression, with Time, Under a River (100 m wide) . . . . . . . . .  63  Ground Temperatures and Permafrost D i s t r i b u t i o n Along a Cut Bank Transect (SYMAP)  70  15.  Computed Temperature F i e l d Under a Traverse Line . . . .  72  16.  Temperature Wave Simulating River S h i f t i n g  77  17.  Diagram to I l l u s t r a t e Sample Solution o f Transient Model  81  ix  Figure 18.  19. 20. 21. 22.  23. 24. 25. 26. 27. 28.  29. ,30.  Page Permafrost History Under a S h i f t i n g Channel: a) I n i t i a l Position b) Present-Day  83  Predicted Mean Annual Ground Temperatures i n the V i c i n i t y o f the Snowbank Zone, S l i p - O f f Slope . . . .  85  E f f e c t of River S h i f t i n g Rate on Magnitude of Thermal Disturbance  89  Ground Temperature Isotherms at Five Microclimatic Sites (September 1969-February 1971)  98  Calculated Values o f Average Daily Surface Heat Flux at Four Microclimatic Sites (April 1970A p r i l 1971)  103  Mean Diurnal Surface Temperature Regimes at Five Microclimatic Sites (July-August 1970)  108  Daily Radiation Totals f o r Five Microclimatic Sites (July-August 1970)  112  Mean Diurnal 10-cm Regimes at Five Microclimatic Sites (July-August 1970)  117  Mean Diurnal 10-cm Temperature Regimes at Two Sites i n the Picea Segment (July-August 1970)  . . . .  121  E f f e c t o f Snow Depth on the Temperature at the Ground Surface (March 1970) . . .  131  Temporal Variation o f One-Meter Temperatures at Ten Sites Across a S l i p - O f f Slope (August 1970July 1971)  135  One-Meter Temperatures Plotted Against Snow Depth at Ten Locations Across a S l i p - O f f Slope . .  135  Details of Permafrost Configuration Along Various Transects Across a S l i p - O f f Slope  140  x  LIST OF PLATES  Plates 1.  Page Study Area and V i c i n i t y (Portion of A i r Photograph A19946-13)  18  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 S l i p - O f f Slope (Bare Ground Segment)  33  Microclimatic S i t e s : a) Salix(1) b) Salix(2) c) Salix-Alnus d) Picea  96  2.  5.  6.  Snow Cover over Bare Ground on a S l i p - O f f Slope . . . . .  130  7.  Snowbank Zone on a S l i p - O f f Slope  130  xi  Chapter 1 INTRODUCTION Permafrost i s defined exclusively on the basis of temperature, and i s interpreted i n t h i s 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 i n one winter, remains frozen through the following summer, and into the next winter (p.14). This d e f i n i t i o n , therefore, includes the pereletok''" of other authors. Permafrost and associated phenomena were f i r s t comprehensively described i n 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, i n numerous volumes, by N.R.C. since 1959), and Dostovalov and Kudryavtsev (1968). The words "freezing" and "thawing", commonly r e f e r r i n g to the change of state between water and i c e , 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 s a l i n e , or i f i t contains no moisture at a l l .  In most s o i l s , and e s p e c i a l l y those with a clay f r a c t i o n ,  substantial amounts of water, i n the l i q u i d phase, can p e r s i s t at temperatures below 0°C (see P. J . Williams 1967).  Ice i n permafrost can occur  as coatings, grains, v e i n l e t s , or massive beds; i n unconsolidated  A glossary of terms i s presented i n Appendix 1  2 materials i t often acts as a cementing agent, making the material rocklike. It has become common to divide permafrost occurrence into two broadly geographical zones, continuous and discontinuous.  In the  continuous zone, permafrost i s present everywhere beneath the surface, except perhaps under large water bodies whose mean annual is above 0°C.  temperature  It i s normally continuous to i t s lower surface, and may  reach a thickness of hundreds of meters.  Continuous permafrost i s more  formally defined by a temperature o f -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 s i t e s , under favorable l o c a l environmental conditions, permafrost may not be present, although nearby i t may s t i l l be quite thick. discontinuous.  Under these conditions the permafrost i s said to be The general pattern of d i s t r i b u t i o n i n Canada has been  mapped by R. J . E. Brown (1967). Many studies have been concerned with the q u a l i t a t i v e effect o f differences i n climate, vegetation, topography, geology and hydrology on the d i s t r i b u t i o n of permafrost.  Although obviously basic to a general  understanding of the problem, such an approach cannot provide s p e c i f i c information on the local configuration of permafrost, which depends on that set of processes c o n t r o l l i n g 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 d e t a i l s of permafrost configuration, can be resolved only by geothermal investigations. with the point of view expressed by Kudryavtsev  The writer agrees  (1967) :  Only concrete studies of frozen layers, t h e i r d i s t r i b u t i o n , occurrence, structure and composition, i n r e l a t i o n to the general complex of the geologic-geographic s i t u a t i o n can y i e l d f u l l - v a l u e i n i t i a l material for general t h e o r e t i c a l 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 i t 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 interrelationships 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 groundwater circulation in the development of taliks beneath water bodies (for example, see Efimov 1964; Mel'nikov 1964; Romanovskii and Chizhov 1967). Although measurements of " f i l t r a t i o n 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 permafrost 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 environment.  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, d r i l l i n g , 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) ii)  iii)  the presence of natural features such as lakes and rivers] a region in which the thermal properties of the surface cover are appreciably different from those characteristic of the area in general; 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, i t is concerned with permafrost dynamics in an area of geomorphic 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  i n the Mackenzie Delta  The Mackenzie Delta i s a low, f l a t area, covering more than 13,000 km^,  spotted with thousands of lakes, and dissected by an  i n t r i c a t e anastomosing network of several large channels and numerous smaller winding channels.  The channels r a r e l y meander, i n the  geomorphic sense, although they may  be sinuous, and they do wander  (Mackay 1963, p. 105) . The present study was  carried out i n 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 i n the study area has been investigated by G i l l  (1971).  The climate of t h i s part of the Delta  i s t r a n s i t i o n a l between a r c t i c and subarctic (see Table 1 for some relevant climatic data): The coastal portion of the Mackenzie Delta area l i e s i n the a r c t i c , the southern portion i n the subarctic...Aklavik and Inuvik are i n the subarctic...The location of Reindeer Station i s t r a n s i t i o n a l . (Mackay 1963, p. 153) R. J . E. Brown (1967) uses the 17°F  (-8.3°C) mean annual a i r isotherm  to delimit the region of continuous  permafrost.  have mean annual a i r temperatures below 17°F  Aklavik and  (Table 1).  conform to the broad geographical patterns of permafrost the region would thus be included i n the continuous 7  zone.  Inuvik  Were i t to distribution, However,  8  Figure 1 THE STUDY AREA - LOCATION AND SALIENT SURFACE FEATURES  II y  I  ?. ?.  ?..°  iniiiiii ?. ?. ?. ?. ?.  ?. ?. ?,  Ililig.lil§5l3  .=>.  fl  .°. ?.  p. p.  ?. P. p. p. P. p.  11111 s 11 y  i ° = «• •? <=• = = =•=• = <?  ~  '  ° - =' s =  1 7  1  s  = ».-!• '777"  7 7 "  I I I I  1.8  -16.5  o6 dd™W  i l l s  ii  -23.3  II  7  3  5.5  10.4  1  2  »  t  z ?. ?  2: s s : ? s i s S 5 i  •? * °! " ~: 7 °  2  II  1.9  4.5  9.4  € 1  I  1  sa  7  7  S  2  i  5 3  c  5 «  •I  : 1 1  °  *  5.  =  ?.  S 2 I 1  1  P f i 1- H  r  iii  !  5  * - : "! *-. * •". K 2 ^ " " - 7 f  ~ 1  l  i l l !  I  2  ?.  S.I.I  J  1.0  2 =  I  7  f i l l -27.5  S S 7.  .7  i -17.6  "!  t a s  ?.  S i l l  *  °  -22.6  ~  i  14.3  .5  « r. f, 2  ?  i l I III  f  a s s '- ? - :  .°.  i l 1 Iii ?  *  .=;  a a  35  -19.9  5 =  nlii  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 discontinuous (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 constitute 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. for almost eight months of the year.  The Mackenzie. Delta is icebound  11 The influence of water bodies on permafrost configuration i s often quite dramatic--Hopkins  et a l (1955) reported that "Permafrost  i s absent or l i e s at great depths beneath  lakes and ponds throughout  Alaska." (p. 117). I f a fresh water body i s deeper than the maximum thickness of winter i c e , i t s bottom sediments w i 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 i s generally only 1.8 to 2.1 m (Lachenbruch 1962).  At Barrow, Alaska, the mean annual a i r temperature  is approximately -12°C, but lakes over 1.8 m deep i n the area do not freeze to the bottom (Brewer 1958b).  Hence, beneath even r e l a t i v e l y  shallow bodies of water, depression of the permafrost table w i l l presumably occur, and t h i s has been confirmed by various investigators (see  Brewer 1958a; Grigor'ev 1959; Vturina 1960; Johnston and Brown  1964; Anisimova 1966).  Often, however, the information i s of a  q u a l i t a t i v e nature, and l i t t l e suitable published data are available to test the physical e f f i c a c y of models proposed f o r these processes by, for example, Lachenbruch  (1957a, b) and W.G.  Brown (1963, 1964).  Johnston and Brown (1964) investigated the d i s t r i b u t i o n of permafrost under and around a small lake, about 275 m i n diameter, i n the Mackenzie Delta.  The lake i s shallow, with a maximum depth of  only 1.5 m, at low water.  (The lakes i n the Mackenzie Delta are  t y p i c a l l y shallow—see Mackay 1963, pp. 130-135).  However, the  maximum thickness of i c e was only 0.75 m, and they state that "It i s u n l i k e l y 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 i n excess o f 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 i t 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) 0 15 30 45 60  Temperature at 5 m (°C) -1.8(?) -4.5 -5.7 -7.0 -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 d r i l l i n g 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 - 1 0 . 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 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 a l 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 i t does appear to confirm the presence of taliks beneath the rivers themselves.  For example:  At Beaver (which is on the Yukon River, in the discontinuouspermafrost 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, i t 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 i n i t i a l l y 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 permai  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 floodplain 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 r e l i e f generally does not exceed 3 to 4 m,  excluding channel cross-sections; between levee systems, r e l i e f 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). by water bodies.  About 50% of the area is covered  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  Vicinity  ( P o r t i o n Of A i r A19946-13)  Photograph  co  19 i t 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 i n i t i o (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 f i e l d , which i t may or may not be possible to differentiate from the major source, that identified 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. various terrain segments:  It is possible to identify  because of the close association between  vegetation and topographic location, along the successional  transect,  terrain segments w i 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); Alnus; 5)Picea  (see Figure 2, Plate 3).  4)Salix-  For a full description of the  relationships between vegetation and topography in this area see G i 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),  i t 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 interpreted in terms of the degradation permafrost  when the surface  and r e - e s t a b l i s h m e n t  boundary c o n d i t i o n s are  of changing.  Variations in the surface energy regime can also, of course, be brought about by changes in climate i t s e l f .  But since the surface  temperature regime is so complexly related to the aerial climate, i t 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 leastsquares (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 significant 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 i t 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 conditions 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 geomorphic 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 h day 6 months 1 year 10 years 50 years 100 years 200 years 500 years 1000 years 5000 years 10000 years Notes:  i)  a = 0,.04 0,,5 9,.4 13. ,2 41. .9 94,,0 132.,0 187. .0 296.,0 419, .0 936,.0 1324.,0  a = 0.06 0.6 11.5 16.2 51.3 115.0 162.0 230.0 363.0 513.0 1147.0 1622.0  a =\0.08 0.7 13.2 18.7 59.0 132.0 187.0 265.0 419.0 592.0 1324.0 1873.0  The depth of penetration, z (m) , was calculated from z = /12oCt  (Terzaghi  1952, p . 2 2 ) .  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. ii)  iii)  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. 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. attempt to gauge the representativeness  This is an  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) f(s,ci) and f ^ . t ) ) .  (i.e.  Determination of first-order variations is  by field observation, and this information forms the basic input into the rest of the study. 2.  (Scales: at-site; real time).  To understand how the process and material sets influence the ground temperature f i e l d ; 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. i)  This is approached through the attempt to:  demonstrate the consistency of the ground temperature f i e l d , when viewed in the framework of simple heat conduction theory, and thereby,  ii)  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 t h e i r associated degrees of v a r i a b i l i t y , i n t r o duced i n Chapter 2, make s p e c i f i c sampling demands.  A major problem,  common to most research, was how to accommodate these demands as e f f e c t i v e l y as possible.  In the present study, two s p e c i f i c p r a c t i c a l  problems faced were the r e s t r i c t i o n s on s p a t i a l sampling and the i n a b i l i t y to monitor parameters on a regular year-round basis.  These problems have  d i f f e r e n t impacts at the various scales of the study. 1.  Areal scale At the areal scale, the primary concern i s with the pattern of permafrost d i s t r i b u t i o n , as i t r e l a t e s to factors of i t s environment.  A  somewhat generalised picture i s sought, i n that the longer-term v a r i a t i o n s associated with the process of geomorphic  change are investigated, with  most of the shorter-term v a r i a t i o n s i n the thermal regime being ignored. (For example, the annual p e r i o d i c v a r i a t i o n s are not considered at t h i s scale.) Ground temperatures.  Temperature  index of the energy status of the ground.  i s viewed as the fundamental 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 i n t e r v a l s along multiconductor cable.  The pods contain-  ing the thermistors were covered with rubber sealant and then s e l f 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 overa l l 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 D r i 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, i s that which could result from stress following installation in a borehole, as the cable freezes in.  32 b i t , giving a hole about 5-6 cm i n diameter. to c i r c u l a t e f l u i d during d r i l l i n g  (Plate 4).  An a u x i l i a r y pump was used In 1969 a calcium chloride  solution was used, i n order to prevent the p o s s i b i l i t y o f freeze-up i n the hole, during d r i l l i n g .  Unfortunately, t h i s caused the magnesium-  zircon rods to corrode and subsequently fracture.  In 1970, ordinary lake  and r i v e r 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 f o r sampling ground materials.  However, i n March 1970, an opportunity arose  to obtain some samples when a seismic l i n e was located i n the v i c i n i t y of the study area (Plate 1). Through the cooperation of Imperial O i l Limited and Gulf O i l 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 a i r , and i t was possible  to c o l l e c t 3-meter integrated samples over the depth of each borehole. These samples were subsequently analysed f o r t o t a l moisture content, grain-size c h a r a c t e r i s t i c s , and organic content, with the view to estimating thermal properties. Other data.  The knowledge of permafrost d i s t r i b u t i o n obtained  from the ground temperature network was extended i n 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, a f t e r successful checking at s i t e s with ground temperature control data. array.  Some p r o f i l i n g was also carried out, using the Wenner  Also, a limited amount o f seismic work was carried out i n  33  Plate 4  Drilling Equipment at a Borehole on a Slip-Off Slope (Bare Ground Segment)  34 1970.  2  E s t i m a t e s o f mean annual l a k e - and r i v e r - b o t t o m temperatures were o b t a i n e d from r e g u l a r measurements o f water  2.  temperature.  Between-site S c a l e Nested w i t h i n the o v e r a l l p a t t e r n o f p e r m a f r o s t d e g r a d a t i o n and a g g r a d a t i o n are t h e v a r i a t i o n s i n t h e ground thermal  regime  a s s o c i a t e d w i t h t h e changes i n t h e n a t u r e o f t h e s u r f a c e c o v e r , prog r e s s i n g from b a r e , newly exposed  sediments t o mature spruce  It i s t o be expected t h a t such s u r f a c e v a r i a t i o n s would  forest.  produce  d i f f e r e n c e s i n m i c r o c l i m a t e between s i t e s . Ground temperatures.  The major e x p r e s s i o n o f v a r i a t i o n at  t h i s b e t w e e n - s i t e s c a l e i s t h e d i f f e r e n c e i n t h e annual ( " p e r i o d i c " ) ground temperature  regime, i . e . t h e mean and t h e f l u c t u a t i o n s  about  the mean, e x t e n d i n g down t o t h e l e v e l o f zero annual amplitude.  For  t h i s purpose t h e r m i s t o r s were l o c a t e d at depths o f 0.5 and 1.5 m i n the major b o r e h o l e s along T r a n s e c t 2, i n a d d i t i o n t o those at depths o f 3, 6, 9, 12 and 15 m. such as at t h e boundary  Where environmental g r a d i e n t s were s t e e p , o f t e r r a i n segments  ( e s p e c i a l l y a c r o s s the  s l i p - o f f s l o p e ) , t h e major b o r e h o l e network was i n t e n s i f i e d by l o c a t i n g intermediate holes (Figure 3). A l s o , s p e c i a l  temperature  t r a n s e c t s were e s t a b l i s h e d a c r o s s the s l i p - o f f s l o p e t o i n v e s t i g a t e the i n f l u e n c e o f d i f f e r e n t i a l temperature.  s e a s o n a l snow a c c u m u l a t i o n on ground  Although t h e major e n v i r o n m e n t a l g r a d i e n t s r u n normal  t o t h e r i v e r , t h e magnitude o f l o n g i t u d i n a l g r a d i e n t s was i n v e s t i g a t e d  The s e i s m i c work was c a r r i e d out by Mr. Ronald Good, o f t h e G e o l o g i c a l Survey o f Canada.  6-13  0-0 Indicates 20m or 30m borehole 0-0 Indicates 9m borehole 0-0 Indicates 3m borehole Snowbank profile borohcies are 1.5m  i 6-12  Salix/Alnus  Fossil Cut Bank  Snowbank Prolile 7  R i v e r  0 I  i  meters 1 1—  Figure 3 T E M P E R A T U R E B O R E H O L E N E T W O R K O N A S L I P - O F F 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 o f comparing  the microclimate of d i f f e r e n t surface types, i n the same a e r i a l environment, i s to examine the r e l a t i v e magnitudes of surface energy balance components.  The net available r a d i a t i v e energy at the ground surface,  R , i s d i s s i p a t e d v i a sensible heat (H) and latent heat (LE) transfer to the a i r , and by conduction into the ground (G) (e.g.see S e l l e r s 1965, p.100).  The r e l a t i v e importance of these energy balance terms can vary  enormously, depending upon p r e v a i l i n g atmospheric and surface conditions. The ground surface thermal regime i s a function o f the mutual i n t e r action o f these energy t r a n s f e r processes.  A comprehensive energy  balance approach was beyond the scope of the present study, and cons i d e r a t i o n was r e s t r i c t e d t o R^ and G only.  I t i s recognised, however,  that evaporation, f o r example, i s an important term i n producing cooling of the surface. One problem i n t h i s aspect of the study was that data c o l l e c t ion was r e s t r i c t e d 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 o f micro-  c l i m a t i c v a r i a t i o n s , over a 6-7 week summer period, between s i t e s located i n the f i v e major t e r r a i n segments.  A meteorological s i t e was  maintained throughout the summer, f o r measurements of solar r a d i a t i o n , temperature  and humidity.  A i r 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 v e n t i l a t i o n . response time was 15  c a r r i e d out.  A l l temperatures  No determination of were logged once per  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 d i s c ,  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 t h e i r assigned calibration  (Weaver 1969).  with the instruments. 0.01  l y min  -1  The c a l i b r a t i o n s used were those supplied  The resolution  (0.698 mW  cm  -2  -1 0.003 ly min the ground.  of the net radiation  systems was  ), and f o r the s o i l heat f l u x systems  -2 (0.209 mW  cm  ).  The radiometers were mounted 1 m above  They were checked d a i l y f o r damage (by animals) and signs  of moisture accumulation; when the l a t t e r 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 i n the instruments  methods of data c o l l e c t i o n and reduction. system was  and  The zero c a l i b r a t i o n of each  checked at frequent, but i r r e g u l a r , i n t e r v a l s , and the  systems were cross-checked against each other.  The o v e r a l l maximum  error i n the radiation measurements i s estimated to be -0.04  ly min*  _2 (2.792 mW addition  cm  ).  Accuracy of s o i l heat f l u x measurements depends, i n  to sensor c a l i b r a t i o n , on the careful emplacement of the disc  i n 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 s i t e . Thus there i s no check on the representativeness of the measured values. The two systems used were cross-checked, and the maximum error i s estimated at +0.012 l y min * (0.836 mW -  cm ). -2  Ground materials were  sampled at each s i t e ; they varied from sandy-silt to organic matter. S t r i p charts were d i g i t i s e d (on a potentiometric d i g i t i s e r ) , and appropriately summarised by computer.  Reduction  the basic p r e c i s i o n o f the measurement systems.  errors are within  On some occasions  data loss d i d 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 d i s t r i b u t i o n , snow density, bottom temperatures o f 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 o f s i t e s selected for betweens i t e comparison, i t was necessary to gauge around-site v a r i a b i l i t y . F a i r l y simple measures were employed because o f equipment l i m i t a t i o n s . Measures included determination of active layer depths, ground temperatures at 10 cm depth (including diurnal variation) , v a r i a t i o n in incident and r e f l e c t e d v i s i b l e light Results are discussed i n Chapter 5.  (using a camera light-meter).  Chapter 4 THE DISTRIBUTION OF PERMAFROST: 1.  OBSERVED AND PREDICTED  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 s t r i c t l y 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; a l 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 2-8 6-2 6-3 6-17 SL-10  52.0 50.0 65.0 65.0 53.0 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 l e 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) 1967* Jan  (O.O)  Feb  (0.0)  1  Lake Temperatures(°C)  1968**  1969**  1970  1968**  1969**  (0.0)  (0.0)  (0.0)  (0.0)  (0-0)  (0.0)  (0.0)  (0.0)  (0.0)  (0.0)  1  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)  July  14.2  15.6  14.8  16.3  Aug  12.6  14.2  10.5  7.0  15.6  14.2  15.0  12.7  8.1  (7.6)  (5.4)  5.4  3  7.3  (7.6)  7.9  Oct  (1.5)  (1.5)  1.5  (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)  3.7  4.0  3.8  4.2  3.5  3.0  Sept  Year  2  Values i n parentheses are estimates based on incomplete or limited f i e l d data, or data from other years. The following temperature data refer to various winter dates: River Lake March 1969 March 1970 1970 Dec Estimate based on measurements  Water  Bottom  Water  Bottom  0.0 0.05 0.0  0.0 0.07 0.0  0.0 0.08  0.0 0.08  for October 1-6 only  'The following temperature soundings were made on 24/7/70 (p.m.), and indicate that the r i v e r i s well mixed to a uniform temperature: #1 Depth(m) 1.0 2.0 3.0 4.0 4.3(bottom)  #2 Temp(°C) 16.7 16.6 16.6 16.7 16.8  Data supplied by D. G i l l  Depth (m) 1.0 2.0 3.0 4.0 5.0 6.0 6.5 (bottom)  (pers. comm.)  Data supplied by C. P. Lewis (pers. comm.)  Temp(°C) 16.7 16.7 16.6 16.6 16.6 16.8 16.8  43 Table 5 Ground Temperatures Beneath a Cut Bank and a Slip-off Slope Cut Bank Depth(m) 6 9 12 15 20  #6-1 (x=lm)  #6-2 (x=36m)  -2.8°C . -2.4 -2.0 -1.7 -1.4  -3.6°C -3.3 -3.0 -2.7 -2.4  Slip-off Slope #6-5 (x=35m) -0.5 0.0 +0.2 +0.4 +0.7  In locations indicative of contemporary geomorphic change, permafrost 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 #  Distance to Channel(m)  Permafrost Thickness(m)  2-2-A  10  2.5  2-3  20  7.0  6-4-A 6-4-B 6-4 6-5  5 15 25 35  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 T y p e K-16 (1-10-2.5) Site 6-4A  ~A  Thickness of permafrost (second layer)  Thickness of permafrost (second layer)  = 1,35 K 7,5 m = 101 m  Electrode spacing,  Um)  Master Curve Type K-22 (1-40-0)  Electrode (pacing.  L(mj  Master Curve Type K-19 (1-20-1)  Site 6-4-B  Site 2-2-A  Thickness of permafrost (second layer)  Thickness ol permafrost (second layor) * 0.82 K 3 m * 2.5 m  * M5x 5 m  I ' ' " I 5 10  '  Electrode spacing,  L(m)  1  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 Viereck 1970).  (see Benninghoff 1952, Tyrtikov 1963,  The pattern of permafrost aggradation i s , however, only  partly caused by the insulating effect of the developing vegetation. For, as the channel migrates laterally, a part of the surface which i t 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 Temperature at 9 m (°C) +0.02  Permafrost Thickness (m) 8.5  Site # 6-4  Distance from River (m) 25  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 i n Table 7 i s actually interrupted by a zone of r e l a t i v e l y temporary degradation (see Figure 7). The configuration of permafrost shown i n Figure 7 was determined by probing (mostly confined to the top 3m) and temperature  data.  The former technique can be mis-  leading at times; f o r example, the temperature  data show that the frozen  ground beneath the t a l i k i s very close to 0°C and w i l l therefore f e e l soft to the probe.  R e s i s t i v i t y p r o f i l i n g 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 f o r  two ground layers, calculated by the Barnes layer method (Barnes 1954), have been plotted i n 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 i n the middle of the transect are i n d i c a t i v e o f unfrozen ground.  The values f o r the lower layer are higher, 270-540 ohm-meters,  and might indicate the presence o f a frozen layer, although close to 0°C.  Dry, unfrozen ground would also produce high values. The t a l i k i n Figure 7 coincides s p a t i a l l y with the zone of max-  imum seasonal snow accumulation  (see G i l l 1971).  Along the s l i p - o f f  slope, the outer belt of willows ( S a l i x ( l ) ) forms an excellent setting for the development of large seasonal snow d r i f t s .  These are formed by  the p r e v a i l i n g winds, and the general shape i s reproduced each year since the extent and volume of snow i n them i s largely independent amount o f snowfall (for example, see Benson 1969).  of the  As the S a l i x moves  across the bar i n colonising new areas, the snowbank location migrates along with i t .  Ground temperatures  i n i t s lee progressively cool, and  47  6-4 I  10  6-5  6-6  6-7  I  i  I  20  30  6-8  6-9  •  40  I  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 gradual 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 # 2-5 2-6 6-11 6-12 6-13 6-14  Permafrost Thickness (m) 29.0 38.0 17.5 22.5 24.5 29.0  Distance from back of slip-off slope (m) 3.0 22.0 2.0 37.0 72.0 107.0  49  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)  Tg  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 a  time since initiation of temperature disturbance (days, years) 2 - 1 2 - 1 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 erfc x  earth's geothermal gradient (°C m *) =  2  C eU  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 temperature field displays some consistency with respect to environmental factors .  This is now attempted through the framework of simple heat  50 conduction theory.  Some assumptions necessary f o r i t s application  here are that: 1. heat transfer takes places by conduction alone (any nonconductive transfer i s ignored); 2. the ground i s 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 t h e i r respective mean water temperatures. A l b e i t scanty data (Table 3), indicate that such an assumption should be s a t i s f a c t o r y . Brewer (1958a) found that lakes were e s s e n t i a l l y isothermal during the i c e - f r e e period. Assumptions  (1) and (2) represent a considerable s i m p l i f i c a t i o n of the  real s i t u a t i o n .  But i t i s possible to go ahead, assuming them to be  v a l i d , and compute an apparent, gross value f o r oC, for input into subsequent heat conduction models.  Before this i s done, however, the actual  ground materials w i l l be described. Ground materials. the  As would be expected f o r a delta  environment,  grain-size d i s t r i b u t i o n s of the f i f t y samples tested f a l l within  f a i r l y narrow l i m i t s .  Characteristics of some of the samples are pre-  sented i n 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 i n -  tegrated sections, i n e v i t a b l y produces some homogenising e f f e c t .  Data  from PB-1, which are f o r 0.6-meter sections, reveal some more detailed stratification.  Total moisture contents, on a dry-weight basis ( w ) , vary w  from almost 100%, i n near surface layers, to 30% at depth.  Total car-  bon content, as determined by loss on i g n i t i o n , varied between only 5 and 7% f o r 30 samples. Brown (1965).  These data are' s i m i l a r to those of Johnston and  They describe (p. 105) a t y p i c a l section as follows:  0 to 100 feet (0 to 30 m)  t h i n l y s t r a t i f i e d sandy s i l t , with layers of decomposed organic material throughout.  51  20 0 H  40 '  60 1  60% •  0 -\  20 1  40% "  20 *4  40 '  60 ±  80 1  100% 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 i n the near-surface layers, where substantial accumulation had occurred (p. 1383). Johnston and Brown (1965) found that v i s i b l e ice segregation was confined mostly to the upper 10 m.  Below this depth they describe the material as  s o l i d l y frozen, with sandy material being well bonded by ice not v i s i b l e to the eye.  R. J . E. Brown (1956) reported that ground ice i n some  Delta s o i l s at Aklavik was either cement ice or thin (up to 16 mm) lets.  vein-  This was the pattern i n 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).  Kersten's  Values f o r conductivity, k, were calculated using  (1949) formulae, and volumetric heat capacity, C, from the  formula: C = XC + w w (de Vries 1963).  XC + m m  X C o o  Here, X i s the volume f r a c t i o n and w, m and o s i g n i f y  water (ice),mineral and organic respectively. , i s given by Apparent  The thermal d i f f u s i v i t y ,  k/C. thermal d i f f u s i v i t y .  The models being employed here  assume s o l e l y conduction i n a homogeneous medium, whose thermal propert i e s are not functions of temperature.  In order to be consistent with  this view of the problem, i t i s considered more appropriate to use an  Table 9 P h y s i c a l and Thermal Properties o f Some S o i l  Borehole  Depth Interval(m)  S o i l Type*  W% w  X% 0  B** (grm cm ^) -  Samples  k (m c a l c m sec CT ) -1  - 1  1  C (m c a l cm -*) (cm -  2  a sec" ) 1  (m  2  a day" ) 1  SL-1  0-3 3-6 6-9 9-12 12-15 15-18  silt silt silt sandy-silt silt silt  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  silt 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  (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  clayey-silt silt clayey-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  * G r a i n - s i z e c l a s s e s are per U.S.D.A. c l a s s i f i c a t i o n . Where only a s i n g l e c l a s s appears t h i s i n d i c a t e s that n e i t h e r o f the other two exceeds 20%. When a c l a s s ( e s ) exceeds 20%, but i s not the main one, i t appears as the m o d i f i e r . ** Values s u p p l i e d by R.J.E. Brown (pers. comm.) All  thermal p r o p e r t i e s p e r t a i n to the frozen s t a t e  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  Figure 10  Temperature (°C) -4 -2  E X A M P L E S OF T E M P E R A T U R E - D E P T H C U R V E S U S E D FOR C A L C U L A T I O N OF A P P A R E N T DIFFUSIVITY  56  4x c 2  cv =  [2(t  where  x^  wave and  TT/P  m  TT/P +  x  t T T / )+nTT] 2  2,-1 day  , (1)  2  P  is the depth of the f i r s t crossing point, P n  the period of the  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. Now,  = _\ /a  v  / f ~ f££ _ n  days  (2)  l  i f a tautochrone is also available for some time t +t  =  7  J  c /cv  / ^ + nP 2  X  t^ , we have,  days  (3)  11  Subtracting (2) from (3.) leads to, ( x  t o  r  - t  =  c " c X  >  /P /-  )  .„ days  (4)  2  c " c cv = ; . (t -t ) ( x  X  )  2  3  2  P "  2 m  day  -1  (5)  Calculations were carried out on data from two boreholes in different terrain segments, and results are presented in Table 10. was taken as 365 days.  The period, P,  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 d i f f i c u l t to fix their crossing point.  2 The overall mean value of 0.063m 2 -1  compares closely to the value of 0.067 m  day  -1 day  calculated by W. G. Brown  et a l (1964) from their Mackenzie Delta data. The values of a Table 9.  determined in this manner are  lower than those  A possible explanation for this is that latent heat effects  57  Table 10 Calculations for Apparent D i f f u s i v i t y , using data from boreholes #2-6 and "2-8 Tautochrone Dates 18/5/70 18/5 18/5 18/5 15/6 15/6  M  t  3  Tautochrone Dates 15/6 12/7 10/8 12/7 10/8 10/8 12/7 15/6 10/8 10/8  - 4/6 - 4/6 - 4/6 - 15/6 - 15/6 - 12/7 - 18/5 - 18/5 - 18/5 - 12/7  -  + 4/6/70 + 15/6. + 12/7 + 10/8 + 12/7 + 10/8  V Days 11 38 67 27 56 29 55 28 84 29  By combining Pairs #' s (2) (3) (4) (3) (4)  -  (4) -  (5) (5) (6) (6)  • • -  (1) CD  (1) (2) (2) (3) (2) (3) (2) (5)  Pair Number  #2-6  1 2 3 4 5 6  4.90 5.15 5.85 6.55 6.50 7.10  (m)  #2-8  5.30 5.55 6.25 6.85 6.80 7.40  #2-6 (x' -x ) am c  0.25 0.95 1.65 0.70 1.40 0.70 1.35 0.65 1.95 0.60  #2-8 2  c  0 0 0 0 0 0 0 0 0 0  day'  1  060 073 070 078 073 067 070 062 062 050  a = 0.067 a = to. 008  (x' -x ) c  c  0.25 0.95 1.55 0.70 1 .30 0.60 1.25 0.55 1.85 0.60  2  day'  0 0 0 0 0 0 0 0 0 0  060 073 062 078 062 050 060 045 056 050  am  1  a = 0.060 a = tO.OO'J  58 i n 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 e x p l i c i t l y , the reduced rate o f penetration i s interpreted i n terms of a lower d i f f u s i v i t y . Theory.  I f the mean surface temperature i s everywhere the same,  and i s steady with time, the steady mean temperature at any point i n the ground i s simply a function o f the surface temperature f geothermal gradient Gg.  IfT  and the earth's  were below 0°C, permafrost would form and  ultimately a t t a i n an equilibrium depth, at which the temperature increase due to i n t e r n a l earth heat just o f f s e t s the amount by which 0°C exceeds T .  (In p r a c t i c e , the equilibrium configuration might not be approached  for perhaps thousands of years, depending on the ultimate thickness see Table 2).  An important and i n t r i g u i n g problem, however, both from a  s c i e n t i f i c and an engineering viewpoint, i s to determine the disturbance of sub-surface temperatures that r e s u l t s when the surface temperature within some f i n i t e region d i f f e r s from that o f the area outside of the region.  A solution to t h i s problem f o r arbitrary-shaped regions (for  example, lakes) has been derived by Lachenbruch (1957a) as follows:  where T^ i s the mean surface temperature within the f i n i t e region.  The  temperature at any point i n the ground i s 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 c i r c u l a r annulus, of central angle X and inner and outer r a d i i  and R^ (Figure 11).  The second term  represents the normal (undisturbed) temperature p r o f i l e f o r the area.  59  Figure 11  M E T H O D O F DIVIDING A G I V E N S U R F A C E A R E A INTO S E C T O R S O F C I R C L E S . 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, simply the radius of the body.  i s set to zero and ^ i s  For t = oo (steady-state) equation (6)  reduces t o : e(x,V,z)= ( T d - T s )  E 3 6 O \V1+(R,/Z)  2  2  2  This i s the form used by W. G. Brown et a l (1964, p. 150). solution has been employed  (8)  ~ v"l + ( R / Z ) /  The basic  i n more elaborate form i n a theory of pingo  formation (Mackay 1962). Lachenbruch (1957b) presents an equation suitable f o r predicting the thermal e f f e c t o f a strip-shaped disturbance, such as a r i v e r , say. Assuming a steady-state condition, the configuration of t a l i k s beneath r i v e r s w i l l depend upon the heat balance of the r i v e r , 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 t a l i k penetrates through the permafrost i s also related to the width o f the r i v e r .  The time-dependent  case also involves  consideration o f c< and t . For a homogeneous medium, and neglecting the e f f e c t s of latent heat, an equation describing the thermal disturbance produced by a r i v e r , whose temperature i s T^, i s : •0(x,z,t) = (T -T )|> (pm) - i K ^ - , m)} d  (9)  s  where the function •  ( j . * ) - * . * ( / » . ) +  i  j  f  ^  ^  l  d  ,  (  1  0  )  2 m = z /(4at) x = horizontal distance from one side of the s t r i p s = width of s t r i p (river) = v a r i a b l e of i n t e g r a t i o n  and where  u  (See Lachenbruch 1957b, pp. 1517-1522). !  Both T^ and f  g  can be varied  over discrete time i n t e r v a l s , thus making i t possible to account, i n some way, For  f o r c l i m a t i c change, f o r example.  the steady-state, (10) reduces to: x  'o and (9) becomes simply: (T 6(x,z) =  d  - T )  "  tan  1  (12)  Equations (6) and (9) both f a i l to account f o r the volumetric latent heat, when freezing and thawing are involved.  There i s no  a n a l y t i c a l solution to the two-dimensional phase change problem however. The one-dimensional thawing or freezing problem has been treated extensively to the l i t e r a t u r e  (see Muehlbauer and Sunderland 1965);  however, there are many problems that are d i s t i n c t l y two- or threedimensional, and cannot be approximated by a one-dimensional analysis. Equations (6) and (9) do s u c c e s s f u l l y account f o r the problem geometry, but the neglect of latent heat e f f e c t s leads to d i s t o r t i o n i n the shape and rate of penetration of the predicted isotherms.  In spite of t h i s  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 correspond to conditions occurring i n the Mackenzie  Delta.  In the f i r s t group of examples (Figure 12) computations have been made f o r the steady-state solution (m=0), f o r various values of s.  The  thermal disturbance was calculated from equation (9), and the ground temperature f i e l d from equation (7). the  It i s evident that as the width of  r i v e r i s increased, a c r i t i c a l width i s reached, beyond which a  through-talik w i l l e x i s t beneath the r i v e r .  As the width i s further  increased, the proportion of unfrozen ground becomes progressively  62  Horizontal distance (meters) -100  -50  0  50  100  Solid lines are 0°C isotherms  F i g u r e 12  STEADY-STATE PERMAFROST CONFIGURATION U N D E R R I V E R S 30, 45, 60, 70, 80 a n d 100 M E T E R S W I D E  63  Horizontal distance (meters) -100 1  i  i  -50 i I  0  1  1  i  i  i  •  •  •  50 i  1 0 0  •  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,  it  is mirrored by a rise in the lower perma-  frost surface, since the normal (undisturbed) geothermal e f f e c t  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 i t 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 landscape (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 a l 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: *Site  6-3 i s  40 m from the s h o r e .  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)  r—\  ept:  e  Q  3.  50  100  200  300  500  750  1000  Steadystate  5  0. 08  0.12  0.14  0.15  0.17  0.17  0.18  0.20  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  20  0. 27  0.40  0.50  0.54  0.60  0.64  0.66  0.74  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  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. this solution (equation(8))  Use of  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 steadystate configuration is very closely approached within 500 years.  Even  for this period of time, though, the two above assumptions cannot be considered altogether valid.  The second assumption is certainly not valid  in the case of the shifting river channel, where quite rapid geomorphological 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 f i r s t 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. 1964).  (See also W. G. Brown et al  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 l i s t i n g ) .  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  a l 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 f o r f ; this gives an average w  value o f 2.5°C/100 m f o r Gg.  An average temperature  gradient o f about  2.3°C/100 m has been measured i n a deep borehole some 35 km north-west of the study area (Jessop 1970).  Although the two s i t e s are c e r t a i n l y  d i f f e r e n t , the deep borehole r e s u l t i s taken as confirmation of the general v a l i d i t y 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 r i v e r .  A value f o r T  covered s i t e s was estimated from borehole #2-8.  of -4.2°C f o r spruceSuch s i t e s are the most  stable, as indicated by the presence of trees up to 500 years o l d , and s should be the best suited to the model.  Observed and predicted temper-  atures are presented i n Table 12, and agreement i s very close.  The  s l i g h t l y larger predicted values f o r #6-1 are at least p a r t l y due to an over-estimate o f the r i v e r e f f e c t — t h e r i v e r has, o f course, not been steady i n i t s present p o s i t i o n f o r such a long period o f time.  For each  of these boreholes, the t o t a l thermal contribution of a l l water bodies i generally on the order o f twice as great as the earth's geothermal ient.  grad-  The thickness of permafrost i n the v i c i n i t y o f boreholes 6-2 and  6-3 i s estimated at about 65 m, which correlates well with a seismic r e f l e c t i o n at 66 m f o r this l o c a l i t y . geothermal  Under the influence of the earth*  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 f o r other points along this transect.  The transect i s 300 m  long; with points spaced every 10 m, 5 minutes o f computer time were required on a Xerox Sigma 9, to compute the ground temperature  field.  The output from this program was read d i r e c t l y into a computer mapping  68 Table 12 Observed ( T ^ ) and Predicted ( T p ) Temperatures, Cut Bank Section re  Temperature Contribution (°C) Gg  Total  1.22 1.64 1.95 2.16 2.38 2.49 2.57 2.59 2.54  0.15 0.23 0.30 0.38 0.50 0.63 0.75 1.00 1.25  1.44 1.97 2.39 2.71 3.12 3.43 3.66 4.03 4.33  T pre -2.8 -2.2 -1.8 -1.5 -1.1 -0.8 -0.5 -0.2 +0.1  0.11 0.16 0.23 0.29 0.36 0.45 0.52 0.67 0.79 0.90 1.00  0.25 0.36 0.48 0.61 0.76 0.91 1.05 1.26 1.40 1.51 1.61  0.15 0.23 0.30 0.38 0.50 0.63 0.75 1.00 1.25 1.50 1.75  0.51 0.75 1.01 1.28 1.62 1.99 2.32 2.93 3.44 3.91 4.36  -3.7 -3.4 -3.2 -2.9 -2.6 -2.2 -1.9 -1.3 -0.8 -0.3 +0.2  -3.6 -3.3 -3.0 -2.7 -2.4 -2.1 -1.8  0.25 0.37 0.48 0.67 0.75 0.89 1.01 1.19 1.31 1.39 1.46  0.12 0.17 0.23 0.29 0.39 0.47 0.55 0.71 0.84 0.95 1.03  0.15 0.23 0.30 0.38 0.50 0.63 0.75 1.00 1.25 1.50 1.75  0.52 0.77 0.01 1.34 1.64 1.99 2.31 2.90 3.40 3.84 4.24  -3.7 -3.4 -3.2 -2.9 -2.6 -2.2 -1.9 -1.3 -0.8 -0.3 0.0  -3.8 -3.5 -3.2 -2.9 -2.5 -2.2 -1.9  Lakes  Rivers  6 9 12 15 20 25 30 40 50  0.07 0.10 0.14 0.17 0.24 0.29. 0.34 0.44 0.54  6 9 12 15 20 25 30 40 50 60 70 6 9 12 15 20 25 30 40 50 60 70  Depth (m)  Mean annual surface temperature  = 4.2°C  For lakes, therefore, (Tj - T )  = 7.4°C  g  For r i v e r s ,  (T, - T ) d s  = 8.2°C  ^obs -2.8 -2.4 -2.0 -1.7 -1.4  -  -  -  -  -  -  69  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. the model.  A major thermal contribution is thus being under-estimated by 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 a n d - 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). accurate.  For stable sites such predictions should be quite  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). isotherms are shown in Figure 15.  The calculated annual  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 i n i t i a l l y , 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 i t 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  T a b l e 13 Observed and P r e d i c t e d Temperatures, w i t h T r a n s i e n t f o r Boreholes on a S l i p - O f f Slope  Correction,  TEMPERATURE CONTRIBUTION (°C) Depth  (m) 3 2-S 6 (f s =-3.0°C) 9 12 15 20 30  V  (1) 0 .08 0 .15 0 .23 0 .30 0 .38 0 .50 0 .75  0 .08  (i)  S h i f t i n g Channel* (ii) ( i iT oit a)l  Other Rivers  Total  pre  obs  +2 .15 +2 .71 + 2.90 + 2.98 + 3.01 + 3.02 + 2.96  -1 .31 -1 .59 -1 .65 -1. .64 -1, .59 -1, .49 -1, .26  • 0 .01 +0 .02 +0 .03 + 0,,04 • 0 .05 • 0..06 +0 .08  (2) *0.85 + 1.14 + 1.28 + 1 .38 + 1.47 + 1.59 + 1. 78  (3) 0 .04 0, .09 0, .13 0. . 18 0 .23 0, .31 0. .45  1+2+3 0. ,97 1,,38 1. 64 1. 86 2. .08 2. 40 2. ,98  -2 .0 -1 .6 -1 .4 -1 .1 -0 .9 -0 .6 0 .0  -1, .8 -1 .6 -1. .3 -1, .0 -0 .8 -• --  3 6 - 3 ,0°C) 9 12 15 20 30 40  0, .15 0, .23 0. .30 0. .38 0. 50 0. .75 1..00  +0 .30 +0 .58 +0..84 + 1.,06 + 1..26 + 1.,51 + 1.,84 +2.,00  -0, .13 -0. ,26 -0, .37 -0, ,46 -0, .52 -0, ,60 -0. ,64 -0. ,59  +0,.00 + 0.01 +0..01 + 0,.02 +0,.02 • 0,,03 +0,,04 + 0.,04  +0.17 + 0.33 +0.48 • 0.62 +0.76 +0.94 + 1.24 + 1.45  0 .05 0, ,11 0, .17 0. ,22 0, ,29 0. .37 0. ,55 0. ,70  0. ,30 0. ,59 0. 88 1. 14 1. 43 1. 81 2. 54 3. 15  -2 .7 -2 .4 -2, . 1 -1, .9 -1 .6 -1, .2 -0, .5 0, .2  -2. .8 -2, .5 -2. .2 -1. .9 -1, .6  3 6 .2°C) 9 12 15 20 30 40 50 60  0. .08 0. 15 0. 23 0. 30 0. 38 0. 50 0. 75 1. 00 1. 25 1. SO  + 0..06 +0. 11 + 0. 16 + 0..22 + 0. 27 +0. 35 +0. SI +0. 66 + 0. 79 +0. 90  -0, .00 -0. ,01 -0. .01 -0. ,01 -0. ,02 -0. 02 -0. ,03 -0. ,03 -0, 03 -0. ,03  0, .00 0. ,00 0. ,00 0, .00 0. ,00 0. ,00 0, .00 0,,00 0. ,00 0, ,00  +0.06 +0.10 +0.15 +0.21 +0.25 +0.33 +0.48 +0.63 +0.76 +0.87  0. .17 0. ,34 0. 51 0. ,66 0. .83 1. 05 1..42 1. 70 1. 89 2. ,02  0. 31 0. 59 0. 89 1. 17 1. 46 1. 88 2. 65 3. 33 3. 90 4. 39  -3. .9 -3, .6 -3. ,3 -3. .0 -2. 7 -2. .3 -1, .5 -0, .9 -0, .3 0. .2  -4. .0 -3. .7 -3. .3 -2. .8 -2. ,5  0. .08 0. .15 0. .23 0. .30 0. ,38 0. .50 0. .75  • 4..27 +4.,07 + 3.,87 + 3,.69 + 3..51 + 3.,27 +2. 88  -4, .20 -3, .90 -3, .61 -3, .35 -3, .10 -2. ,72 -2. ,10  0, .03 0. .05 0. ,07 0, .10 0, ,12 0. ,15 0. ,19  + 0.10 + 0.22 +0.33 + 0.44 +0.53 + 0.70 + 0.97  0, .03 0, .05 0. ,07 0. .10 0. .12 0. 15 0. 23  0.21 0.42 0.63 0.84 1.03 1.35 1.95  -0. .3 -0. 1 0. 1 0. ,3 0. ,5 0. ,9 1.,5  -0.0 -0.0 -0.1 -0.2 -0.2  2-6  (  Gg  2-8  3 6 9 12 15 20 30  -• ---  ------  ---  Shifting Channel** (4) 0.06 0.12 0.18 0.24 0.30 0.40 0.57 0.05 0.09 0.14 0.18 0.23 0.30 0.43 0.56 0.02 0.05 0.07 0.09 0.12 0.16 0.24 0.32 0.39 0.46 0. .06 o. . 13 0. . 19 0, .25 0, .31 0. .41 0. .55  * T h i s i s t h e channel c o n t r i b u t i o n , w i t h t h e t r a n s i e n t c o r r e c t i o n : ( i ) = s t e a d y - s t a t e 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 ) = t h e recovery i n temperature due t o t h e presence o f t h e r i v e r b a r ( t j assumed = 100 y e a r s ) ( i i i ) = the c o n t r i b u t i o n from t h e channel i n i t s p r e s e n t p o s i t i o n ( f o r t j = 100 y e a r s ) * T h i s r e p r e s e n t s the s t e a d y - s t a t e c o n t r i b u t i o n from t h e channel i n i t s present p o s i t i o n , and was t h e v a l u e used i n the s t e a d y - s t a t e model. Comparison o f v a l u e s under (2) and (4) i n d i c a t e the e r r o r i n v o l v e d i n t h e s t e a d y - s t a t e 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 by the thermal diffusivity of the ground. With a = 0.05 m day  -1 (a value  somewhat lower than that for frozen ground, since the area of the bar was i n i t i a l l y 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 r e a l i s t i c . One final contribution to the ground temperature has to be considered, 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 above.  , t = 93 years, and with values for s and T^ as used  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 i t s e l f , #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* snowbank migration.  subsequent vegetation succession and  Thus, the use of a constant T for any particular  site does not simulate its thermal history r e a l i s t i c a l l y . Transient-state: is a continuous process.  Refined Model.  In reality the river migration  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 i n i t i a 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 i n i t i a 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  ©  ©  Temperature  (13)  (15)  Lake 3  (jl)  0  boreholes  i  meters  100  i  I  Transect 6  shift  Shoreline moves from x = ««> to x - x, at t - 0  t=0  =•7  (x, s)  Present position  Diagrammatic example of river shifting in equal steps of s  Figure  16  T E M P E R A T U R E W A V E S I M U L A T I N G RIVER  SHIFTING  78 s h i f t i n g has not been monotonic. ing  There has been an average rate of s h i f t -  of about 1.1 m y e a r * over the past 30 years. -  I t was decided to use  a lower, "apparent" rate o f s h i f t i n the model, however, which would i n corporate some unknown lag time involved i n the formation of the second cut  bank, thereby hopefully reducing the s h i f t i n g process to an equiv- .  alent monotonic form.  I f the r i v e r i s assumed to have been s h i f t i n g at  a constant rate of 0.5 m year positions would be 460 years.  the time between the i n i t i a l and present The thermal h i s t o r y could, f o r example,  be computed on the basis of 10-meter steps, i . e . corresponding to 20year i n t e r v a l s . In order to reproduce the thermal h i s t o r y mathematically, assumptions have to be made regarding the thermal regime which existed when the channel was i n i t s i n i t i a l p o s i t i o n .  The i n i t i a l condition f o r t h i s  model was taken to be the steady-state s o l u t i o n with the channel i n i t s i n i t i a l p o s i t i o n , p r i o r to migration. Lachenbruch (1957b, p. 1521) gives an equation f o r 9 i n the case of an ocean which has transgressed, or regressed, by a number o f stages of movement.  For a s h i f t i n g r i v e r , i f 3 stages C t (=0), tx , t ) are Q  2  involved f o r example (see Figure 16), the equation would be,  (13)  79 2 Here, the notation m ( t - t p means the value of m=z /4a t f o r t = ( t - t ^ ) , etc.  The movement from x=°°to x=x^ at time t (=0) i s counted as stage 1. Q  In equation  (13), the f i r s t group o f 3 terms represents the warming i n -  fluence o f the r i v e r ( i . e . permafrost degradation), whereas the second group of 2 terms accounts f o r the thermal recovery behind the migrating r i v e r ( i . e . permafrost aggradation).  Latent heat effects are ignored.  Now, i f n stages o f movement are involved, equation  j [ ( i i Mt^-  6(x,z,t) = ( t - f ) d  <  s  V  i>{  r  .mct^j  - vvj[H~ ' - ) -*v~— (  m(t  t)  .-ct-vjj  1  X  +  [  *  (  ^  ^ct-t.))- ^  (  ^  (13) becomes,  ^jm( t-t.))J for t>t n-i  Equation  (13) assumes that f  r i v e r has passed by.  (14) '  v  i s the same before and after the  Now, as already mentioned, t h i s i s not the case.  However, t h i s can be handled i n the same way as f o r a c l i m a t i c change-viz.  i f (T -f d  s  ) =  f o r t < t j , and some new ( f - f d  g  ) = A  2  for t ^ t j ,  the r e s u l t , f o r a stationary s t r i p i s , 6(x,z,t) = kx  ,m(t))- </> (^~-  ,m(t)jj for t>t, l  (see Lachenbruch 1957b, p. 1521).  (  1  5  Further, one can see that i f d e t a i l s  of some c l i m a t i c change are also known, t h i s can be e a s i l y incorporated. F i n a l l y , the e f f e c t of a number o f stages of shoreline movement, combined with that o f 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 temperature 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 a l 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).  Figure 17  DIAGRAM TO ILLUSTRATE SAMPLE SOLUTION OF TRANSIENT MODEL  00  82 The shape of this wave was formed in accordance with temperature measurements 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 configuration in the vicinity of the migrating river, using v = 0.5 m year * 2 - 1 and oc = 21.9 m year  2 - 1 (0.06 m day  ).  Observed and predicted temper-  atures are shown for the borehole locations.  The i n i t i a 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 i n i t i a l position, a curtain-shaped through-talik exists  beneath the river, with the permafrost boundaries plunging steeply downwards.  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 disturbance, 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 permafrost boundaries in Figure 18a).  One notes a remarkable uniformity of  temperature, at depth, beneath the river i t s e l f .  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 P E R M A F R O S T HISTORY U N D E R A SHIFTING C H A N N E L  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 i t s e l f . 6 r ' '  Deviations v (T , -T ) 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-  t e r i s t i c 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. satisfactory.  It is in this zone that the model is least  Figure 19 PREDICTED MEAN ANNUAL GROUND T E M P E R A T U R E S IN THE VICINITY O F THE S N O W B A N K ZONE, SLIP-OFF SLOPE  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 transfer by groundwater flow along taliks. considerable amount of heat.  This could conceivably involve a  Table 14 Sample Calculations to I l l u s t r a t e Effects o f Latent Heat Term on Depth o f Freezing and Ground Temperature Calculations Input Data Soil Water content Organic content Dry density I n i t i a l (uniform) temperature T Step change at surface T Time since step change t  Q  s  = = = = = = =  sandy-silt_ 0.40 gm gm_ 0.05 gm gm_ 1.42 gm cm 4.0°C -3.0°C 50 years  Solution (1)  Solution (2)  For a homogeneous medium,  Depth of freezing z = aVt~, where a i s a constant which i s the root o f the transcendental equation,  exp(-a'/4a )  = erf  u  erf (a/2 v/TTTj) For the depth o f freezing, set T and solve f o r z.  0°C,  For T , input z and solve. The equations were solved for values o f a of 0.0046 cm2 s e c (0.04 m d a y ) , 0.0058 (0.05), and 0.0069 (0.06). - 1  2  z, depth o f freezing T at z = 20 m T at z = 40 m  h. Jll  exp(-a'/4af)  T a  erfc(a/2/5TT)  C T u  s  The subscripts f and u r e f e r to frozen and unfrozen; L i s the volumetric latent heat, a l l other variables are as previously defined. The equation was solved v i a an i t e r a t i v e procedure. Input values ( a l l c.g.s.):  - 1  Results  jo  k C af L f  f  = = = =  Solution (1) a=0.04 21.6m -0.2°C +1.9°C  0.05 24.2 -0.5 +1.6  0.06 26.5 -0.7 + 1.2  0.00627 k = 0.00306 0.545 C = 0.799 0.0115 = 0.00383 45.2 (assume a l l water freezes at 0 C) u  u  a  u  Solution (2) 10.3 m +1.1°C +2.7°C  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. is a function of the rate of migration.  The effect of varying the speed  of migration is illustrated in Figure 20. year \  The latter  As v is increased to 1 m  temperatures on the cut bank side (point #400) tend to be just  slightly cooler, while those under the slip-off slope (point #100) a l i t t l e warmer.  are  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 predicted 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 borehole 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. i n i t i a l position.  A fossil cut bank was taken as delineating an 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 i t s e l f  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. A l 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 i n 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  i t has a changing effect on the conditions of  for example,  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 i s sometimes d i f f i c u l t to resolve the effects of vegetation per se.  The interactions between vegetation and perma-  f r o s t have been variously studied (see f o r example, Benninghoff 1966;  Drury 1956;  Tyrtikov 1963;  1969;  Viereck 1970;  R.J.E. Brown 1965,  1966;  1952,  Running  G i l l 1971).  Various t e r r a i n segments have been i d e n t i f i e d i n the study area, and although there are variations i n thermal regime within each segment, the differences between segments are more s i g n i f i c a n t .  This  i s demonstrated by an analysis of variance conducted on active layer depths (Table 15).  The r e s u l t s indicate that the units do indeed have  some meaning i n terms of variations i n thermal regime, since active layer development represents the integrated effects of both summer and winter regimes. Brief descriptions of f i v e s i t e s used i n most of the microclimatic studies (between-site and around-site scales) are given i n Table 16; four of the. s i t e s are shown i n Plate 5. The following discussion i s organised into three sections: differences i n annual thermal regime, v a r i a t i o n s i n summer microclimate (including active layer regime), and winter differences. 2.  Annual Thermal Regime Ground temperature observations were carried our i r r e g u l a r l y over the study period (1969-1971), being concentrated i n the summer months.  Regular, intermediate temperature values have been estimated  for each s i t e using Fourier synthesis.  The observed values f o r each  depth were f i t t e d to a compound Fourier series using UBC procedure continuing u n t i l the average residual (J ^ Q  FCF*, the  - p T  S  r e  )  This program permits Fourier curve f i t t i n g on unequally-space points.  w a s  data  94  Table 15 Analysis o f Variance - Active Layer Depths in the Five Terrain Segments (July 1970) SOURCE OF VARIATION  DEGREE OF FREEDOM  Active layer depths  SUM OF SQUARES  MEAN SQUARE  F  4  136926.133  34231.533  Error  145  3533.367  24.368  Total  149  140459.500  ** Exceeds the five percent  1404.771**  l e v e l of s i g n i f i c a n c e  Mean Active Layer Depths i n Five Terrain Segments Ranked and D i f f e r e n t i a t e d by the Newman-Keuls Test  SITE  5: 4: 3: 2: 1:  Picea Salix-Alnus Salix(2) Salix(l) Bare ground  MEAN ACTIVE LAYER DEPTH (cms)  NUMBER OF MEASUREMENTS  30.8 62.6 99.2 103.3 110.6  A l l differences are s i g n i f i c a n t at the f i v e percent  30 30 30 30 30  level  95  Table Characteristics  Site  4.  of  16  Five Microclimatic  Vegetation  Sites  Soil  Bare ground-Equisetum ( F r e q u e n t l y submerged in summer)  E q . f l u v i a t i l e (about 10% c o v e r * )  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 o f S . a l a x e n s i s (av. diameter 1-1.5cm, av. h e i g h t 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 in spring)  More s c a t t e r e d growth o f S.alaxe n s i s (av. diameter 4-6cm, av. h e i g h t 3-4m). More dense ground cover o f Eq.arvense, and o t h e r spp.*  0-10cm: S i l t , k-0.0014 10-25cm: S i l t , k=0.0015  Salix-Alnus (Only o c c a s i o n a l l y inundated, by s p r i n g flood)  Dense growth o f S a l i x spp. and Alnus c r i s p a * . up to 2.5-3m h i g h . Ground cover o f Rubus a r c t i c u s , Pyrola grandiflora, and f e a t h e r mosses (Prepano~ c l a d u s u n c i n a t u s , Tomenthypnum nitens)*  0-10cm: Moss and p e a t , w i t h 2-3cm o f silt, k=0.0001-0.0006 10-25cm: M a i n l y s i l t , k=0.0023  Mature canopy o f P.glauca, up to 20m h i g h , w i t h a dense unders t o r y o f Alnus c r i s p a and S a l i x spp. Ground cover s i m i l a r t o ( 4 ) , but a l s o Hylocomium splendens*.  0-10cm: Moss and p e a t , k=0.0001-0.0006 10-25cm: S i l t w i t h organic layers, k=0.0009  S, P i c e a ( R a r e l y inundated by spring flood)  * See G i l l (1971) * These are sample values o n l y , and are e s t i m a t e s based on the p r e v a i l i n g s o i l m o i s t u r e c o n d i t i o n s at the time o f 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 . 0 5 ° 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 retarded.  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 MICROCLIMATIC SITES (September 1969 - February 1971)  99  average air temperatures were 2° to 9°C colder. depths were greater in 1970 to 1971,  At a l l sites, snow  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  are greatest at site 1 (17.7°C at 50 cm).  fluctuations  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 insulating effect during the cold season.  At site 4, the temperature  maximum at 50 cm was only 3.7°C (August 1970). March 1970, was - 9 . 3 ° C .  The winter minimum in  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 - 1 0 . 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 warming 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 i s this which accounts more f o r the higher mean value at s i t e 1.  Site 1 i s about  2°C warmer than s i t e s 2 and 3 i n summer, but i n winter s i t e 2 i s about 6.5°C warmer than s i t e 1, and s i t e 3 i s about 5°C warmer than 1.  By  June, these winter differences are overcome by the homogenising effect of the spring flood.  When comparing s i t e s 2 and 3 to s i t e s 4 and 5,  the differences are again greater during winter.  The foregoing cer-  t a i n l y indicates that i t i s the winter regime which i s the most important i n maintaining s i t e s 2 and 3 at the highest mean temperatures of any of the s i t e s . The differences observed at the 50-cm depth can be mostly followed through at the 3-meter depth.  Site 5 i s s t i l l the coldest,  ranging between -2.0° to -6.8°C (1969-1970).  This i s followed by s i t e  4 (-1.2° to -5.7°C), s i t e 1 (-0.4° to -2.8°C), s i t e 3 (0.0°C to -0.2°C) and l a s t l y s i t e 2 (+1.1° to -0.2°C).  The very small range at s i t e 3  r e s u l t s from the damped winter wave, and latent heat effects where the ground i s continually close to 0°C.  The very warm temperature at  s i t e 2 i n October 1969 i s 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 temperature i n 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 s i t e 1 may also be  due to latent heat effects i n the. moist ground above 1.5 m; the 1.5meter 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 i t to the air in winter.  The heat flux density at the ground surface determines the  quantity of heat entering and leaving the ground; i t 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 variations in ground thermal properties will also cause some differences. Heat flux values during i n i t i a 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 isothermal, 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  Figure 22  1971  CALCULATED VALUES OF AVERAGE DAILY S U R F A C E H E A T F L U X AT F O U R MICROCLIMATIC SITES (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 i t s e l f 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 conclusive 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). tures are homogenised on cloudy days.  As expected, tempera-  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 t a 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 f a l l 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  Table 17b  Analysis o f Variance - Mean Daily A i r Temperatures at Five M i c r o c l i m a t i c Sites ( a l l days, July-August 1970) SOURCE OF VARIATION  DEGREE OF FREEDOM  Analysis o f Variance - Mean D a i l y A i r Temperatures at Five M i c r o c l i m a t i c S i t e s (sunny days, July-August 1970)  SUM OF SQUARES  MEAN SQUARE  F 0.7979  Sites  4  18.042  4.511  Within  160  904.526  5.653  Total  169  922.568  DEGREE OF FREEDOM  SUM OF SQUARES  SQUARE  Sites  4  16.006  4.001  Within  160  424.969  4.722  Total  164  440.975  SOURCE OF VARIATION  Mean Daily A i r Temperatures ( a l l days)  SITE 5 4 3 1  MEAN DAILY AIR TEMPERATURE C°C)  Picea Sal ix- Alnus S a l i x (2) Sal i x (1) Bare j round Equisetum  F -test i s not  significant  13.1 13.8 13.2 13.8 13.8  MEAN  F 0.8474  Mean D a i l y A i r Temperatures (sunny days)  SITE  NUMBER OF MEASUREMENTS 33 33 33 33 33  5 4 3 2 1  Picea Salix-Alnus S a l i x (2) S a l i x (1) Bare ground Equisetum  F -test i s not s i g n i f i c a n t  MEAN DAILY A IF TEMPERATURE (°C) 13.8 14.6 13.8 14.6 14.6  NUMBER OF MEASUREMENTS 19 19 19 19 19  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  4  242.503  60.626  Within  160  331.545  2.072  Total  164  574.048  Sites  F  29.257**  * * Exceeds the five percent level of significance  Mean Daily Surface Temperatures Ranked and Differentiated by the N-K Test  SITE 5: 3: 4: 2: 1: 5  MEAN SURFACE TEMPERATURE(°C)  3  33 33 33 33 33  10.7 .11.4 12.3 12.9 14.2  Picea Salix(2) Salix-Alnus Salix(l) Bare ground 4  NUMBER OF MEASUREMENTS  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 FIVE MICROCLIMATIC SITES (July-August, 1970)  s  109 materials (see Table 16): i) Sites 1, 2 and 3 have a similar mineral s o i l , with some variation in l i t t e r amounts, ii)  Sites 4 and 5 have surface layers of moss and peat overlying s i l t y s o i 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 moisture 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 l e heat is accumulated in the  ground during the day, there is l i t t l e 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 . 0 9 ° 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. smaller range.  The latter, being tree-covered, has the  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 f a l 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 respectively (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 site 2 which is warmer than 3 (Figure 23).  1 is warmer than  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  Table 19b  Analysis o f Variance - Minimum Daily Surface Temperatures at Five M i c r o c l i m a t i c S i t e s (July - August, 1970) SOURCE OF VARIATION  DEGREE OF FREEDOM  SUM OF SQUARES  MEAN SQUARE  Sites  4  400.974  100.244  Within  165  476.721  2.889  Total  169  877.695  F 34.696**  A n a l y s i s o f Variance - Maximum D a i l y Surface Temperatures at Five M i c r o c l i m a t i c S i t e s (July-August, 1970) SOURCE OF VARIATION  4: 5:  Salix-Alnus 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  MEAN SQUARE  Sites  4  3074.038  768.509  Within  165  438.205  17.528  Total  169  3512.242  F 43.844**  Mean D a i l y Maximum Surface Temperatures Ranked and D i f f e r e n t i a t e d by the N-K Test  Mean Daily Minimum Surface Temperatures Ranked and D i f f e r e n t i a t e d by the N-K Test  MEAN MINIMUM SURFACE TEMPERATURE (°C)  SUM OF SQUARES  ** Exceeds the f i v e percent l e v e l o f s i g n i f i c a n c e  ** Exceeds the f i v e percent level o f s i g n i f i c a n c e  SITE  DEGREE OF FREEDOM  NUMBER OF MEASUREMENTS  34 34 34 34 34  Any two s i t e s underscored by the sane 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 level of s i g n i f i c a n c e  SITE  3: 5: 2: 1: 4:  S a l i x (2) Picea S a l i x (1) Bare ground-Equisetum Salix-Alnus  3  5  MEAN MAXIMUM SURFACE TEMPERATURE (°C)  NUMBER OF MEASUREMENTS  13.2 16.9 16.9 18.9 19.6  34 •54 34 34 34  2  1  4  Any two s i t e s underscored bv 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 o f s i g n i f i c a n c e  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-,  22 23 24 25 26 27 28 29 30 31 1  7  8  10 11  4  12  13 14  15  16 17 18  19 20 21  August  July Q Site 1  9  | Site 2  | Site 3  § Site 4  | Site 5~  No data  Figure 2 4 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 temperatures) .  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. scan was easily accomplished in 10 minutes.  Each complete  An analysis of variance was  performed, considering the data as a stratified random sample (Table 20). At a l 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  4  249.144  62.286  Within  295  284.018  0.963  Total  299  533.163  Sites  F 64.694**  * * Exceeds the five percent level of significance  Mean Incident Light Values Ranked and Differentiated by the N-K Test  5: 3: 4: 2: 1:  5  NUMBER OF MEASUREMENTS  MEAN LIGHT VALUES*  SITE  12.42 13.36 14.04 14.07 15.19  Picea Salix(2) Salix-Alnus Salix(l) Bare ground 3  4  60 60 60 60 60 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 G i 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). warmer than 5.  Similarly, site 4 is  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 o f 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  4  1550.362  387.591  413.487**  Within  160  149.979  0.937  Total  164  1700.341  Sites  **Exceeds the five percent level of significance  Mean 10-cm Temperatures Ranked and D i f f e r e n t i a t e d by the N-K Test  SITE 5: 4: 3: 2: 1:  Picea Salix-Alnus Salix(2) Salix(l) Bare ground  MEAN 10-cm TEMPERATURE(°C) 4.8 6.8 10.6 11.6 13.0  NUMBER OF MEASUREMENTS 33 33 33 33 33  A l l differences are s i g n i f i c a n t at the f i v e percent level  12  Hours  16  (Local Time)  20  24  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. Appendix 6.  Daily heat flux totals are listed in  Heat flux densities were generally small values (less than  0.1 ly min 1 ), and this made data reduction quite d i f f i c u l t .  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 parallels 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 ) and Ground Heat Flux (G) at Five M i c r o c l i m a t i c S i t e s (July-August, 1970)* n  S i t e Pairs  No. Days R„ ( l y day-1) G (ly d a y l ) G/RJI  1  2  1  3  1  4  1  5  9  9  6  6  6  6  7  7  207. 2  47.8  218. 9 187.1  336.5 179.0  215. 1 172.9  16. 9  13.1  28.9  9.9  17. 9  7.5  16. 3  3.1  7. 7  7.0  8.6  5.5  8.3  4.3  7. 9  6.5  (%)  R/Rl (%)**  85.5  G/G (%)**  77.5  x  -  53.2  80.4  23.1  34.2  41.9  19.0  *Paired observations were made between s i t e 1 and the other s i t e s i n turn. **The r a t i o o f the value at the p a r t i c u l a r s i t e (2,3,4 o r 5) to the corresponding value f o r s i t e 1.  Table 23 Mean D a i l y Maximum and Minimum 10-cm Temperatures at S i t e s 1, 2 and 3 (July-August 1970)  1  Maximum  14.7°C  Minimum  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 repositioned 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). A l 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 2 6  M E A N D I U R N A L 10cm. T E M P E R A T U R E R E G I M E S A T T W O S I T E S IN T H E Picea S E G M E N T ( J u l y - A u g u s 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  Sites  SUM OF SQUARES  MEAN SQUARE  F  269.679**  4  2571.177  642.794  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  5: 4: 3: 2: 1:  Picea Salix-Alnus Salix(2) Salix(l) Bare ground  MEAN 25-cm TEMPERATURE(°C) 0.7 4.1 9.2 9.6 11.2  NUMBER OF MEASUREMENTS 33 33 33 33 33  A l 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 in ground thermal regime between sites (Table 25). sites 2 and 3 does there seem to be any overlap.  differences  Only in the case of 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 the winter season.  ground climate in  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  Table 25b  Analysis o f Variance - Half-Hourly 10-cm Temperatures at Three M i c r o c l i m a t i c S i t e s : 1,4,5 (August 23-24, 1970)  Analysis o f Variance - Half-Hourly 10-cm Temperatures at Three M i c r o c l i m a t i c S i t e s : 1,2,3 (August 25-26, 1970)  SOURCE OF VARIATION  DEGREES OF FREEDOM  SUM OF SQUARES  MEAN SQUARE  F  SOURCE OF VARIATION  Sites  2  1317S.498  6587.749  855.828**  Sites  Within  1320  14 84.987  1.125  Total  1322  14660.485  **E.xceeds the f i v e percent level o f s i g n i f i c a n c e  5: Picea 4: Sali.x-Alnus 1: Bare ground  MEAN 10-CM TEMPERATURE (°C)  MEAN' SQUARE  2  310.030  155.015  Within  1152  456.936  0.397  Total  1154  766.966  F 390.815**  Mean 10-cm Temperatures at 1,2,3 Ranked and D i f f e r e n t i a t e d by the N-K Test  NUMBER OF MEASUREMENTS  441 441 441  5.0 6.1 12.2  A l l d i f f e r e n c e s are s i g n i f i c a n t at the f i v e percent  SUM OF SQUARES  "Exceeds the f i v e percent l e v e l o f s i g n i f i c a n c e  Mean 10-cm Temperatures at 1,4,5 Ranked and D i f f e r e n t i a t e d by the N-K Test  SITE  DEGREES OF FREEDOM  level  SITE  3: S a l i x (2) 2: S a l i x (1) 1: Bare ground  MEAN 10-CM TEMPERATURE (°C)  NUMBER OF MEASUREMENTS  S.6 S.S 9.S  A l l d i f f e r e n c e s are s i g n i f i c a n t at the f i v e percent l e v e l  385 385 385  125 One can i d e n t i f y a twofold influence on the ground thermal regime due to the presence o f a snow cover (Gold 1963): 1) I t interposes a layer with low thermal conductivity between the  a i r and the ground, and thus protects the l a t t e r against  cooling (and warming).  The insulating e f f e c t of snow i s  greatest f o r lowest densities since the thermal conductivity of snow i s a function of grain-to-grain contacts ( i . e . , density).  (Other processes of heat transfer are not con-  sidered here, but see, f o r example, Yen 1963). 2) I t increases the e f f e c t i v e depth, below the surface, of points within the ground  ( i . e . , a point 1 m i n the ground,  and beneath 1 m o f 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 e f f e c t s 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 i s  reduced; Gold (1963) showed that the snow cover induced a Fourier component with a period of a half-year into the annual regime.  In winter,  ground temperatures at snowy s i t e s are higher than at s i t e s with no snow, assuming they were at the same  temperature i n autumn.  Many studies have shown that a snow cover protects the s o i l from rapid temperature changes, and maintains higher ground temperatures ( f o r example, Bay et a l 1952; Crawford 1952; Potter 1956; Beckel 1957; Gold 1958, 1963, 1967; Annersten . 1964, 1966).  Gold (1963) showed, at an  Ottawa s i t e , that snow cover was the main factor i n maintaining the mean annual ground temperature from 1.25° to 3.25°C higher than the a i r temperature. Where the winter season i s longer, t h i s 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 f a l 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 significant 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 26b  Table 26a  A n a l y s i s o f Variance - Snow Depths i n Three T e r r a i n Segments (December 1970)  Analysis o f Variance - Snow Depths i n Six T e r r a i n Segments (March 1971) SOURCE OF VARIATION  MEAN SQUARE  SUM OF SQUARES  DEGREE OF FREEDOM  SOURCE OF VARIATION  F  Sites  S  97324.167  19464.833  Within  114  7676.200  67.335  Total  119  105000.367  289.074**  6: 1: 5: 3: 4: 2:  Channel Ice Bare ground Picea S a l i x (2) Salix-Alnus S a l i x (1)  2  39302.578  19651.289  Within  42  5530.400  131.676  Total  44  44832.978  6  1  5  20 20 20 20 20 20  29.9% 22.4 11.3 3.0 8.5 10.6  41 59 75 80 116  3  F 149.240**  Mean Snow Depths Ranked and D i f f e r e n t i a t e d by the N-K Test  NUMBER OF MEASUREMENTS  COEFF. OF VARIATION  29  MEAN SQUARE  Sites  Mean Snow Depths Ranked and D i f f e r e n t i a t e d by the N-K Test  MEAN SNOW DEPTH (CM)  SUM OF SQUARES  "Exceeds the f i v e percent l e v e l o f s i g n i f i c a n c e  **Exceeds the f i v e percent l e v e l o f s i g n i f i c a n c e  SITE  DEGREE OF FREEDOM  •  .1  Any two s i t e s u n d e r s c o r e d by t h e same l i n e a r e n o t s i g n i f i c a n t l y d i f f e r e n t at t h e f i v e p e r c e n t l e v e l  SITE  1: Bare ground 3: S a l i x (2) 2: S a l i x (1)  2  A l l differences  MEAN SNOW DEPTH (CM) 26 50 98  COEFF. OF VARIATION  NUMBER OF MEASUREMENTS  46.0% 4.4 16.0  are s i g n i f i c a n t at the f i v e percent l e v e l  15 15 15  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 exposure 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 (cm)  38.1  86.5  45.9  47.2  42.3  Coefficient of Variation %  44.4  22.0  3.5  6.4  9.5  The pattern has also been observed in previous years (see G i l l 1971).  129  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). up to 170 cm were measured. shown in Plate 7.  In the drift area snow depths  This distinctive accumulation pattern is  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,  in snow depth are most c r i t i c a l at shallow snow depths.  variations  The exponential  distribution is consistent with the simple heat conduction model of temperature 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  o o  80  o o  60E o  CL Hi  o o  a i o  oo o o  40-  o o o o  20  -25  o  -20  -15  —i—  -10  Temperature (°C)  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. eratures  The greatest difference observed in surface temp-  in summer was only about 10°C. This seems to indicate that.on  the slip-off slope spatial variations in thermal regime are more significant 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 l e wind action.  In the present study area, the more exposed,  windy sites have somewhat denser snow (Table 28). hance the snow's value as an insulator.  The low densities en-  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 i t s e l f . snowdrift area (Salix (1)),  Values drop in the more sheltered  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 i t s e l f , the bare ground is less exposed  133  Table 28 Snow cover characteristics along two transects across a slip-off slope  Point Bare Ground Snowb ank J'  It  r  Salix(2)  1  1 2 3 4 5 6 7 8 9  Snow(cm) 23 40 4 23 70 110 64 44 48  Transect 1 0-25 cm k** Y* .31 .36 .33 .33 .27 .20 .14 .13 .13  .65 . .88 .74 .74 .50 .27 .13 .11 .11  25-50 cm Y _  k  50-100 cm Y  k  _  .33  .74  -  -  .28 .32 .25 .27 .26  .53 .70 .43 .50 .46  .30  .53  3 0-25 Point 1 2 Bare Ground 3 4 5 Snowbank \ 1I 6 7 Salix (.2)-. 8 9  Snow(cm) 50 77 20 37 98 115 68 49 45  Y *  .22 .19 .17 .19 .18 .21 .13 .13 .14  3 * Density (gm cm ) * * Thermal conductivity (c.g.s.xlO )  k** .33. .25 .20 .25 .22 .30 .11 .11 .13  25-50 cm k Y .33 .29 .23 .27 .30 .24 .23 .24 .23  .74 .57 .36 .50 .53 .39 .36 .39 .36  50-100 cm Y  k  1  .31 .30  .65 .53  134 and average densities are lower (Table 28).  Thus sites on the point i t s e l f  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). data from transect  2 is discussed  The  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 i t s e l f ; 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 accumulation 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 A T T E N SITES A C R O S S A SLIP-OFF SLOPE (August 1970-July 1971)  140-1 A 7  120  100  I  80  10 60  10 •  • August 1970 • December 1970 A March 1971  *8  40  if*  20  6.V -5  -4  0  '  1  Temperature (°C)  Figure 29  ONE-METER TEMPERATURES PLOTTED AGAINST SNOW DEPTH A T TEN LOCATIONS A C R O S S A SLIP-OFF S L O P E  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 d a y 1 ) from the Top one-meter Ground Layer at Three Sites on a Slip-Off Slope December 1970-March 1971 Ground 1/12/70 15/12/70 1/1/71 15/1/71 1/2/71 15/2/71 1/3.71  -  15/12/70 31/12.70 15/1.71 31/1/71 15/2/71 28/2/71 15/3.71  -1.9 -1.7 -2.0 -1.8 -1.9 -2.0 -1.0  S  a  l  i  x  -0.4 -0.1 -0.4 -0.2 -0.4 -0.3 -0.2  ^  S  a  l  i  x  -0.8 -0.6 -0.9 -0.7 -0.8 -0.8 -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) Maximum Minimum  1  Bare ground 2 3 4  1 Snowbank Zone  5  1  6  7  8  1  Salix(2) 9 10  -1..2 -1.,3 -1.0 -1., 1 -0.4 +0.3 +0.4 +0..2 -0.2 -0.4 3,.9  4.,0  3.8  2,.6  2 .2  2.1  2.5  2..3  3.5  4.0  -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. involved in this were discussed in Chapter 4.  The thermal processes  Maycock and Matthews (1966)  describe a situation where i t 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 d i s t r i b u t i o n of frozen ground along a number o f transects (on a second s l i p - o f f s l o p e — s e e  Figure 3) was determined by over two hundred 4  hand borings i n August 1970. using a hand d r i l l .  A l l borings were made to a depth of 3m,  The results from three of the transects are shown  i n Figure 30, together with the snow cover data f o r March 1971. The complicity o f the snowbank i n the pattern of t a l i k v a r i a t i o n i s c l e a r l y indicated; both the t a l i k and the snowbank are more extensive i n the downstream d i r e c t i o n .  There i s then a wider zone of warmer ground  temperatures at the downstream end, as shown i n Table 31.  As was shown  for transect 2, the zone o f warmer temperatures correlates with the zone of reduced winter cooling; s p a t i a l variations i n summer regime are not so important.  The maximum and minimum temperature data i n Table 31 further  substantiate t h i s explanation. The warming e f f e c t 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 5-1 Distance n D  ^ U n J  h  (m) 3 6 9  Snowbank Zone 5-2  10 -0.8 -0.5 -0.1  5-3 5  -0.1 -0.0 -0.1  Salix(2) 5-4 5  +0.1 -  -0.7 -0.5 -0.2  The s i t e s i n the snowbank zone are warmer at least to depths of 6 m.  By  9 m the differences have been eradicated, and the ground i s frozen a l l the way across the slope.  The unfrozen  thus forms a "basin", or pseudo-talik.  zone associated with the snowbank Data from transect 7 reveal a  Frozen, i n this context, means s o l i d l y frozen.  140 Willows start I  Transect 5  Willows  0  -2  -4  Transect 5-A  Willows  Transect 7 See Figure  Figure 30  3 for location  of  Transects  DETAILS O F P E R M A F R O S T CONFIGURATION A L O N G VARIOUS T R A N S E C T S ACROSS A SLIP-OFF SLOPE  141  Table 31 Temperature data from snowbank transects 5 and 7 ( A l l temperatures are at a depth of 1.5 m)  Transect 5 Snowbank Zone 2  Site No. Distance (m)  3 2.5  Temp. (°C): Mean Annual •1.8  4 2.5  5 2.5  6 2.5  7 2.5  8  10  2.5  -0.8  -0.2  -0.1  -0.1  0.3  0.6  .0.3  -0.9  -1.4  Maximum  0.6  1.1  1.3  0.2  0.0  1.9  2.6  1.9  -0.2  -0.3  Minimum  -7.6  -2.7  -0.8  -0.4  -0.1  0.0  0.0  -0.1  -2.2  -3.3  Transect 7 I Site No. Distance  1  (m)  5  Temp. (°C): Mean Annual -2..2 Maximum Minimum  2  0.,0 -8.; i  Snowbank Zone 3  2.5  4 2.5  5 2.5  j  6  7  8  2.5  2.5  2.5  9  10  5  5  -0..2  0.,8  1..1  1..3  1,.0  0,.9  1..0  0..9  0..0  3..1  4..7  5,.0  4..7  4.,9  4..8  3. 8  -0..3  - o . ,2  0..0  0,.1  0..0  0,.0  0..0  0.,0  142 s i m i l a r pattern, but with a wider unfrozen zone:  J  Snowbank Zone  7-2  7-3  Distance (m) Depth  3 6 9  10 -0.3 -0.1 -0.2  | 7-4  10 +0.1 -0.1 -0.2  7-5 10  +0.1 0.0 -0.2  -0.3 -0.1 -0.2  A f i n a l stage i n the analysis of t a l i k v a r i a t i o n might be to account f o r the d i f f e r e n t i a l snow accumulation along the s l i p - o f f slope. The fetch to the north-west  (a p r e v a i l i n g wind d i r e c t i o n ) i s greater at  the downstream end, which might account f o r some of the difference. However, on the other s l i p - o f f slope, where t h i s difference i n exposure i s not r e a l l y present, a s i m i l a r d i f f e r e n t i a l snow accumulation i s s t i l l found to some extent.  The S a l i x ( l ) band of willows i s narrower at the  upstream end, although i t seems that this would not be important once the d r i f t has been i n i t i a t e d .  F i n a l l y , there are differences i n topography;  the outer slope i s steeper at the upstream end (Figure 30), and i t may  be  that more of the snow there i s blown along rather than across the slope, and does not end up i n the snowbank zone. F i n a l l y , the s i m i l a r i t y between the snowbank e f f e c t and that due to unfrozen water bodies should be noted. water beneath  The presence of unfrozen  lake and r i v e r i c e , maintains bottom temperatures near 0°C  throughout the winter.  This reduction i n winter cooling leads to warmer  mean annual temperatures, and the net e f f e c t 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. differences segments.  For example,  significant  in net radiation were found to exist between major terrain 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 through to the subsurface regimes. materials are markedly different, of small ground heat fluxes.  carry  At the other sites, where ground low ground temperatures are a result  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 s o i l , which tends to preserve 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 t s e l f 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 i n i t i o .  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, sprucecovered 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 f i e l d . 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 accommodate 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)  A l 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 temperatures 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 i t s e l f .  APPENDIXES  149  150  APPENDIX 1 Glossary of Terms  Active layer  The top layer of ground subject to seasonal freezing and thawing  Depth of zero annual amplitude  The depth to which seasonal temperature fluctuations extend into the ground. Beneath this, temperatures remain constant year-round  Frost table  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)  Geothermal gradient  The increase of temperature with depth in the earth, due to the heat received from sources within the earth  Pereletok  A frozen layer at the base of the active layer which remains unthawed for one or two summers (Stearns 1966)  Permafrost table  The surface which represents the upper limit of permafrost  Talik  An unfrozen portion within the body of permafrost. It usually implies thawed ground that was probably permafrost at some time (Stearns 1966)  Through-talik  A thawed zone that perforates the permafrost  Pseudo-talik  A thawed zone that does not perforate the permafrost. The permafrost table is locally depressed, while an upward indentation is formed in the base of permafrost  Terrain segment  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)  Zero curtain effect  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 C  THIS PROGRAM COMPUTES DISTANCES AL0N3 RAYS FROM ANY BASE POINT 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 EFFECT OF THE WATER BODY ON THE GROUND TEMPERATURES (AT ANY DEPTHS} AT THAT BASE POINT REF • LACHENBRUCH*-.1957! - U « S t G » S » - BULLETIN..* 1052-B THE PROCEDURE IS REPEATED FOR ALL WATER BODIES IN THE AREA AND THE TOTAL EFFECT SUMMED 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 - R L L N  £  C C C  C C C C C C C C CC C C C C  IN THE PROGRAM BELOW* THE OUTLINES ARE IN INCHES* WHILST THE OUTPUT IS CONVERTED TO METERS AND <MS . _. . DISTINCTION IS MAINTAINED BETWEEN LAKES AND RIVERS IC-1 (LAKE) I-C*2 (R-UVXR4 : :  THE PROGRAM* AS LISTED* USES A LIBRARY ROUTINE (SOLVD) T O SOLVE-A-PAIR OF SIMULTANEOUS EQUATIONS." T H E VARIABLES A* DET* TEST ARE REQUIRED BY THIS PROGRAM  S.EAL_kAJ3S.DJ DOUBLE PRECISION A* DET* TEST DIMENSION-R1(500)*R2(500)*X(200-)*Y(20.0)ARV1(50)*JRV2(50) ... DIMENSION A(2*3)*B(2*2)*Z(2*2)*T(10*10) D IMENSION SSTEMP(20)*DTHETA(20)*D(20)#TTEF1(20)*TTEF2(20) COMMON C  RVl*RV2*Rl*R2*ID I F F * I  ..... READ IN INPUT DATA  c c  C C C C C  SAME*ILAKE*KC :  IF- IAR-0* . LAKE- AREAS - ARE CALCULATEDF-IF IAR-1* THEY.ARE NOT. . . KD-NUMBER OF DEPTHS FOR WHICH THE TEMPERATURE EFFECT IS TO BE CALCULATED -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 E N I E D . SCALE»SCALE OF BASE MAP (RATIO FORM) 10  READ(5*10) IAR*KD*LAMBDA*SCALE FORMAT!II*I2*F2»0*F6»0) SC-SCALE/39.3701  C 11 C — 1 13  1020  1030  111 2  C C  C  -  -~  D U J - T H E D E P T H S FOR W H I C H THE T E M P E R A T U R E EFFECT IS CALCULATED READ-15+-1-14 ( D L K - U X - « ^ » J C D J F0RMAT(2CF3»0) READ IN T H E BASE POINT «I»D«' COORDINATES) R E A D t - 5 j - 1 3 j - E N D - a 3 Q O ) I DM2^-XQJLYJQ : FORMAT(I3/2F10.5) REWIND 8 A N G L E — « _ L A j a B D A./-3. 6-QJ RADLAM-LAMBDA*.01745 IT0T-180.0/LAMBDA W R I T E (6* 1 0 2 0 ) IDN2.JX0JJ*0 — FORMAT!1H1/25X*»** 3E0THERMAL FUNCTION IS T E A D Y - S T A T E ) t S I T E S «JI3* U X * ' t X 0 » » j F 6 . 2 * • Y0»'iF6.2*») **•) W R l X £ - ( 4 4 - 1 0 3 . 0 ) I D-t-JCLi.XP-U.iCDJ . FORMAT(//IOXJiZ'115X*10 IF5•l»5X)) DO 1 1 1 K - l ' K D T T E F 1 (K )" 0 •0 „ . . TTEF2(K)"0.0 K I - 1 Mi«fl  INK-O INUM-1 J l - 0 KC-500 DIGITISED O U T L I N E S ARE READ I N FROM UNIT 8 END OF ANY OUTLINE I N D I C A T E D BY Qj_Q QJJQ ..... READ IN LAKE OUTLINE 3 IL-IKI-1)*7+l IU«IL*6.READ(8,12*END-850)IDN1*lZ»<X(I)*Y(I)» I-IL*IU> 12 F0RMAT(I3iIl<l*F5«2> DO h J ^ I L ^ D J : IF(X(J)»NE«0.0) 30 TO 4 IF(Y(J).EQ.O.O) QO T O 5 »t C O N T I N U E ...... - .--  __  .  ICDUNToICOUNT+7 KI-KI+1 5  6  8  20  22  GO_io_a  ICOUNT=ICOUNT+(J-IL)  ..... Z E R O OUT D O 6. J B I J K D SSTEMPIJI-O. DO 8 J » 1 J K C R.U.J-L*-OJ R2(J>»0« KC-0 Y1»Y( 1 ) X1«X~( 1 ) Y2«YI 2) X2=X-t-2-)—  ARRAYS  _  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 — V E O X l - X O IFIVECI'EQ.O.O) GO T O 20 S LOR£4»4-T4-"0W-WV4C1 DIV»SQRT( l.t>SLOPEl*SL0PEl) C0N»Y0-X0*SL0PE1 CY»1. QO TO 22 CY"0. S L O P i E J f l * CON-XO VEC1-Y1-Y0 CONTINUE RV1(1)»SQRT((Yl-Y0)*¥2+(Xl-X0)**2> IDIFF-0 ISAM£"-1 : ..... CHECK FOR TANGENT CONDITION ..... SIGN1»Y2*CY-SLOPE1*X2-CON SIGN2-YII COUNT)*CY-SLOPEl*XlICOUNT)-CON-  1  IF < SIQN1130*32*34 30  IF(SIGN2)36*38*38  32  IF-i-S I G i s i 2 - l 3 8 - i - 3 6 . j j - 3 8  34  IF(SIGN2)38*38*36  36  :  ISAME-ISAME+1 RV1(ISAME  )»RV1(1 )  C C  .....  FIND  OTHER  INTERSECTION  POINT(S)  3 - 8 - C O NXIiNU E DO  > 2 J I C Q U N T  100  XI»X(I) YI-YJI>  -  X I P « X ( I - l ) YIP=Y(I-l) S- I G N « Y I » C Y - S L O P E H r X l - C O N  .  SIGN-SIGN/DIV C  •••••  TEST  IF-LS.I&N) 40  FOR  IF-U-USQtQ) GO TO 54  C  GO GO  TO TO  SIGN  100 10.0  J2-2 1F{J1.EQ«J2)  -GO—TO-100  I F I J L E Q ' O )  GO  ••••• 54  OF  J2»l IF(J1.EQ«J2)  50  CHANGE  40*60*50  SET  UP  To  THE  100 TWO  EQUATIONS  AND  FIND  INTERSECT  A<1*1UCY A(1*2)--SL0PE1  . C  At1*3)>C0N •• CHEC K  T0  S E E.  IF  T H E . S L O P E . .IS  INF INIT E  •  XT-XI-XIP IF(XT»EQ»C«0)  GO  TO  56  SLO-P-E2a-( Y I - Y I P L ^ X I  -  A (2J 1 )a 1• A(2*2)--SL0PE2 A(2*3)«YI-SL0PE2*XL.  .  .  _  56  QO T O 5 8 A t 2*1)«0«  '.  _Al2i2J.-lj  -  A(2*3)»XI CALL SOLVDlA*2*2*3*0.0D0*DET*TEST) QO TO 7 0 Z(1* 1 ) - Y l Z(2*l1-XI . .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 » • » • • IF A TANGENT* R VALUE IS IGNORED SIGN1-YIP*CY-SLOPE1*XIP-CON IF(I.EQ«ICOUNT) 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 GO TO 6 3 62_S IGN2-i-Y-lACX?-£L0PE 1» X 1 -CON 63 IFtSIGNl16**65*66 64 IF(SIGN2>100*70>70  58 60  65  IF(SIGN2)70*100*70  66  IF(SIGN2«GT»0.0>GO  70  Z(1*1)»A(1*3) Z-L2*-U«A-t2*3-) VEC2«Z(2*1)-X0 R-SQRT((Z<l*l)-Y0)**2 +VEC2»VEC2) t^jj_t_CHECK TO S F E I F THIS VECTOR  C  -  TO 1 0 0  IS IN THE  SAJlE_J)IRECTlON  AS T H E B A S E VECTOR IF(VEC2»EQ«0.Q) VEC2«Z(1*1)-Y0  V-SIGN«VE-C1^V-£C2  80  IF(VSIGN.GT»0.0) IDIFF-IDIFF+1 RV2( I D I F F )«R GO T O 1 0 0 ISAME-ISAME+1 R_V 1 1 1 S  100 J 1 - J 2  A MEJJLR  GO -  TO  80 -  -  -  C C C  IS THE BASE POINT WITHIN THE LA<E OUTLINE? IF IDIFF IS > Oi AND ODD* THE BASE.POINT IS INSIDE THE LAKE • • • • • INOEX"MOD(IDIFFJ 2 ) 1 COUNT--1 CO-UN** 4 X(ICOUNT)»X1  Y(ICOUNT)»Yl  C C  -  -  COMPUTE  INTERSECTIONS  FOR  OTHER  RAYS  C  -C C  .....  C  FIND  ANGLE  OF  BASE  LINE  THETABATAN-( S L O P E D  ISUM-i  K-i  C C  ••••• 200  CHECK  WHETHER  IF(INUM'EQ.O)  GO  IF! INDEX.GT»0) CALL GO  204 205  G0  LAST  RAY  INTERSECTED  THE  LAKE  SUCCESSIVE  RAYS  •••••  210  TO. 2 0 4  EXSORT  TO  CALL  THE  TO  205  INSORT  CONTINUE  C  FIND  NEW  SLOPE  AND  GO  235  EQUATION  FOR  INR-0 IF(ILAKE«EQ«1) £  .....  IS  THIS  IFIINK.EQ.O) IK--1  THE GO  TO  TO  FIRST  OR  SFCONO  GROUP  OF  RAYS  .»•«.  220  I-IVUM--0 GO  _  C  c  TO  230 IF  THE  PREVIOUS  RAY  GO.T.O_.THE...AEXJ  WAS PA  THE  ST_.QE_  LAST  TO  INTERSECT  T.H E . C 0 M P U . T A T 1 0 N .  THE  LAKE  210  IF(INK.EG'1) Q0 T O 555 I K = -<  ...  INK-1 . . . 30 T O 230 220 IK-1  _  1 NUM*0  230 ISUM-ISUM+1 IFIISUM»QT.ITDT) S O T O 555 T H E T A » T H L T A + ( RADLAM*FLOATdK) ) 00 T O 236 235  ISUM»ISUM+1 IF4-ISUM-«-G-T-t-I-T0T )  30 T O 555  THETA»THETA+RADLAM CHECK T O 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 O F J l . » . » • SIGN"Y1*CY-X1*SL0PE-C0N SIGN-SIGN/DIV  :  IF(SIGN»GT.O.) G O T O 260 J l - 1  GO—T0_2-7_Q 260 Jl-2 270 CONTINUE THDEG»THETA/0.01745  FIND INTERSECTS FOR EACH NEW R A Y  -.  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 T O 320 J2«2 1F(Jl•EQ•0) GO To 400 IF(J2.EQ«J1) GO TO 500 SET UP THE TWO EQUATIONS AND FIND INTERSECT CHECK TO SEE IF THE SLOPE IS INFINITE >n'J 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 A(2J1)-0. A(2J2)B1* Ai2i3)>XI A(ii 1)-CY A l l J_2_li»3UiJP_E A(li3)»C0N CALL SOLVDIA,2J2•3>0•ODO,DET>TEST> GO TO 350 INUM-I :  310 C £  320  325 330  :  340  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*400,350 350  SIGN2-»-QT-J-0 t 0 ) Z( If 1 ) - A ( 1 * 3 )  GO  -  T-O—4&Q  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  C C  CONVERT.. DISTANCES TO REAL. UNITS • • • •. DO 600 J-liKC Rl(J)«Rl(J)*SC 600  R2iJJ-PR21JJJLSC  COMPUTE THE AREA O F 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-SXARXaXi  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  710  CONTINUE DO  720  K»1*KD  7 2 0 - S S T E M P ( K ) » S S T E M P ( X ) •ANGLE C  ASSIGN  VALUES  IF(IC»EQ»2>  GO  To  TO  .  APPROPRIATE  -  _.. ~  SUB-TOTAL  730  D.0_225_-K"1J.XD 725 T T E F 1 ( < ) » T T E F 1 ( K ) + S S T E M P ( K ) GO 730-  CONTINUE DO  735  TO 770 735  -- -  K»l*KD  TTEF2(K)"TTEF2(K)+SSTEMP(K)  7J74^0I^-I-NUE 300 1040  W R I T E I 6*  1040)IDN1*ISSTEMP(<)tK-l*<D)  FORMAT(//5X* F 1  IF( IAR.EQ»0 J 1010  FORMAT{/2XJ'AREA  C  GO GO 850  1045  <LAKE5•*13*')«t7X*10(F7.6*3X)/)  W R I T E ( 6* 1 0 1 0 )  TO  TO  THE  AREA  •'*F5.2*' NEXT  SQ  KMS')  LAKE  2  WRITE(6*  1045)  FORMAT(//2Xi  WRITE(6*1044)(TTEF(K)tK"l*KD) 3JJMf_F-0RMAJ4-U<0*-2-4-XJ-1UXF7 . 6 J 3 X - L ) C  GO GO 900 1060  TO  TO  THE  NEXT  BASE  POINT  1  WRITEI6* 1060)  -  F 0 R M A T ( / / / * 4 0 X i T H I S  C  STOP ENO  :  . . .  IS  THE  LAST  BASE  POINT  SUBROUTINE DIMENSION  INSORT 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  ILAKE-1 IF(ISAME'EQ'1 5  CALL  )  QO  TO  12  SS0RT(RV1J ISAME)  _.  M-ISAME-1 DO  10  I=1*M*2  KC»KC*1  10  R2(KC)»RV1(I) R I1 K O - R V 1 ( I+ l )  12-KC»KC+i  —  R i l K O - C O R2(KC)»RV1(ISAME) I S.A ME«.Q IFI I D I F F » Q T » 0 )  3 0  TO  15  RETURN -15-  I F (IDIFFJEQ'-1)—QO—T-0-22 CALL  SS0RT(RV2JIDIFF)  M-IDIFF-1  0.0-2 0_X MU-IU-Z KC-KC+1  R2(KC)»RV2(I) 20-Rl(KC)-RV.21Itl-l 22  KC»KC*1  R1 (KC ) " 0 • 0 R.21KCl.RVgt I D I F F ) IDIFF-0 RETURN END-  SUBROUTINE EXSORT DIMENSION 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 ^ - D X F F _ * 4 - S J ^ £ J _ I L A X £ J-K-C ILAKE«0 5 CALL S S O R T ( R V l i l s A M E ) M-ISAME-1 DO 1 0 I " 1 * M * 2 KC=KC+1 R24-KC-U-RY-U-I-)  10 R I ( K O - R V l ( 1 + 1 ) ISAME-O —-  I F {IDIFF...i Q T » 0 ) S 0 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 2 0 > 1 * M * 2 KC"KC+1 R 2 ( K C ) « R V 2 ( I-) 20 R 1 ( < C ) « R V 2 ( I + 1 ) IDIFF-0 RETURN END S U B R O U T I N E SSORT t A R R A Y * N) DIMENSION ARRAY(50) NN*N«1 DO 10 I » 1 * N 00 1 3 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 - 1 3  T1«ARRAY(J) ARRAY!J)"ARRAY(J+l) A RRA-Y-tJ*U-*-Hl 13 C O N T I N U E 10 C O N T I N U E R E T U R N ... . END  _  165  APPENDIX 3  Computer program to compute thermal effect of a shifting river  THIS  PROGRAM  DISTURBANCE  COMPUTES THE  ON  .1N—TH I S  VERSION*  AND  THE  THERMAL  THE  SHIFTING  FORMULATED THE  FORM  ARRAY  OF  T-HE.-R IS  WAVE  A  LY.£R_lS_ALLfl THE  IS  EFFECT  OF  W E 0_TO_MI.GSA.TE-.  CALCULATED  (THE  PROGRAM  USES  A  BY  A  TEMPERATURE  OF  VE3ETATION  SPECIFIED  BY  THE  ARRAY  INFORMATION  ON  THE  RATE  LIBRARY  STRIP-SHAPED  INTEGRATION  A CR  OSS_T.HE._SUREA.C E  ACCORDINGLY. WAVE*  WHICH  "A* • AT  ROUTINE'  A  WHICH  COMPANION THE  THETA(25*100)  DIMENSION  T I M E O O ) * A ( 3 0 ) :  TSHIFT )/«1.0-fY*Y)  FUNCI Y ) - E X P ( - A M * ( 1«0 + Y*Y) PI-3.14159 IN  -  INPUT  DATA  SO DX  -  THE THE  WIDTH OF T H E R I V E R HORIZONTAL GRID INTERVAL  DZ  -  THE  VERTICAL  IX  -  THE  GRID  NX  -  THE  NUMBER  CF...COLUMNS  IN  NZ  -  THE  NUMBER  OF  THE  ALPHA  GG TS  •  -  THE  GRID  POSITION ROWS  THERMAL  SURROUNDINGS  THE  GEOTHERMAL THE  RATE  OF  THE  IN  READI5*102)ALPHA FORMAT(F4«3)  THE  AT  TIME  ZERO  GRID  . .__  GRID (M*M/DAY)  TEMPERATURE.PR  CHANNEL  READ(5*100)S0J0X*DZ*IX*NX*NZ 1J_J__F_Q S M A I L S FJL_Q.*_3.I_3_ 1  RIVER  GRADIENT  .•- T H E . G R O U N D . S U R F A C E -  INTERVAL OF  DIFFUSIVITY  THE  TSHIFT  102  .  "SIMPSON" )  JD 1 « £.M S J O J S - X J J J _ 1 * _ Z _ _ 5 J  READ  TAIL  .  _  DIMENSION  COMMON  IS  SUCCESSION*  X H E-W A V E - C H A N G E - S _ W . I X R _ T H E _ V . E G E T A J . I O N _ S U C . C E S S I A N J . EXTERNAL FUNC LOGICAL IE  A  RIVER)  EFFECTS  IS  PROVIDES  THERMAL  (E•G •  SIMULATED  INCLUDE  THE  "TIME"  GROUND  DISTURBANCE  RIVER  TO  THE  SURFACE  SHIFT  I OR.. T O  ..DISTURBANCE  OF  167  cn  Of Ul  m o •  to «-• X  CO J 111  z z  CO  2-1  <  X CJ  °i o  ui  o  <  Q  c r a iii a u cij  u i tt  or ui >  Ul  o  a. E  r  oinI Z CM, v: IsJ 00 o !o » • m »-i rv IM cn\N \ Nai« cn v •ico oCD a o UM— O O «-t Of * 1 * \D -» O- i •r-l CVJ U t n — x ; —C3 O — i »-« I— m o z\ c ox ui r>z >- O' I— *«a n x ui z a c n c n < •» ! IM I i • U J o icn N Y o - « t v i rrj IM V Q_ X x Ul I cn IZ! r— o roc • cn«-•• —tn ~ut. CTjrT X z z— x J v: o or o O I-i — O *| «-« Z — V < • Ul T U »-• B cu *x xcncuCD Q *-_I«o «* >a iI-i* o i n o O i n• -» I— E c n > o Q _ — o or oo o « CO tM c n io3 XB IMIM B — — — — c u u cu «-l cu «-« < V U IMyat E ae •-• • •% m CU Ul - <t ^< • n •-• iiiiii a •4 — •» T u jt -t-tn n • cnV V V --t ajUlaOf<ti ^ cox ora .< I— • oO, fl— —-et I—i tUl- • c u — ro o a o x O O IM o o X _J I— X Q a • c r i >-l Isl I— I XT • • cu CUa — Oo V 4 o r ; < c .-I V Ui Ul V U • >: ^ w > < r r a. <t ii) a uio O — c n*-rUl U«* Oo u i cn < <r <r < H c ny u iu o ofl— I x o • o : u ir u. Q M x o o o x OC Of CJ t r : -toe oo o Q Q -4 ir — a zo o c u ax m ^" <* <i o CJ — a. ui o U IT I Q  X  tr --cC; ' IM IM O  i I  <1  X  (I)  E  •  \  •  X  <  Ul  .-i  X  r - W X  X  2  B  LT  H  _l  —I  I f l r - l f l H « J . « — <  —  U) —  <*  I  X  _l  «  N. *  M  UI —  M  »-  «-«  X  H  X  X  i  •  C J CJ  CJ  •  E  X 5£  I-  _l  168  _3i  U.  (/);  in ui u  IM  CJ  •! ISI V  to  S  x X  o cn a.  _  IM  _ UJ in T LL  »— in —• ru  ^1 •» — •x X ~*  sc — o X i  X o  x O •rt n < u x mi x •» »-« «-«  rt O  _ «U — —  I  _ —j »-!  lil < U l 4 a. »-• rr n o d o o i— z o _ o ore*  O  in ui  :  J  *o o oi o : ru ru  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)  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  3.0  6.0  9.0  12.0  6.0 0.5 -1.1 -2.7 -4.3 -6.1 -7.9 -7.2 -4.6 -1.6 3.1 7.8 8.0 0.3 -1.6 -3.0 -4.4 -5.9 -7.3 -5.7 -3.0 -0.2 5.0  -0.2 -0.1 -0.7 -1.3 -2.2 -3.4 -4.0 -4.5 -3.8 -2.2 -0.8 -0.3 -0.1 -0.1 -0.5 -0.9 -1.5 -2.1 -2.8 -2.6 -2.1 -1.5 -0.9  -0.5 -0.5 -0.4 -0.4 -0.6 -1.0 -1.3 -1.9 -2.5 -2.5 -1.8 -1.0 -0.8 -0.7 -0.6 -0.5 -0.5 -0.6 -0.6 -0.9 -1.4 -1.8 -1.3  -0.4 -0.3 -0.2 -0.2 -0.2 -0.4 -0.5 -0.6 -0.7 -0.8 -0.8 -0.6 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 -0.6 -0.7 -0.8  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 0.1 0.1 0.1 0.1 0.1 0.1  0.2 0.2 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.2 0.2 0.2 0.2 0.2 0.1 0.1 0.1 0.2 0.2 0.2  Site 2 (Salix (1))  Depth (m)  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  3.0  6.0  9.0  12.0  5.1 0.8 -0.1 -0.7 -1.2 -1.7 -2.1 -2.1 -1.7 -0.9 4.8 6.1 6.1 1.5 0.0 -0.4 -0.6 -0.9 -1.2 -1.0 -0.5 0.0 3.5  2.4 1.7 1.2 0.6 0.2 -0.1 -0.4 -0.6 -0.6 -0.6 -0.3 -0.1 -0.0 -0.0 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1  0.6 1.0 1.1 1.0 0.8 0.5 0.1 -0.1 -0.1 -0.2 -0.2 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 -0.2 -0.2 -0.1 -0.1 -0.1  0.0 0.0 0.0 0.0 0.0 0.1 0.1 0.0 0.0 -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 0.0 0.0 0.0 0.0 0.0 0.0 -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 0.0 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 0.0 0.0 0.0 0.0 0.0 0.0 0.0  Site 3 (Salix(2))  Depth (m)  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  3.0  6.0  9.0  12.0  4.1 0.3 0.5 1.1 1.9 2.8 3.8 3.7 3.0 1.5 4.0 5.3 5.9 1.2 0.2 0.7 1.3 2.0 2.7 2.4 1.6 0.9 3.3  -0.2 -0.2 -0.2 -0.2 -0.3 -0.5 -0.6 -0.7 -0.9 -0.9 -0.7 -0.4 -0.3 -0.2 -0.2 -0.2 -0.2 -0.3 -0.3 -0.4 -0.4 -0.4 -0.4  0.0 0.0 0.0 0.0 0.0 0.0 -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 -0.1 -0.1 -0.1 0.0  -0.2 -0.2 -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 -0.1 -0.1  -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 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 -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 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1  174  Site 4 (Salix-Alnus)  Depth (m)  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  3.0  6.0  9.0  12.0  15.0  1.1 0.1 -2.5 -5.0 -6.8 -7.9 -9.0 -8.6 -7.0 -3.5 -0.1  -0.7 -0.3 -0.8 -1.4 -2.8 -4.6 -6.4 -6.9 -6.5 -4.8 -2.4 -1.3 -0.9 -1.1 -1.3 -1.6 -2.3 -3.6 -5.0 -5.7 -4.6 -3.7 -2.0  -1.7 -1.3 -1.3 -1.2 -1.9 -3.1 -4.3 -5.0 -5.5 -5.3 -3.8  -2.5 -2.3  -2.3  -1.7 -1.8 -1.7 -1.7 -1.7 -1.7 -1.7 -1.7 -1.7 -1.7 -1.7 -1.8 -1.8 -1.8 -1.8 -1.8 -1.8 -1.8 -1.8 -1.8 -1.8 -1.8 -1.8  -1.4 -1.4 -1.4 -1.4 -1.4 -1.4 -1.4 -1.4 -1.4 -1.4 -1.4 -1.4 -1.4 -1.5 -1.5 -1.5 -1.5 -1.5 -1.5 -1.5 -1.5 -1.5 -1.5  3.2  3.5 1.0 -1.5 -3.9 -5.8 -7.0 -8.2 -6.9 -4.6 -2.1 1.3  -2.6 -2.2  -2.0 -1.7 -1.4 -1.7 -2.4 -3.1 -3.6 -3.9 -4.3 -3.8  -2.2 -2.2  -2.1 -2.1  -2.2  -2.4 -3.0 -3.5 -3.6 -3.2 -2.8 -2.6  -2.4  -2.2  -2.0 -1.7 -1.8 -1.9 -2.4 -2.9 -3.1  -2.2 -2.2  -2.1 -2.0 -2.0 -1.9 -2.0 -2.1  -2.2  -2.3 -2.4 -2.5 -2.5 -2.4 -2.3  -2.2  -2.1 -2.1 -2.0 -2.1 -2.1 -2.2  175  Site 5 (Picea)  Depth (m)  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  3.0  6.0  9.0  12.0  15.0  0.5 -0.2 -2.8 -5.8 -7.6 -8.9 -10.2 -9.9 -8.3 -4.4 -1.1 0.8 1.6 -0.5 -2.7 -4.8 -6.6 -8.0 -9.4 -8.0 -5.2 -2.4 -0.3  -1.4 -1.1 -1.7 -2.4 -3.9 -6.0 -7.9 -8.4 -7.8 -6.2 -3.4 -2.1 -1.6 -2.0 -2.4 -2.7 -3.6 -5.2 -6.7 -6.8 -5.6 -4.6 -2.9  -2.6 -2.2 -2.1 -2.1 -2.8 -4.4 -5.8 -6.5 -6.8 -6.5 -4.8 -3.7 -3.1 -2.8 -2.4 -2.2 -2.4 -3.5 -4.7 -5.3 -5.5 -5.4 -4.7  -3.7 -3.4 -3.2 -3.0 -3.0 -3.3 -3.6 -4.0 -4.4 -4.8 -4.9 -4.5 -4.1 -3.8 -3.5 -3.2 -3.0 -3.1 -3.2 -3.4 -3.8 -4.2 -4.5  -3.5 -3.3 -3.2 -3.1 -3.0 -2.9 -2.8 -3.0 -3.1 -3.3 -3.4 -3.5 -3.7 -3.6 -3.4 -3.2 -3.1 -3.0 -3.0 -3.0 -3.1 -3.2 -3.4  -2.7 -2.7 -2.7 -2.7 -2.7 -2.7 -2.7 -2.7 -2.7 -2.7 -2.7 -2.7 -2.8 -2.8 -2.8 -2.8 -2.8 -2.8 -2.8 -2.8 -2.8 -2.8 -2.8  -2.5 -2.5 -2.4 -2.4 -2.4 -2.4 -2.4 -2.4 -2.4 -2.4 -2.4 -2.4 -2.4 -2.5 -2.5 -2.5 -2.5 -2.5 -2.5 -2.5 -2.5 -2.5 -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 o  (1)  where z increases with depth to Z  q  , the depth at which AT is zero.  If  the depth-variation of C is known, then, AQ = /  z  i  z  C  AT dz + /  2  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.* AQ - QQ - Qz o  Therefore, (3)  The surface heat flux density is then given by (Scott 1964)  %,t  =A Q / A t  +  Q  zQ,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, QQjt  = [E ° C . A T . A Z t L.AX] /At + Qz o  t  If the thermal conductivity at z is known, then, ' o  o  (5)  APPENDIX 6 l  Net Radiation and Ground Heat Flux Data (ly day" ) at Five Microclimatic Sites (July-August 1970) Site 1 22/7 23/7 24/7 25/7 26/7 27/7 28/7 29/7 30/7 31/7 1/8 2/8 3/8 4/8 5/8 6/8 7/8 8/8 9/8 10/8 11/8 12/8 13/8 14/8 15/8 16/8 17/8 18/8 19/8 20/8 21/8 22/8  Rn  201.5 294.5 367.4 336.0 293.3 300.6 382.0 381.8 115.1 246.9 136.1 231.1 119.3 248.1 313.1 197.1 277.8 228.4 222.6 70.3 76.9 156.6 289.2 205.5 290.3 225.3 211.3 265.0 122.0 262.3 169.4  --  Site 2 G  18.1 25.0 35.6 27.2 21.7 27.1 31.7 34.0 9.4 20.8 11.7 15.6  R n  G  178.0 107.2 21.3 218.6 28.8 272.2 16.4 .171.3 25.1 16.8 15.3 7.4  Site 3 R n 97.6 137.8 169.5 146.1 165.2 184.2 198.5 219.0 92.2 147.6 117.7  —  --  11.5 23.4 14.6 20.6 16.0 14.3 20.2 10.3 19.7 15.2 20.9  181.3 236.0 200.9  --  230.1 120.4 223.8 144.9  --  12. 0 14. 8 16. 5 11. 5 14. 5 10. 7 12. 9 10. 1 11. 3  168.3 107.8 167.4 131.5  G  Site 4 R  n  Site 5 G  i  _ _  R n  G  58.4 48.1 50.9 22.4 25.2 37.9 64.0 52.6 60.4 43.1 46.2  4.0 3.5 2.9 1.2 1.6 2.8 3.9  7. 8 8. 8 9. 7 11. 2 10. 0 12. 1  261. 1 268. 8 104. 6 184. 4 121. 3 180. 7 106. 3 206. 4 239. 7 173. 6 232. 7 189. 8 180. 4 72. 2  5 .3 7 .9 5 .9 7 .4 4 .3 9 .0 9 .5 _ .  BIBLIOGRAPHY Anisimova, N. 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