UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

The snowmelt hydrology of a small alpine watershed Jordan, Robert Peter 1978

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Notice for Google Chrome users:
If you are having trouble viewing or searching the PDF with Google Chrome, please download it here instead.

Item Metadata

Download

Media
831-UBC_1978_A6_7 J67.pdf [ 15.25MB ]
Metadata
JSON: 831-1.0094465.json
JSON-LD: 831-1.0094465-ld.json
RDF/XML (Pretty): 831-1.0094465-rdf.xml
RDF/JSON: 831-1.0094465-rdf.json
Turtle: 831-1.0094465-turtle.txt
N-Triples: 831-1.0094465-rdf-ntriples.txt
Original Record: 831-1.0094465-source.json
Full Text
831-1.0094465-fulltext.txt
Citation
831-1.0094465.ris

Full Text

THE SNOWMELT HYDEOLOGY OF A SHALL A L P I N E WATERSHED by EGBERT PETES JORDAN B.Sc, University of B r i t i s h Columbia, 1972 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE CF MASTER OF SCIENCE in THE FACULTY OF GRADUATE STUDIES Department of Geography Me accept th i s thesis as conforming to the required standard THE UNIVERSITY OF Efi.ITISH COLUMBIA September, 1978 © Robert Peter Jordan, 1978 In p r e s e n t i n g t h i s t h e s i s in p a r t i a l f u l f i l m e n t o f the r e q u i r e m e n t s f o r an advanced degree at the U n i v e r s i t y o f B r i t i s h C o l u m b i a , I a g r e e that the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and s t u d y . I f u r t h e r ag ree t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y p u r p o s e s may be g r a n t e d by the Head o f my Department o r by h i s r e p r e s e n t a t i v e s . It i s u n d e r s t o o d that c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . Department o f Geography The U n i v e r s i t y o f B r i t i s h Co lumbia 2075 Wesbrook P l a c e V a n c o u v e r , Canada V6T 1W5 Oct. 6, 1978 i i ABSTRACT A study o f the mass and energy balance of a s m a l l a l p i n e watershed was conducted i n the summer of 1976, with the aim of ap p l y i n g snow hydrology theory at a watershed s c a l e i n a remote environment. The f i e l d area i s i n the Coast Mountains near B r a l o r n e , B.C. The study c o n c e n t r a t e s on the measurement o f snow a b l a t i o n , the movement of meltwater w i t h i n the snowpack, the generat i o n of stream r u n o f f d u r i n g and f o l l o w i n g snowmelt, and the energy balance a t the snow s u r f a c e . Standard methods f o r measuring snow a b l a t i o n , used i n the f i e l d s o f g l a c i o l o g y and snow s u r v e y i n g , are analysed i n terms of t h e i r accuracy and p r e c i s i o n , and the sampling d e n s i t i e s r e g u i r e d f o r t h e i r a p p l i c a t i o n . Simple f i e l d i n s t r u m e n t a t i o n i s used t o study the movement of meltwater i n the snowpack, and t h i s i s analysed i n terms of the theory of flow through a porous medium. The movement of meltwater through the snow i s found t o be the most important process a f f e c t i n g the shape and timing of the stream hydrograph. The movement of water along the base of the snowpack and through t h e s o i l a l s o has an i n f l u e n c e on the shape of the hydrograph. In the a l p i n e meadow environment s t u d i e d , s a t u r a t e d s o i l and i c e c o v e r i n g ground beneath the snow c o n t r i b u t e t o a r a p i d stream response. A water balance i s c a l c u l a t e d f o r the watershed, based on measurement of stream d i s c h a r g e , snow a b l a t i o n , and p r e c i p i t a t i o n , and on c l i m a t o l o g i c a l estimates of evaporation. An energy balance f o r the season i s a l s o c a l c u l a t e d , supported by m i c r o c l i m a t o l c g i c a l measurements f o r part of the season. Radiation i s found t o c o n t r i b u t e 90% of the energy r e g u i r e d f o r i i i snowmelt, and a simple model for the ca l c u l a t i o n of net radiation from solar radiation i s developed. Empirical methods are found to be suitable for the calculation of turbulent energy transfer over snow. Some observations are made of the water balance in th€ l a t e summer, and these indicate that water stored in the s o i l durinq snowmelt i s important i n maintaining streamflow later in the season. 4v TABLE OF CONTENTS CHAPTER 1. INTRODUCTION .................................. 1 1.1 Objectives ......................................... 1 1.2 Physical Environment ............................... 4 1.3 Mapping ............................................ 11 1.4 Instrumentation and Data Analysis .................. 12 CHAPTER 2. SNOW ACCUMULATION AND ABLATION ................ 15 2.1 Watershed Sampling Networks ........................ 16 2.2 Density Measurements 22 2.3 Errors i n the Snow Sampler Density Measurements .... 27 2.4 Watershed Ablation as Determined by Stake Measurements ....................................... 32 2.5 Detailed Ablation Measurements 38 2.6 Observations on Ice at the Base of the Snowpack .... 45 2.7 Regional Representativeness of Ablation at the Study Site 49 2.8 Summary ........................... ..... * •. . •....... 51 CHAETER 3. WATER MOVEMENT IN THE SNOWPACK ................ 53 3.1 Theory and Previous Studies ........................ 54 3.2 Instrumentation ............... ...... ............... 62 3.3 Liguid Water Content Measurements .................. 67 3.4 Experimental Results: Application to the Theory .... 71 3.5 Qualitative Observations of Meltwater Movement ..... 81 3.6 Experimental Results: Application to Watershed Response ... ................... .... ................. 87 3.7 Conclusions and Recommendations .................... 97 CHAPTER 4. RUNOFF GENERATION ............................. 100 4.1 Previous Work ...................................... 100 4.2 Discharge Measurements and Hydrograph Separation ...101 4.3 Observations of Runoff Processes ................... 105 4.4 Hydrograph Analysis ................................ 109 4.5 Con elusions .........•..•.»»•.»»,........»•••.......,121 CHAPTER 5. THE WATER BALANCE 123 5.1 The Water Balance Eguation ......................... 123 5.2 Ablation, Runoff, and P r e c i p i t a t i o n Calculations ...124 5.3 Evaporation Estimates .............................. 126 5.4 Water Balance Results ...128 CHAPTER 6. THE ENERGY BALANCE AND THE ESTIMATION OF SNOWMELT ........... .......... ....... . ..... .... . 134 6.1 Instrumentation and Observations ................... 136 6.2 Radiation Modelling ................................ 139 6.3 Aerodynamic Estimates of Turbulent Fluxes .......... 143 6.4 Daily Melt Totals 155 6.5 Discussion ........................ ...............•.162 CHAPTER 7., THE LATE SEASON WATER BALANCE ................. 163 7.1 S o i l Moisture and Groundwater Depletion ............ 163 7.2 Evaporation Estimates 167 7.3 The Water Balance ................... ..173 V 7.4 Stream Response to P r e c i p i t a t i o n and Other Events ..176 7.5 Summary .... .... .................................... 180 CHAPTER 8. CONCLUSIONS ...................................181 REFERENCES 185 APPENDICES .190 1. Maps ....................., , 191 2. Climate Data Summary .......,.. 194 3. Seasonal Hydrograph and Plot of Climate Data ..,,.,...197 4. Stage - Discharge Relation 199 5. Data Used for Radiation Modelling ....................200 6. Energy and Hater Balance Summary 201 v i LIST OF TABLES 1.1 Summary of snow course data for 1976 ................. 9 1.2 Climate data for 1976 ... 9 2.1 Snow sampler and p i t density measurements ............ 30 2.2 Summary of June 10 snow sampling tests ............... 30 2.3 Ablation stake calculations ,.37 3.1 Calorimetry r e s u l t s 68 3.2 Calculation of the f r a c t i o n a l derivative ............. 80 3.3 Observed wave front speeds ........................... 80 4.1 Hydrcgraph recession c h a r a c t e r i s t i c s .................117 5.1 Snowmelt volume estimates ............................ 125 5.2 Evaporation estimates 129 5.3 water balance summary ................................ 130 6.1 Roughness lengths over snow 147 6.2 Energy balance summary ...............................159 7.1 S o i l analyses ........................................ 165 7.2 Late season evaporation ..................171 7.3 Late season water balance summary ....................174 7.4 Water balance of rainstorms ,.. 174 v i i L I S T OF F I G U R E S 1.1 location map ......................................... 5 1.2 Photograph of McGillivray Pass ....................... 6 1.3 Summary of snow course data for the Bridge River region .......................... ..................... 10 2.1 Photograph of watershed .............................. 21 2.2 Snow depth and water eguivalent d i s t r i b u t i o n s ........ 21 2.3 Snow p i t density p r o f i l e s 24 2.4 seasonal density curves 25 2.5 Seasonal water equivalent curves ..................... 35 2.6 P a r t i a l snow cover area curves ....................... 36 2.7 Schematic diagram of p a r t i a l area snowmelt ........... 36 2.8 schematic diagrams of ablation calculations by the small stakes method .................................. 40 2.9 Ablation as calculated from small stakes ............. 43 2.10 Comparison of small stakes and ablation gauge ........ 43 2.11 Photographs of basal i c e 46 3.1 Conductivity - c a p i l l a r y pressure r e l a t i o n s .......... 59 3.2 Propagation of a flux wave with time ................. 59 3.3 Photograph and diagram of lysimeter .....64 3.4 Photograph of tensiometers ........................... ,64 3.5 Calorimeter measurements: l i g u i d water content and dens i t y ......................... ............... ...... 70 3.6 Capillary pressure - flux - saturation r e l a t i o n s ..... 70 3.7 Lysimeter flow and snowmelt waves for 3 days 73 3.8 Plot of U v vs. V ...73 3.9 Plot of flux - c a p i l l a r y pressure r e l a t i o n ........... 76 3.10 Plot cf f r a c t i o n a l derivative, 60, and conductivity ... 79 3.11 Dye tests ............................................ 83 3.12 Tensiometer record f o r several days .................. 88 3.13 Lysimeter record for June 28 - July 18 ............... 90 3.14 Progress of the meltwater wave through the snowpack .. 94 3.15 Times of peak stream discharge ....................... 97 4.1 Example of hydrograph separations .................... 103 4.2 Photographs of overland flow ......................... 107 4.3 Photograph of standing water ......................... 107 4.4 Times of peak and low flows ..........................111 4.5 Stream hydrograph recession limbs ....................112 4.6 Lysimeter recession limbs ............................ 112 4.7 Synthesized recession hydrograph derived from x©c€ssion d3 ts. • •« • * * • •«* • • * • • • • • »• • • •« #•»-#•• * • * *'• • • • *• • •» 113 4.8 Hydrograph of peak flow event ......121 5.1 Cumulative mass curve of water balance data 131 6.1 Photograph of radiometers , 137 6.2 Photograph of temperature and wind p r o f i l e instruments .... .... ...........* ...............137 6.3 Graph of albedo for the season .....142 6.4 Plot of estimated and measured Q* .................... 142 6.5 Examples of temperature and wind p r o f i l e s ............ 148 vdiii 6.6 V a r i a b i l i t y of wind speed over time, J u l y 16 ......... 152 6.7 Energy balance c a l c u l a t i o n s f o r s e v e r a l days .........153 6.8 P l o t of c a l c u l a t e d d a i l y melt vs. observed melt and uatershed r u n o f f .................................... .160 7.1 S o i l moisture and groundwater l e v e l s ................. 166 7.2 P l o t of c a l c u l a t e d e v a p o r a t i o n vs. evaporimeter data .172 7.3 Hydrograph s e p a r a t i o n procedure f o r r a i n s t o r m s .......177 7.4 Hydrograph f o r Sept. 12 t o Oct. 9 177 LIST OF SYMBOLS Note: The units most commonly used are given. Other units occasionally used are shown in brackets. Conversions to S.I. units are indicated where appropriate. a area, m3 a constant in empirical wind function, 1 m-2mb-* (eg. 6 ft ablation, cm {mm, kg m~2sec— b constant in empirical wind function, J m~3mb_* (eg. 6 B Bowen r a t i o , Q^/Qg C cloud cover Cn cloud number cov. Covariance Cv c o e f f i c i e n t of variation e base of natural logarithms e vapour pressure, mb (1 mb = 100 Pa) e s saturation vapour pressure, mb E evaporation, mm (mm/day, m3) f a function g acceleration due to gravity, 9.80 m/sec2 h snow depth, or thickness of a snow layer, m h ^ a i r entry c a p i l l a r y pressure for the boundary drying curve, cm h c c a p i l l a r y pressure, cm k von Kantian* s constant, O.UO K unsaturated hydraulic conductivity, cm/hr Kg saturated hydraulic conductivity, cm/hr K* net solar radiation, W/m2 K4, incoming solar r a d i a t i o n , H/m2 Kt reflected solar radiation, H/m2 l a t e n t h e a t o f f u s i o n , 3 . 3 3 x 1 0 s J/kg I * n e t l o n g w a v e r a d i a t i o n , H / m 2 Li i n c o m i n g l o n g w a v e r a d i a t i o n , H / m 2 L\ o u t g o i n g l o n g w a v e r a d i a t i o n , H / m 2 H s n o w m e l t v o l u m e , m 3 P p r e c i p i t a t i o n , mm {mm/day, m 3) q s t r e a m d i s c h a r g e , m 3 / s € C ( 1 / s e c ) Q t o t a l d i s c h a r g e , m 3 c E l a t e n t h e a t f l u x o f e v a p o r a t i o n , H / m2 Oft s o i l h e a t f l u x , 1 / J B 2 QH s e n s i b l e h e a t f l u x , H / m 2 l a t e n t h e a t f l u x o f m e l t i n g , H / m 2 Q * n e t r a d i a t i o n , H / m 2 Q * e e s t i m a t e d n e t r a d i a t i o n , H / m 2 r c o r r e l a t i o n c o e f f i c i e n t B r u n o f f , mm (mm/day) B i fiichardson number s s l o p e o f t h e s a t u r a t i o n v a p o u r p r e s s u r e c u r v e , m b / ° C s s a m p l e s t a n d a r d d e v i a t i o n s . e . . S t a n d a r d e r r o r o f e s t i m a t e S* e f f e c t i v e s a t u r a t i o n , {O-&i)/06 t t i m e , s e c {hr , day) t * h y d r o g r a p h r e c e s s i o n c o n s t a n t , h r T t e m p e r a t u r e , ° C o r K u s e t t l e m e n t o f a snow l a y e r , mm u w i n d s p e e d , m / s e c OF s p e e d o f a wave f r o n t , c m / h r ov s p e e d o f a f l u x w a v e , c m / h r xi. V meltwater flux, cm/hr w surface wastage of a snow layer, mm W l i g u i d water content by weight We water equivalent, cm z height, m (cm) z 0 roughness length, mm c* albedo ex constant i n empirical evaporation eguation (eg. 7.1) & psychrometric constant, mb/°C AS change i n storage, m3 £ long-wave emmissivity £ exponent i n the K (S*) r e l a t i o n T\ exponent i n the K(h c) r e l a t i o n & volumetric water content Bi i r r e d u c i b l e water content X exponent i n the S* (he.) r e l a t i o n p snow density, gm/cm3 _pw density of water, 1.000 gm/cm3 pc p volumetric heat capacity, J °c- iwr3 o- Stefan-Boltzmann constant, 5. 67x10~» W m~2K-* 0 porosity 0 C e f f e c t i v e porosity, 0-Bi CJ f r a c t i o n a l derivative, K-ldK/d0 sdi ACKNOWLEDGEMENTS This research project could not have been conducted without the help of Dan Hogan, my f i e l d assistant, and Prof. Michael Church, who provided academic advice and National Research Council research funds. Thanks i s also due to Anthony Wankiewicz, who developed and b u i l t some of the instruments used in this project, and on whose work much of this study follows. Prof. Brian Sagar of Simon Fraser University and Prof. J. Ross Mackay of U.B.C. loaned instruments for the project. Oleg Mokievsky-Zubok of the Glaciology Divi s i o n , Environment Canada, and Harry Hunter and David Thompson of the Hydrology Divi s i o n , B.C. Ministry of Environment, provided snow survey equipment; I am also indebted to them for stimulating my interest in snow hydrology during my periods of employment with them. I also wish to thank Walter Kienas of Gold Bridge, B.C., for l o g i s t i c a l support; Paul Kleinschrot of Seton Portage, B.C., and the Varsity Outdoor Club of D.B.C. for the use of t h e i r cabin; Suth McLaren of Hhitecap Resorts Ltd, for allowing me to work on t h e i r property; Joanne Pottier f o r typing the f i r s t draft of the thesis; and Profs, Olav Slaymaker and Tim Oke for c r i t i c a l l y reading the manuscript. 1 CHAPTER 1 INTRODUCTION 1.1 OBJECTIVES The Coast and Insular Mountains of B r i t i s h Columbia experience the highest snowfall and generate the greatest runoff of any part of North America. On the i n t e r i o r slope of the Coast Mountains, t h i s runoff provides abundant water to otherwise semi-arid areas downstream. A small proportion of the runoff i s used for i r r i g a t i o n and for power generation; as the proportion increases, management of t h i s resource may become more important. Throughout the region, hydrometeorological data are scarce, and information on hydrological processes in t h i s high snowfall environment i s also lacking. In 1976, the writer undertook a study of the mass and energy balance during snowmelt of a small alpine watershed i n t h i s region. Using observations made during the spring and summer of 1976, three problems have been studied: 1, To investigate the re l a t i o n s h i p between the snowmelt process and the resu l t i n g runoff hydrograph, in terms of the passage of meltwater through the snowpack and the underlying ground to the stream channel. 2, To apply the ex i s t i n g theory of snowmelt and meltwater flow processes i n a remote and poorly known environment, and to obtain some useful information about the hydrology of this environment. 3, To simplify the instrumentation and methods used i n measuring the physical properties and energy balance of melting snow, to f a c i l i t a t e physically based studies of snow hydrology 2 in remote environments. Many snow hydrology studies in the past have f a l l e n into two f a i r l y extreme categories. The f i r s t i s that of spe c i a l i z e d , t h e o r e t i c a l l y oriented or experimental studies on a small s i t e scale, and the second i s that of empirical studies designed for forecasting runoff on a large scale. This project i s an attempt to integrate the two approaches, and to apply the theory and res u l t s of small-scale studies to a larger scale, which might be of management significance. Recently, several integrated snow melt-runoff generation models have been developed (for example, Anderson, 1976; Dunne et a l , 1976), drawing on theory and experimental work i n both micrometeorology and snow hydrology. The theory involved i n these models i s guite well developed, but what i s lacking i s r e l i a b l e input data for various environments. There i s also a necessity for further testing of some of the assumptions and theories used i n these models, and for knowledge of those parameters and processes which vary considerably from one environment to another. This study w i l l hopefully begin to provide some of thi s information for the high-snowfall mountain environment. Male and Gray (1975) discuss the problems associated with the development of integrated models i n a diffe r e n t environment, that of the Canadian prairies.., Such integrated models are applicable to the management of watersheds during the snowmelt season, es p e c i a l l y watersheds which are prone to flooding or are subject t c a sc a r c i t y of water. Hith respect to the l a t t e r watersheds, the storage of winter precipation i n the snowpack and i n the ground following 3 snowmelt i s of prime importance to the annual water balance. Both t h e o r e t i c a l and observational work i s needed on the mechanics of the release of t h i s water, and on ways to obtain s i m p l i f i e d inputs into models which predict t h i s release. Sith respect to flood-prone watersheds, an understanding of the release of meltwater over a shorter time scale i s needed. For deep snowpacks i n p a r t i c u l a r , the rates of snowmelt, and the timing of snowmelt runoff with respect to climatic inputs, are important; t h i s study w i l l provide some quantitative r e s u l t s on the response of the atmosphere-snowpack-stream system in one par t i c u l a r environment. However, the groundwater l e v e l s and the thermal and moisture status of the underlying s o i l are also c r i t i c a l in determining the runoff response of a watershed; knowledge i n t h i s area i s lacking. This study w i l l attempt to provide some q u a l i t a t i v e information on the role of these factors. Work on the scale of a small headwater watershed i s desirable for several reasons. F i r s t , i t i s small enough to permit a physically based experimental approach, and i t i s possible to observe the processes occurring over the whole watershed, rather than treating the watershed as a "black box". Secondly, the i n c l u s i o n of stream discharge i n the study i s the f i r s t step i n extending s i t e - s c a l e studies to the scale of a f u l l watershed; as information i s gained on the hydrologic system at the headwater scale, i t can gradually be extended to larger and more heterogeneous watersheds. An alpine meadow area i s a desirable environment for the study because i t i s simpler in i t s hydrologic processes than most other environments i n a B r i t i s h Columbia, and i t i s where most of the water i s stored i n the spring and summer i n any large, unglacierized mountain watershed. ,. 1.2 PHYSICAL ENVIRONMENT The study area i s located i n McGillivray Pass, on the divide between the Bridge Eiver and Seton River watersheds, about 45 km NNE of Pemberton and 20 km SE of Bralorne. The study watershed i t s e l f i s a small headwater stream of McGillivray Creek, at an elevation of about 1900 m and with an area of about 0.04 km2. The watershed i s on the lower part of a slope which faces predominantly to the north-east; the r e l i e f of the watershed i s about 130 m, with most of t h i s being i n a r e l a t i v e l y small area i n the upper part of the watershed,. Topographic and vegetation maps are included i n appendix 1; figure 1.1 i s a location map, and f i g . 1.2 gives an overview of the physiography. The valley of McGillivray Pass is a narrow, SE-N8 trending trough, about 8 km long in the alpine and subalpine region, with a f l o o r ranging in elevation from about 1700 to 19 00 m, and bounded by two p a r a l l e l ridges with elevations up to 2590 m. The pass was the route of valley g l a c i e r s which at various times t r a v e l l e d i n both directions between the main Bridge River and Seton River valleys; several l a t e r a l moraines, one terminal moraine, and a major meltwater channel f l o o r the valley. The underlying geology of the ridge on the south-west, including the study watershed, consists of fine-grained sediments of upper T r i a s s i c age, while the ridge on the north-east consists of F i g . 1.1 Location map. 6 F i g . 1.2a Looking west into McGillivray Pass, with Mc G i l l -ivray Creek i n the foreground and Cadwallader Creek beyond. The location of the study watershed i s shown by arrows. F i g . 1.2b Looking south-east down McGillivray Creek. Arrows locate the study watershed. 7 T r i a s s i c or older metasediments, s c h i s t s , and ul t r a b a s i c i n t r u s i v e s (Cairnes, 1937) . Quartz d i o r i t e s of the Coast plutonic complex underlie a large area beginning about 1 km south of the study watershed. This area i s much more rugged, with extensive outcrops, compared with the more subdued topography i n the region of sedimentary and metamorphic rocks. The lower elevations of the v a l l e y , below about 2000 m, are th i c k l y blanketed i n g l a c i a l and c o l l u v i a l deposits, and outcrops are scarce. The lower elevations are heavily vegetated, mainly with lush alpine meadow vegetation, but with small areas of sub-alpine f o r e s t i n favourable locations. Most of the area of the study watershed i s covered with hummocky or undulating s i l t y t i l l (see ch. 7 for a more detailed description of s o i l s ) . The lower 20% of the watershed consists of what appears to be a set of g u l l i e d terraces; these consist of t i l l covered in places with a thin veneer of f l u v i a l material. The upper 20% includes outcrops of bedrock and areas of l o c a l colluvium and s t a b i l i z e d t a l u s , as well as areas of t i l l . S o i l s are thin, with the B-horizon extending to a depth of about 15 to 30 cm i n most places where p i t s were dug. Scattered clumps of alpine f i r grow i n well-drained locations; trees cover about 3% of the watershed. McGillivray Pass i s situated on the i n t e r i o r side of the Coast Mountains, i n a zone of steep p r e c i p i t a t i o n gradients from the wet, highly g l a c i e r i z e d crest of the range, to the dry i n t e r i o r plateau to the north-east. The average snow accumulation on May 1 at the McGillivray Pass snow course i s 68 cm water eguivalent, compared with 131 cm at the Tenguille Lake 8 snow course, only 30 km to the south-west and at a si m i l a r elevation. In early May, 1976, the study area had about twice the snow water equivalent of the snow course, which i s 4 km to the north-west and 150 m lower. The vegetation i n the region indicates a strong l o c a l gradient of precipation from d r i e r i n the north-west to wetter i n the south-east, along the l i n e of the main va l l e y . Thus, i t appears that the upper part of McGillivray Creek i s considerably wetter than the Bridge River valley and i t s t r i b u t a r i e s immediately to the north and north-west, and the valley of Seton and Anderson Lakes to the east; rather, i t i s more t y p i c a l of the Birkenhead and L i l l o o e t drainages to the south and south-west. Hydrometeorological information for the region i s sparse., No streams i n the region are gauged, with the exception of the Bridge River reservoirs. The closest climate s t a t i o n with a reasonably long period of record i s Shalalth, 2 7 km to the east at an elevation of about 250 m. (Two other stations, Pemberton and Lajoie Dam, have incomplete records of 7 and 13 years, respectively.) There are fi v e snow courses i n the region. One of these. Mission Ridge, 5 km from Shalalth, includes an instrument s i t e which records snow water equivalent by means of a recording snow pillow, as well as a i r temperature, during the winter and spring seasons. The summer of 1976 was unusuallly wet and cold i n the Coast Mountains. This followed a winter of above average snow accumulation at higher elevations, and the r e s u l t was that the snowmelt season extended well into August, and extensive snow patches at higher elevations i n the region did not melt before 9 H S L E Jul SUMMARY OF SHOW CODBSE DATA FOB 1S76. Snow water equivalent in mm at s elected snow SNOI COOBSE DATE 1 976 AVERAGE YRS McGillivray Pass Apr. 1 820 675 22 Ma y 1 734 6 83 24 May 15 719 669 4 June 1 560 452 5 Mission fiidge Apr. 1 945 723 8 May 1 960 740 9 May 15 757 6 83 6 June 1 579 456 6 Tenguille Lake Apr. 1 1684 1259 23 May 1 1814 1309 19 May 15 1704 1221 20 June 1 1654 1079 22 . RECORD (Source: B.C. Dept. Environment, Snow Survey Bulletins.) I I M J JLs.2 CLIMATE DATA FOR 1976. STATION MONTH Shalalth TEMPERATORE(°C) PRECIPITATION(MM) SONSHINE(HR) AVERAGE 1976 AVERAGE 1976 AVERAGE 1 976 May 13.2 14.8 36 June 15.9 18.4 27 July 19. 1 21.5 7 Aug. 17. 8 21.0 38 Sept. 16. 9 16.3 7 May 11. 1 12.0 82 53 187 J une 13. 0 14.7 64 48 241 July 16. 1 17. 1 32 32 247 Aug. 1 5. 3 16.8 81 48 143 Sept. 14.9 14.5 49 67 191 240 23 9 300 247 180 1 Vancouver UBC i s used for temperature and pr e c i p i t a t i o n . For sunshine, the average of three Vancouver stations i s used. (Source: Environment Canada, A.E.S. climate data.) 10 Mission Ri<*3e ( l«50m) McGillivray P«ss (1750m) Gveen Mountain (1710 M ) Tevupille L a M M O * ) Bt-alo _i i I960 1170 1176 F i g . 1.3 Summary of snow course data f o r the Bridge River region. Data i s for May 1. (Source: B.C. Dept. Environment, snow survey data.) 11 the onset of winter. At lower elevations, however, warm weather e a r l i e r in the spring resulted i n a lower than normal snowpack below 1500 m by early Hay, Climate and snow course data f o r the spring and summer of 1976 are summarized i n tables 1,1 and 1,2, and f i g , 1,3 shows some snow course data over the l a s t 25 years. The snow course at McGillivray Pass does not have a long period of record f o r readings taken l a t e r than May 1, However, at the Tenquille Lake snow course, with 19 years of record, the water eguivalent on May 1, 1976, was 181 cm, which i s 1,39 times the average, and on June 1, i t was 165 cm, or 1.56 times the average. Fig.,2.5 shows the trend of snowmelt at the study s i t e throughout the summer; from May 11 to June 14, the net snowmelt was only 6 cm, while over the following month i t was 60 cm. For the purpose of discussing snowmelt i n t h i s t h esis, the snowmelt period i s considered to s t a r t on June 14. However, warm weather with considerable melt occurred during the f i r s t week of May as well, before the measurement period began. 1.3 MAPPING Before the f i e l d season, an uncorrected planimetric map of the watershed was constructed from a i r photographs, to be used for f i e l d work. Because the surface divide of the watershed could not be determined accurately from a i r photographs, i t s exact location was not known u n t i l the watershed was snow-free. In August, 1976, a topographic survey was made using a theodolite i n the lower 3/4 of the watershed, and using compass and hand-level traverses in the upper part, which was of d i f f i c u l t access. After the f i e l d season, an accurate contour 12 map w a s d r a w n ( a p p e n d i x 1) , w i t h t h e q u a l i t a t i v e h e l p o f t e r r e s t r i a l s t e r e o p h o t o g r a p h s t a k e n f r o m t h e r i d g e o v e r l o o k i n g t h e w a t e r s h e d f r o m t h e n o r t h - e a s t . T h e a r e a o f t h e w a t e r s h e d a s m e a s u r e d o n t h i s map i s 3 9 , 3 1 0 s g u a r e m e t e r s . 1 . 4 I N S T R U M E N T A T I O N AND D A T A A N A L Y S I S T h e b a s i c i n s t r u m e n t a t i o n f o r t h e s t u d y c o n s i s t e d o f a w a t e r l e v e l r e c o r d e r m e a s u r i n g s t a g e b e h i n d a V - n o t c h w e i r , a t h e r m o h y d r o g r a p h a n d m a x i m u m - m i n i m u m t h e r m o m e t e r s i n a S t e v e n s o n s c r e e n , a n a c t i n o g r a p h f o r t h e m e a s u r e m e n t o f s o l a r r a d i a t i o n , a n d r a i n g a u g e s a t t w o p o i n t s i n t h e w a t e r s h e d . A s i t e f o r d e t a i l e d m e t e o r o l o g i c a l o b s e r v a t i o n s a n d s n o w m e l t m e a s u r e m e n t w a s e s t a b l i s h e d i n a f a i r l y f l a t , u n i f o r m a r e a i n t h e l o w e r p a r t o f t h e w a t e r s h e d . F u r t h e r i n s t r u m e n t a t i o n a t t h i s s i t e i s d i s c u s s e d i n s u b s e g u e n t c h a p t e r s . T h e i n s t r u m e n t s w e r e i n s t a l l e d a n d r e g u l a r o b s e r v a t i o n s s t a r t e d o n M a y 1 1 . A n e t w o r k o f 15 w o o d e n s t a k e s w a s e s t a b l i s h e d o n t h i s d a t e f o r t h e m e a s u r e m e n t o f s n o w m e l t o v e r t h e w a t e r s h e d . H e a t h e r o b s e r v a t i o n s w e r e t a k e n a t l e a s t f o u r t i m e s d a i l y ; t h e y w e r e a l s o t a k e n a t t h e b a s e c a m p , 4 km f r o m t h e s t u d y a r e a . S o m e c o n v e n t i o n s r e g a r d i n g t h e a n a l y s i s o f d a t a s h o u l d b e m e n t i o n e d h e r e . 1 . I t i s c o n v e n i e n t t o a s s i g n t o e a c h d a t e a s e q u e n t i a l d a y n u m b e r ; t h e s e a s o n w a s n u m b e r e d b e q i n n i n g w i t h M a y 1 1 , 1 9 7 6 , a s d a y 1 . 2 . A l l d a t a c o l l e c t e d o n c h a r t r e c o r d e r s w e r e r e d u c e d u s i n g a n e l e c t r o n i c d i g i t i z e r , a n d a n a l y s e d b y c o m p u t e r ; t h i s a l l o w e d a h i g h e r d e g r e e o f p r e c i s i o n t h a n w o u l d m a n u a l r e d u c t i o n o f s u c h 13 data, and f a c i l i t a t e d the application of corrections and transformations. 3. In general, S.I, units are used. However, when convenient, other compatible metric units are also used. For example, c.g.s. units are used in the analysis of snow-water re l a t i o n s , since most of the available l i t e r a t u r e i s i n these units, and the c.g.s. system r e s u l t s i n more convenient numbers than does the S.I. system. a. Shen discussing measurement and sampling errors, a l l plus-or-minus tolerances are assumed to correspond to 95% confidence l i m i t s , which are roughly eguivalent to plus or minus two standard errors i n normally distributed data. In some cases, actual standard errors are reported; i n these cases, the plus-or-minus sign i s not used. The standard error of a measurement i s defined here as the expected value of the sample standard deviation, i f the measurement were to be repeated many times. (The term "error", when used by i t s e l f , r e f e r s to the imprecision of measurement and also to the possible presence of an unknown bias.) In general, when ca l c u l a t i n g errors, the e r r o r analysis r e l a t i o n s given i n Parratt (1961) and Snedecor and Cochran (1967) are used. These can be summarized b r i e f l y , for uncorrelated random variables, as: S 2 (CX) C 2 S 2 (X) (1. l a ) s 2 (x+y) s 2(x) • s 2(y) » (1.1b) s 2 {xy) {xy) 2 [ s 2 ( x ) / x 2 + s 2 ( y ) / y 2 ] or C v 2(xy) C v 2(x) + C v 2 ( y ) (1.1c) and s 2 [ f (x) ] 2; { f (x) ] 2s 2(x) 1 (-1 .Id) where x and y are random variables (or more precisely, the means, x and y, of samples of the random variables x and y) i s the sample variance, c i s a constant, and C v i s the c o e f f i c i e n t of va r i a t i o n , s{x)/x. 15 CHAPTER 2 SNOW ACCUMULATION AND ABLATION To determine the water balance during the snowmelt season, i t i s necessary to measure the t o t a l snow accumulation i n the watershed at an arbi t r a r y s t a r t i n g time, and to measure the ablation (and on occasion, accumulation) over the watershed throughout the season. To accomplish these objectives, the variation i n both depth and density over area and time must be determined. Therefore, networks of permanent snow depth stakes and density sampling points were established at the beginning of the season. Also, a more detailed stake network and sampling schedule were established in the area of the meteorological s i t e to f a c i l i t a t e the studies of meltwater movement and the surface energy balance. Ablation i s defined as the loss of water i n a l l phases from the snowpack (LaChapelle, 1959). This consists of both the l o s s of ice through melting and subsequent drainage, and the associated release of pore water (which i s commonly 5 to 158 of the snow mass); i t also includes evaporation, which can usually be neglected. Accumulation i s the opposite of t h i s , and consists of both new snow and of any rain which i s retained as pore water. The term "snowmelt", as used in t h i s study, i s e s s e n t i a l l y synonymous with "ablation"; i t ref e r s to the amount of water which drains from the snowpack, and therefore does not include evaporation. Snowmelt i s normally expressed i n m3, while ablation i s usually given i n mm. 16 2.1 WATERSHED SAMPLING NETWORKS Two commonly used approaches to determining snow accumulation and ablation over a watershed are the stake network method and the index snow course method. In the f i r s t method, a number of stakes are planted over the watershed in either a random d i s t r i b u t i o n , or more commonly, i n a pattern which representatively covers the watershed, but i s designed for ease of access. The water eguivalent of the snowpack i s then determined at each stake as the product of snow depth and the density at each stake; t h i s density i s usually obtained from a density versus time curve derived from several measurements of density taken i n snow p i t s over the season. This method i s commonly used to determine the mass balance of g l a c i e r s (see for example Ostrem and Stanley, 1969, and Young, 1974), and has also been applied to studies of the ablation of seasonal snow (for example, Bartos and Rechard, 1974). The second method i s i n common use for the purposes of ca l c u l a t i n g water storage i n seasonal snowpacks and forecasting snowmelt runoff in watersheds throughout North America (O.S.D. A. S o i l Conservation Service, 1972)• Several snow courses are established in the watershed; each snow course consists of a number of sampling points at fix e d locations {usually ten) over a distance of several hundred meters. A snow core i s taken and weighed at each point using a snow sampler. The water eguivalent of the snow course i s taken as the mean of the weights at the ten sampling points, and the snow storage i n the watershed i s assumed to be a li n e a r function of the water equivalents of the snow courses. 17 A combination of these two approaches was used i n t h i s study. Changes i n the depth of snow were determined by means of a stake network, while density was determined largely by means of snow course measurements. A network of 15 snow depth stakes was established at the beginning of the f i e l d season, with the f i r s t reading made on May 11. In addition, four stakes were used for the more detailed ablation measurements at the meteorological s i t e . The number of stakes was l i m i t e d by the number which could f e a s i b l y be transported to the s i t e ; as discussed below, a larger number might have been desirable. A completely random d i s t r i b u t i o n and a geometric g r i d pattern were both rejected because of the d i f f i c u l t y of surveying the stake locations. Instead, fiv e s t r a i g h t - l i n e transects were subjectively chosen, which were approximately evenly spaced throughout the watershed, and which did not pass through clumps of trees or areas of d i f f i c u l t access. The transects were marked on a map of the watershed, and stake locations were plotted at ar b i t r a r y , equally spaced distances along each transect. The stakes were then planted at these locations, which were measured along the transects using a tape. Thus, the stake network was s t r a t i f i e d , with the transects being subjectively chosen tc be representative of the t e r r a i n throughout the watershed, but by spacing the stakes along each transect at egual pre-defined i n t e r v a l s , they were located randomly with respect to l o c a l topographic variations. Before the stake network was established, the watershed was divided into three regions, based on l o c a l r e l i e f and vegetation c h a r a c t e r i s t i c s . Subsequent analysis of the stake data was then 18 s t r a t i f i e d according to these pre-defined regions..The regions were as follows (see f i g . 2.1): Begion 1: the lower part of the watershed, consisting of several f a i r l y uniform terraces and gentle slopes, with short alpine meadow vegetation. Region 2: the ce n t r a l part of the watershed, consisting of hummocky t e r r a i n , with a number of scattered clumps of trees interspersed with meadow vegetation. , Region 3: the upper part of the watershed, consisting of steeply sloping, variable t e r r a i n , and including several small b l u f f s and extensive clumps of trees and shrubs as well as meadow vegetation. The area of t h i s region was underestimated by about 30% at the time the stake network was established; t h i s was because i t was not possible to delimit accurately the surface drainage divide u n t i l the ground was snow-free. Thus, part of t h i s region was not covered by the snow stake network. The ablation stakes were made of 3/4 inch wooden dowelling, three to four meters in length, painted white. They were planted to the ground surface. The stakes were read by placing a rul e r across the snow at the base of the stake to eliminate the eff e c t of the small melt p i t surrounding the stake. The precision to which the snow l e v e l at each stake could be read varied from about ±0,3 cm for f a i r l y smooth snow at a le v e l l o c a t i o n , to as much as ±5 cm on steep slopes l a t e in the season with an uneven snow surface. On the average, the measurement error i s probably about ±1.0 cm. Thus, the error f o r the surface lowering at one stake between any two measurements would be ±1. 4 cm, and the error f o r the average surface lowering represented by a l l 15 19 stakes would be 1,4 cm/Vl"5, or ± 0,4 cm. For a region containing 5 stakes, t h i s error would be ±0.6 cm, , Since considerable v a r i a b i l i t y in surface lowering between stakes was observed (see section 2.4), es p e c i a l l y i n region 2, i t would have been desirable to have a larger number of stakes i n regions of greater v a r i a b i l i t y . However, the number of stakes necessary to reduce the error variance to a desired l e v e l cannot be known u n t i l some measurements of surface lowering have been made. A ten-station snow course was established i n October, 1975, with sampling points distributed f a i r l y uniformly over the lower two-thirds of the watershed. The main c r i t e r i a for the location of the sampling points were that the ground surface be f a i r l y uniform and representative of the surroundings of that point, and that the immediate v i c i n i t y of the point be free of trees or low bushes which might affect snow accumulation. The watershed i s small enough that ten points spaced roughly 50 ra apart could adeguately represent the t e r r a i n over the watershed. The points were located by markers placed on nearby trees or by reference to other recognizable features. During the study season, the snow course was measured at i n t e r v a l s of roughly one week, taking samples at each point from an area roughly three meters i n diameter. More freguent sampling might be desirable, but i t would be l i k e l y to cause excessive disturbance of the sampling points, even though snowshoes were used during sampling to minimize trampling of the snow surface. A "standard" or "Mt. Bose" snow sampling k i t , of the type used for routine snow course observations i n western North America, was used. 20 Because of the non-random d i s t r i b u t i o n of the snow course points, and the systematic errors to which snow sampler measurements are subject,the snow course measurements were not used to determine the watershed snow water eguivalent d i r e c t l y but only to measure changes i n density over time. The snow course measurements were supplemented by more detailed sampling to determine the actual density. The regions, the stake network, and the snow course are shown on the maps i n appendix 1. To determine the actual volume of snow i n the watershed at the beginning of the season, a grid of depth soundings was taken on May 23, using a th i n metal snow probe. The g r i d consisted of soundings at 10 m i n t e r v a l s along l i n e s determined by the stake network; about 160 points were sounded i n a l l . Also on the same date, density samples were taken at a l l the stake locations using the Mt. Rose sampler, with two or three samples taken at every stake. Using densities calculated as described below, i t i s possible to construct a map of snow water eguivalent. The map i s shown i n appendix 1; a d i s t r i b u t i o n curve of snow depth and water eguivalent i s shown i n f i g . 2.2. The precision of the map i s d i f f i c u l t to assess. If the error in each sounding due to the sounding operation i t s e l f and due to l o c a l v a r i a b i l i t y i n the ground surface i s ±10 cm (an arb i t r a r y guess) , the average depth determined by 160 soundings wculd be i n error by ±0.8 cm. If the average snow density cf the watershed i s in error by ±0.015 gm/cm3 (see below), the error of the t o t a l snow water equivalent of the watershed would be about ±3%. This error i s due almost e n t i r e l y to the error i n density. 21 F i g . 2.1 Photograph of watershed, showing regions. 3 0 0 \ \ \ r \ Show Dep+li (cw,) Show Dep^ (t»s«J o«\ coi»n+ of Soundings) appendix I ) 0 20 GO 80 100 Frequency ( % above) F i g . 2.2 Snow depth and water equivalent areal distributions, 22 In drawing the map, the sounding data were supplemented by information cn snow depth d i s t r i b u t i o n obtained from photographs of the watershed taken during the period of p a r t i a l snow cover; t h i s tends to increase the precision of the map over that obtainable from the soundings alone. On the other hand, sounding data are sparse in a few areas of the watershed; t h i s reduces the precision of the t o t a l snow volume c a l c u l a t i o n . The t o t a l water equivalent on May 23 calculated from the map was 48,000 m3, or an average water eguivalent over the watershed of 122 cm. As f i g . 2.5 shows, t h i s compares very well with the average water equivalent of 119 cm for the same date obtained from the stake network. 2.2 DENSITY MEASUREMENTS Five snow p i t density p r o f i l e s were measured over the course of the season. The method used was that described by Ostrem and Stanley (1969). Two 500 ml snow tubes, 19.6 cm long, were used to take two p a r a l l e l v e r t i c a l samples to a horizontally placed thin s t e e l plate which was inserted into the snow at a depth of about 18 cm. The actual lengths of the cores taken were measured to the nearest 0.5 cm, and the cores were weighed on a triple-beam balance. The snow column above the plate was then cleaned out and the process was repeated; thus, a continuous v e r t i c a l column of snow was sampled. The accuracy of an i n d i v i d u a l density sample i s li m i t e d by the precision of the length measurement (about ±3%, or ±0.015 gm/cm3), but the actual length of the entire snow column was measured with a tape to calc u l a t e the average density, which therefore should be precise 23 to within about ±0.3% for a 2 m deep snowpack. The snow p i t density measurements, although precise, are point measurements and therefore are l i m i t e d i n t h e i r areal representativeness by the l a t e r a l inhcmogeneities of the snowpack, es p e c i a l l y concentrations of meltwater, discontinuous ice layers, and the presence or absence of a basal ice layer. Two examples of density p r o f i l e s are shown in f i g . 2.3. Seme intere s t i n g features of the p r o f i l e s are the near uniformity of density with depth, the presence of an old depth hoar layer which remains recognizable long after i t has undergone metamorphism due to the passage of meltwater, and the presence of a basal ice layer, the significance of which w i l l be discussed below. The density of the basal ice, when present, was measured separately by weighing a sheet of known dimensions, since i t could not be penetrated by the sampling tubes. The main purpose of the snow p i t density measurements was to c a l i b r a t e the Mt. Rose snow sampler. The accuracy of the snow sampler i s discussed below; i t was found to over-read the density by about 9%, and therefore a l l snow sampler density measurements were corrected by t h i s amount. Snow course measurements and p i t measurements were used to plot a curve of density over the snowmelt season ( f i g . 2.4). This curve i s v a l i d for the lower two-thirds of the watershed, in which the snow course was located. To modify the curve to be representative of the whole watershed, the densities taken at the stake locations on May 23 were used. These 32 density samples were corrected to remove the snow sampler bias, and were s t r a t i f i e d according to the previously 24 50 150 200 1 1 t i l hew snow lew icy layer lew Jir+y l«y«r 1 DENSITY PROFILE, JUNE 12 Mean oVnsi+y 0-525 jm/cw' Deptli 2 3 7 C M 2 +•>)« ity layerj Z- 'Sil* ice layers 2- '/icw ice layers DENSITY PROFILE, 50 JULY 3 Mean density 0-568 Depth 157 C M £ +Wm ice Uyt»-ice layer o loo _c -f-a_ ice _ near old Jept*. hoar /S .tar«te. ice 1 5 0 I I I I I I I, I I 1 I I I I I I I I I 0.0 0.1 O-Z 0-3 0.<r OS 0-i 0.1 0.9 0-0 0.| 0.1 0.1 0.<i O.S 0.4 0.1 0.» 0-1 Dehsi+y (gw/cm 3 ) Pensi+y (f/c*3) F i g . 2.3 Snow p i t density p r o f i l e s . (UO (3W/CH,») 0.55" 0.50 0 SnoW course dUhiHitS X Pit aensl+i«i A Shot/ S a m p l i n g «t p i+S D Snow s a i n p l i x j a f stakes X X V X h«y II F i g . 2.4 10 M«Y20 20 M«t30 30 Juml 50 J W 21 (0 Ju\y1 Seasonal density curves. 10 10 M M 26 chosen t e r r a i n regions, A one-way analysis of variance for each region showed that there were no s i g n i f i c a n t differences at the 5% l e v e l between the densities at the stakes within either of regions 1 and 2, which contained 5 and 7 stakes respectively. There was a s i g n i f i c a n t difference within region 3, which however contained only 3 stakes. The differences between the average densities of the three regions were s i g n i f i c a n t at the 5% l e v e l . The average densities for regions 1, 2, and 3 respectively were i n g i / c i 3 , 0.491, 0.483, and 0.452, and the ov e r a l l mean of a l l 15 locations was 0.480. These differences in density are probably due to the effect of differences i n elevation and i n exposure to solar r a d i a t i o n , and they should become les s as the season progresses and the snowpack reaches a uniform, dense state. These density calculations were used to draw three density curves roughly p a r a l l e l i n g the one based on snow course and p i t densities; these were assumed to converge l a t e r in the season. Since no further sampling was made of density across the e n t i r e watershed, the curve for region three i s rather speculative, /From the scatter in the points on f i g . 2.4, and from other considerations discussed below, the densities on these curves are estimated to be subject to an error of ±0.01 gm/cm3 for regions 1 and 2, and about ±0.02 for region 3. The error i s probably somewhat greater after about July 25, but since snow depths were very low after t h i s date, a greater error does not resu l t i n an increased error i n the calculated water balance. The density curves were used in conjunction with the stake readings and soundings in each region, A s i m i l a r curve was drawn 27 for the top 30 cm or so of the snowpack at the meteorological s i t e , using p i t density p r o f i l e s and measurements in small p i t s dug occasionally at the s i t e . This curve was used for ca l c u l a t i n g ablation as measured from the small surface layer stakes at the s i t e . 2.3 ERRORS IN THE SNOl SAMPLER DENSITY MEASUREMENTS The at. Rose snow sampler i s known to be subject to a systematic error i n measuring snow density (Work et a l , 1965). In order to assess t h i s systematic error and correct for i t , samples were taken at the s i t e of each snow pit density measurement. The r e s u l t s are shown i n table 2.1. A f i f t h set of snow p i t measurements was taken on July 24, but since the snow was very shallow, sampling was not done with the Mt. Rose sampler. On the average, the Mt. Rose sampler was found to read 9% hiqher than the snow p i t density measurement. This figure i s i n agreement with the r e s u l t s of Work et a l (1965), who found that the sampler over-read by 1% to 1251 in deep snow at Mt. Hood, Oregon, They suggested that the bias i s due to the design of the s t e e l b i t , which entrains additional snow into the tube as i t i s forced through the snow. The variation i n the sampler : p i t r a t i o s i n table 2.1 i s about ±48, and i s greatest at the shallower depths. This i s probably due to the e f f e c t of l a t e r a l v a r i a t i o n i n density, which i s net removed by the single point density measurement taken i n the snow p i t . Because of t h i s v a r i a t i o n , a set of ten or more Mt, Rose samples, when corrected for the sampler bias, probably provides a density measurement which i s at least as precise as a single snow p i t measurement. 28 Further studies involving multiple snow p i t measurements at a s i t e would be desirable to assess the systematic and random errors involved i n snow sampling. The random error i n snow sampler density measurements i s due to two sources. One i s the precision with which a single sncw core can be extracted and i t s depth and weight measured, and the other i s the ef f e c t of the l a t e r a l inhomogeneity of the snowpack. The sampling tubes are graduated in inches of snow depth, and the spring scale i s calibr a t e d d i r e c t l y i n inches of water eguivalent. 1 The depth of a single sample can be read to about ±0.6 i n , the weight of a sample to ±0.5 i n , and the tare weight to ±0.3 i n . Therefore, using egs. 1.1, for snow 100 i n {254 cm) deep and with a s p e c i f i c gravity of 0.54, the standard error of a single density sample would be 0.0033 gm/cm3, and for the average of ten samples, i t would be 0.0011 gm/cm3. For snow 20 i n (51 cm) deep, the corresponding figures would be 0.017 and 0.0053 gm/cm3. These figures indicate the error due only t c the resolution of the instrument. The actual precision of measurement would be s l i g h t l y less due to additional variation in the entrainment and loss of snow from the sampler during the sampling operation. To assess the e f f e c t s of l a t e r a l inhomogeneity, variation i n the sampling procedure, and operator error, a set of tests was performed on June 10. Four sets of 10 samples each were *The diameter of the snow sampler b i t i s 1.485 inches, chosen so that one inch of water eguivalent corresponds to a weight of exactly one ounce. Host snow samplers in B r i t i s h Columbia have now been re-calibrated i n metric units, although t h e i r physical dimensions remain the same. 29 taken, with a l l 10 samples within a small area, which was l e v e l , c l e a r , and of f a i r l y uniform snow depth (about 200 cm), while the fourth set was taken at a d i f f e r e n t s i t e . The f i r s t set of samples was taken in the normal manner by the writer, who had considerable previous experience at snow sampling. The second set was taken by the f i e l d a s sistant, who had no such previous experience. The t h i r d set was taken by the author using a different procedure involving s p l i t samples. This procedure i s sometimes necessary i n deep dense snow when i t i s impossible to drive the sampler to the bottom of the snowpack. One core i s taken to a depth which can be e a s i l y reached; after weighing, a second core i s taken by c a r e f u l l y lowering the sampler down the hole and driving i t the res t of the way to the base of the snowpack. The t o t a l core weight i s taken as the sum of the weights of the two cores. However, i t i s suspected that some snow i s unavoidably knocked from the sides of the hole and i s included in the second core. S p l i t samples were necessary i n about 25% of a l l cores taken during snow course measurements i n May and June. For t h i s experiment, s p l i t samples were purposely taken, although they were not needed at the test s i t e . The fourth set of samples was taken by the writer at a location on a moderately steep slope adjacent to a group of trees; t h i s i s a s i t e which would be considered d i f f i c u l t for sampling i n comparison with the f i r s t s i t e . The r e s u l t s of the tests are summarized i n table 2.2. The main conclusions which can be reached are: 1. The standard deviation of density measured by the sampler at one location i s about 0,012 gm/cm3. This i s much 30 i i B L I I i i SNOW SAMPLES AND P I T DENSITY MEASUREMENTS.„ CATE SNOW P I T SAMPLER S A M P L E S : P I T NO. OF DEPTH D E N S I T Y D E N S I T Y RATIO SAMPLES (tn) {q/cm3) (q/cm3) May 19 2 . 3 7 0 . 5 0 1 0 . 5 4 0 1 .078 5 J u n e 12 2 . 3 7 0 . 5 2 5 0 . 5 7 4 1 .093 10 J u l y 3 1 . 5 8 0 . 5 6 8 0 . 5 9 6 1 . 0 4 9 10 J u l y 13 1 .18 0 . 5 5 3 0 . 625 1. 130 10 mean 1 .088 T A B L E 2j,2 SUMMARY OF J U N E 10 SNOW SAMPLING T E S T S . SAMPLING METHOD A. N o r m a l s a m p l i n g p r o c e d u r e DENSITY SAMPLE STANDARD ( g / c m 3 ) D E V I A T I O N 0 . 5 4 9 0 . 0 0 9 9 REMARKS i c e a t 5 p o i n t s B . S a m p l i n g by u n t r a i n e d o p e r a t o r 0 . 554 0 . 0 1 2 1 i c e a t 3 p o i n t s C . S a m p l i n g w i t h s p l i t s a m p l e s 0 . 586 0 . 0 1 3 4 i c e a t 5 p o i n t s D . S a m p l i n g a t " d i f f i c u l t " s i t e 0 . 543 0 . 0 1 2 0 i c e a t 1 p o i n t N o t e s : 1. T e s t s A , B, and C were c o n d u c t e d a t t h e same l o c a t i o n . 2 . A l l t e s t s c o n s i s t e d o f 10 s a m p l e s w i t h a s t a n d a r d ( M t . Rose) s a m p l i n g k i t . 31 g r e a t e r than t h a t estimated from the r e s o l u t i o n of the instrument, which f o r snow 2 m deep should be about 0.003 gm/cm3. 2. The standard d e v i a t i o n s c f the f o u r s e t s of samples are net s i g n i f i c a n t l y d i f f e r e n t at the 5% l e v e l . > 3. The d i f f e r e n c e i n d e n s i t y measured by the two op e r a t o r s i s not s i g n i f i c a n t a t the 5% l e v e l . 4. The de n s i t y measured by the s p l i t sample method i s 6.7% g r e a t e r than t h a t measured by normal sampling; t h i s i s a s i g n i f i c a n t d i f f e r e n c e at the 5% l e v e l . A l l s p l i t samples taken dur i n g snow course measurements were t h e r e f o r e c o r r e c t e d by t h i s amount. (A rough t a l l y of a l l s p l i t and normal samples taken during snow sampling throughout the season showed t h a t the s p l i t samples averaged about 55? higher i n de n s i t y . ) I t was noted that the standard d e v i a t i o n o f the d e n s i t y a t the ten snow course p o i n t s averaged about 0.020 gm/cm3 throughout the season. 2 The a n a l y s i s o f va r i a n c e o f t h e snow samples at the b a s i n s t a k e s on May 23 produced an estimate of the standard e r r o r o f 0.022 gm/cm3. T h i s suggests that the v a r i a t i o n i n d e n s i t y due t o inhomogeneity of the snowpack i s gr e a t e r over the watershed as a whole than a t a s i n g l e l o c a t i o n . In summary, the standard e r r o r of the d e n s i t y determined as the mean o f ten samples i n snow of a t l e a s t one meter i n depth i s expected t o be: 1. In completely homogeneous snow ( i . e . c o n s i d e r i n g instrument r e s o l u t i o n o n l y ) : about 0.002 gm/cm3 or l e s s . , 2 F o r snow depths o f about 1 m or gre a t e r , the standard d e v i a t i o n was i n the range of 0.016 to 0.025. For shallower snow, i t was g r e a t e r , up to 0.040. 32 2. In natural snow at one location: about 0.0035 gm/cm3. 3. Over the area of the snow course: about 0.Q07 gm/cm3. In addition, variations i n the amount of l i q u i d water in transient storage i n the snowpack at diff e r e n t times of day and under dif f e r e n t melt rates could produce variation i n density of about ±0.01 gm/cm3. However, most snow course measurements were taken at about the same time of day, i n mid-morning, so t h i s source cf error should be minimal. The scatter of points about the density curve i n f i g . 2.4 i s about ±0.01 to 0.015; i f t h i s corresponds to two times the standard error, i t i s i n good agreement with the error estimates above. The error associated with the density curve i t s e l f i s scmewhat less than the error associated with one density measurement because the curve i s derived as an average curve through several points. 2.4 WATERSHED ABLATION AS DETERMINED BY STAKE MEASUREMENTS The water equivalent (We) of the snowpack at any one stake at one time i s the product of the snow depth (h) and the density (P) at that stake as indicated by the density curves i n f i g . 2.4. The ablation (A) over the period of time between two stake readings i s the difference between the water eguivalents at the two times. The units of We and A should then be gm/cm2; however, i t i s convenient to express them i n units of length, which i s the equivalent of replacing density by s p e c i f i c gravity: We = h-£- (2.1a) A = We0-We, (2. lb) where ow=1.000 gm/cm3, the density of water. The numerical 33 equivalence of density and s p e c i f i c gravity in c.g.s. units makes i t convenient to use thi s system of units for calculations involving snow water eguivalent. , Stake readings were taken at i n t e r v a l s of from three to nine days and the water eguivalent was calculated at the time of each reading. The water equivalent and ablation for each measurement period were tabulated for each stake, and a two-way analysis of variance was performed for each region of the watershed to examine the differences between and within reqions. The r e s u l t s of t h i s analysis showed s i q n i f i c a n t differences in ablation between regions and also between stakes within most regions. In region 2, there was an obvious difference between the two transects of stakes, with the stakes in the lower transect consistently reading higher ablations than those i n the upper transect. Therefore, region 2 was subdivided i n t o two regions. After t h i s r e v i s i o n , the variations between stakes in each region, although s i g n i f i c a n t i n some regions, did not fellow any areal pattern, so the watershed was not further subdivided. The var i a t i o n i n ablation rates was considered to be at a scale smaller than the scale of stake coverage, and was probably due to the huamocky nature of the topography, especially i n region 2. The ablation i n each region, therefore, was calculated as the mean of the ablations measured at the stakes i n that region. The components of variance for the residual error and the e f f e c t of stake differences were combined to estimate an error variance for the calculated ablation i n each region..The resulting standard errors for each ablation period ranged from 0.5 CJB in region 1 to 1,1 cm i n region 2a., The t o t a l volume of snowmelt over the watershed was calculated for each ablation period by multiplying the ablation over the period by the area of each region. The ablation c a l c u l a t i o n s are summarized i n table 2.3, and the water equivalents for each region are shown i n f i g . 2.5. After July 14, bare areas of ground began tc appear, and therefore, i t was necessary to adjust snowmelt t o t a l s for the p a r t i a l area of snow cover. Photographs were taken of the watershed from the ridge overlooking i t from across the valley on six occasions from July 14 to Sept. 1. The area of snow cover in each region of the watershed was calculated from the photographs and a series of snow cover curves was drawn ( f i g . , 2.6) . If a curve of water equivalent (We) against area (a) i s drawn, as in f i g . 2. 7, and i f the ablation rate i s assumed to be constant over the snow covered area, then under conditions of p a r t i a l snow cover the t o t a l volume of snowmelt over a period can be expressed as: where We0and He, represent the water eguivalent curves, and a 0 and a, represent the area of snow cover, at the beginning and end of the period, respectively. If the water equivalent curve i s assumed to be linear (which i s approximately true on the average, except at the two extremes of the area range), eg. 2.2a can be approximated by: (2.2a) M = ( H e 0 - i e , ) a , • 1/2 (He0-He, ) (a 0-a, ) = 1/2 A(a0+a,) (2.2b) where the ablation A=WeQ-He 120 100 180 -t-£ 8 T — r © Rej ion • Region 2a A Rej ion 2 b X Resion 3 - j - S«ow course 40 20 (suspect mdin j ) o M c G i l l i v r a y Pass snow c o u r s e <* T e n a / i l l e L a k e s n o w c o u r s e (+100 c m ) Mission Ridlje Snow pillow Ajw.lO Apr.20 Apr. 30 0 10 May 10 May 20 20 May 30 30 June n 80 10 Fig. 2.5 Seasonal water equivalent curves. Stake and snow course data are shown, as well as the record from several nearby snow courses. i 1— 1 1 1 1 r F i g . 2.6 P a r t i a l snow cover area curves. M = (We0-We,)a, + We 0 d Q Wa+er i We 0 (ak (We) Wc,(a)^ Area of Snow Cover («) F i g . 2.7 Schematic diagram of p a r t i a l area snowmelt. 37 TABLE 2^3 AELATION STAKE CALCULATIONS. Ablation i n mm water eguivalent, Snowmelt volume i n m3 by region. by region. PEBIOD DAYS 1 2A 2B 3 I 1 2A 2B 3 May 11-13 3 -13 -15 -30 -3 | May 14-19 6 42 64 55 54 I May 20-22 3 21 24 21 23 | May 23-31 9 -14 -16 -16 -28 J June 1-6 6 -4 -1 -16 -16 J June 7-13 7 38 45 29 -8 J June 14-19 6 104 110 93 91 | 1470 990 48 0 1010 June 20-25 6 74 95 71 63 | 1040 860 360 700 Jn.26-Jl.3 8 157 175 161 171 | 2200 1590 830 1890 July 4-8 5 137 155 134 161 | 1920 1410 690 1780 July 9-13 5 105 131 96 108 | 1480 1 180 500 1200 July 14-17 4 128 139 124 131 | 1800 1240 640 1450 July 18-23 6 187 182 191 | 2540 90 0 2030 July 24-27 4 118 110 112 | 1C60 510 1100 July 28-30 3 86 112 | 350 1000 Notes: 1. After July 13, snowmelt volumes are calculated using p a r t i a l area snow cover curves; see table 5.1. 2. Areas of regions are: 1 : 14030 m2 2A: 9070 m2 2B: 5150 m2 3 : 11060 m2 38 The snowmelt volumes after July 24 were calculated using eg. 2.2b. Some stakes were hare after July 24; therefore a f t e r t h i s date, ablation was calculated using a decreasing number of stakes, and the precision was reduced. The ablation figures after July 31 are only very rough estimates. Because of the s u b j e c t i v i t y involved in the c a l c u l a t i o n of snowmelt volumes, especially under conditions of p a r t i a l area snow cover, the errors are d i f f i c u l t to estimate. The snowmelt volumes for each of the periods from June 14 to July 30 are probably subject to an error of about ±5$ to 10%, while over the e n t i r e period of June 14 to July 30, the error i s probably well under 5%, Snowmelt volumes were not calculated for the period before June 14, because of the lack of appreciable melt during t h i s period, and the d i f f i c u l t y of measuring ablation accurately under conditions of frequent accumulation. 2.5 DETAILED ABLATION MEASUBEBENTS The method of c a l c u l a t i n g ablation described above becomes r e l a t i v e l y less precise as i t i s applied over shorter time periods, and i t becomes unacceptably imprecise for periods of one day or l e s s ; t h i s i s because ablation i s calculated as a small difference between two large values of the snow water equivalent. For t h i s reason, i t i s preferable to measure ablation over short time periods by means of small stakes which are inserted into the top half-meter or so of the snow. Small bamboo garden stakes, about 0.6 cm in diameter and 90 cm long, were used. They were painted white, and a cardboard disc about 2 cm in diameter was attached to the base of each stake to prevent 39 them sinking i n t o the snow. Two cl u s t e r s of four stakes each were placed, one near the meteorological instrument s i t e and the other at the s i t e of the instrumented snow p i t , which varied i n location but was always within 40 m of the meteorological s i t e . LaChapelle (1959) describes a method by which ablation over short periods can be accurately measured by observing snow settlement rates and subsurface density changes. In t h i s method, settlement i n the surface layer i s measured by planting several stakes at d i f f e r e n t depths, and plotting the apparent change i n height of the snow surface (Ah) against the depth of the stake <h); see f i g . 2.8a. For any stake, the apparent height change of the snow surface consists of actual loss of snow or wastage (w) and settlement i n the snow layer (u): Ah = w • u . (2.3) I f settlement i n the surface snow layer i s uniform with depth, the settlement occurring at a stake should be roughly proportional to the depth of the stake, and the wastage can be determined by extrapolating the curve in f i g . 2.8 back to the "point where h=0. This method was successful early in the season when the snow surface was r e l a t i v e l y smooth and settlement rates were high. However, after June 17 the scatter i n the points was such that a trend could not be determined i n the plot of Ah vs. h. The error i n reading each stake was estimated to be about ±0.1 cm on about June 6, increasing to 0.3 cm on about June 17 and to 1.0 cm from July 1 to the end of the season, while the settlement i n a surface layer about 50 cm thick was i n the order of 0,5 to 1.0 cm per day early i n the season, and about 0.2 cm 40 a. Graphical determination of surf-ce wastage and settlement by LaChapelle's (1959) method. Data from the period June 6, 1820 hrs, to June 8, 1900 hrs. b. I l l u s t r a t i o n of Ah, w, and u over a measurement period t Q to t 1« F i g . 2.8 Schematic diagrams of ablation c a l c u l a t i o n by the small stakes method. 41 per day or less after abour June 20., Since the proportional rate of settlement of a snow layer i s equal to i t s proportional rate of density change 3 the ef f e c t of settlement was computed by using a density curve as described i n section 2 above. I f the thickness of a snow layer from the surface to an arbit r a r y base l e v e l at the end of a measurement period i s h,, the thickness of the same snow layer at the beginning of the period i s h,+u, and the density at the end and beginning of the period i s p, and p 0 , then i n the absence of subsurface melt or l i g u i d water storage changes (see f i g . 2.8b): <h,+u)p0 = h,p, or: u = h, (£ -1) . (2.4a) JO From eq. 2.3: w =Ah - u (2.4b) and ablation i s then: A = vpQ . (2.4c) Eqs. 2.4 were used to calculate short-term ablation from June 14 to the end of the f i e l d season, using the density curve to obtain p( and p 0 . The values of Ah and h| were taken as the means of the readings for the four stakes i n each cluster. Stake readings were normally taken in the early morning and late afternoon. A graph was made of cumulative ablation ( f i g . 2.9), and daily ablation was estimated by interpolating the midnight values. Some days were missed due to bad weather and other interruptions in the f i e l d work; these days were f i l l e d i n by interpolation on the graph. The error inherent i n the daily ablation values varies considerably from day to day, but 3By l e t t i n g Ah=u, and expressing eg. 2.4a as a d i f f e r e n t i a l with respect to time, one obtains: 1 dh 1 dP h dt ~p dt . 42 probably averages about ±0.3 cm, or ±10% to 15%, and i s due mainly to the precision with which the stake heights can be read. {The precision of the small stake readings i s greater than that cf the large stakes, due to th e i r smaller diameter and thei r freguent re-setting.) Due to the cumulative nature of the measurements, the proportional error i s reduced over periods longer than one day. Besides the error i n reading the stakes, the accuracy of the ablation ca l c u l a t i o n s depend on the v a l i d i t y of the assumptions on which eqs. 2.4 are based: 1. The density, and the de n s i f i c a t i o n factor P,/fo~1r are constant throughout the surface snow layer. This assumption i s often in error over short time periods due to the melting out of ice layers and due to subsurface melt under strong radiation conditions, but the errors tend to cancel out over periods of several days. 2. The l i q u i d water content of the snow does not vary over time. Error from t h i s source i s minimized i f the density measurements and stake readinqs are taken at the same time each day, preferably i n the early morninq. The da i l y ablation values for the c l u s t e r of stakes at the meteorological s i t e are tabulated i n appendix 2. These values were used i n the daily energy balance calculations in chapter 6. As a backup to the small stakes, readings were also made of four large stakes planted to the ground, and ablation was calculated as described i n section 4. Over a period of about one month, from June 28 to July 30, the cumulative ablation measured by the two methods was: 1. Snow p i t site : large stakes 84.7 cm small stakes 85.7 cm F i g . 2.9 Ablation as calculated from small stakes. 44 2. Meteorological s i t e : large stakes 87.4 cm small stakes 83.3 cm. During the month of July, two "ablation gauges" were i n s t a l l e d . Each of these consisted of two stakes about 1 m in length inserted i n the snow, and joined by a 1 m horizontal cross-bar. Eleven equally spaced marks were made along the cross-bar, and the distance to the snow surface below each mark was measured with a tape. These devices were i n s t a l l e d for the purpose of observing suncup formation, but they also provide an alt e r n a t i v e means of measuring surface lowering. A comparison of surface lowering measurements using one of the ablation gauges and the small stakes at the meteorological s i t e i s shown in f i g . 2.10. The scatter of the points indicates a measurement error of about ±0.7 cm over one-day periods, A similar plot (not shown) comparing the sets of small stakes at the two locations showed s l i g h t l y l e s s scatter, about ±0.5 cm. LaChapelle (195 9) describes another method for the c a l c u l a t i o n of short-term ablation, involving the measurement of detailed density p r o f i l e s of the upper snow layer using small sample tubes. He points out, however, that t h i s method i s feasible only with f a i r l y fine-grained snow and a smooth snow surface. This method was applied successfully during the period of June 6 to 8, which was the only period of s i g n i f i c a n t melt before June 14. At l a t e r dates, the snow was too coarse to sample accurately with the small 50 ml snow tubes, and the large 500 ml snow tubes did not give a density p r o f i l e with enouqh resolution to use LaChapelle's method. However, the density samples taken i n small surface p i t s were used to e s t a b l i s h the curve of density throuqhout the snowmelt period. 45 2.6 OBSERVATIONS ON ICE AT THE BASE OF THE SNOWPACK A prominent feature of the snowpack during the f i e l d season, and one of considerable hydrological significance (see chapter 4), was the layer of basal ice which was freguently observed at the ground-snow interface.,From observations during snow course readings and soundings, and la t e in the season during break-up of the snow cover, i t was estimated that the basal i c e covered at least 75% of the watershed, and was t y p i c a l l y 0.5 to 3 cm thick, photographs of the ice are shown i n f i g . 2. 11. The nature of the basal i c e , and some of the factors influencing i t s formation, were observed in snow pi t s and in snow sampler cores. In early and mid May, about half of the area sampled had cold snow (that i s , snow colder than 0°C) i n the lowest 20 to 40 cm, and the ground underneath was frozen. In some areas, basal i c e 1 to 2 cm thick was observed. By mid June, frozen ground and cold snow were rare, and basal i c e was increasingly common,* Two runoff events had occurred by June 14; a rainstorm on May 26-27 produced about 30 mm of runoff (but no noticeable melt), and a period of warm sunny weather on June 6-8 produced about 45 mm of melt. These two events had "ripened" the snow (i . e . had warmed i t to an isothermal state), and caused meltwater to reach the ground, l a r g e l y eliminating the cold snow and frozen ground. (In addition, some melt may have occurred during warm weather in the f i r s t week of May.) The basal i c e was probably formed when t h i s water froze at the ground-snow •On June 1, basal i c e was observed at 4 out of 10 sampling points of the snow course, and by July 15, i t was observed at 8 points. F i g . 2.11b Basal ice exposed after melting of the snowpack. Note the small meltwater channel in the ice. 47 interface, and by doing so released latent heat which thawed the frozen ground and snow. Cold snow of a cemented nature was sometimes observed early i n the season i n the lowest 10 or 20 cm of the snowpack; t h i s indicates that some meltwater was frozen in the snowpack, but because of the high permeability of the snow, most of the water froze at the ground surface. The basal ice was usually compact and transparent, unlike ice layers within the snowpack, which suggests an o r i g i n of frozen l i g u i d water rather than metamorphosed snow. The ice was v i r t u a l l y impermeable; t h i s was demonstrated by pouring a bucket of water over the ice i n a snow p i t , where some of the water remained ponded for over an hour. As the season progressed, there was very l i t t l e tendency for the basal ice to disappear. In depressions and i n areas of apparently high s o i l water movement, i t tended to decompose into slush, but i n most areas i t remained hard and c l e a r , and remained as a sheet covering the ground at the edge of bare patches as the snow cover disappeared. On August 1, with about 35% of the watershed bare, there was s t i l l i c e at 6 out of 7 snow course points which had snow. A s o i l heat flux plate and two thermistors had been buried near the meteorological s i t e the previous October. These indicated near-zero heat flux and s o i l temperatures of 0°C throughout the snowmelt season, which supports the inference that very l i t t l e melt occurred at the base of the snowpack. A v i s i t to the s i t e was made the following spring, in May 1977, after a winter of very l i g h t p r e c i p i t a t i o n . Two pit s were dug, one i n a s l i g h t l y elevated, convex area and one nearby in a 48 s l i g h t depression, where some meltwater subsidence hollows were v i s i b l e i n the snow. The snow depth was about 115 cm. In the f i r s t p i t , there was no basal i c e , but the ground was s o l i d l y frozen. The bottom 10 cm of the snow consisted of well-developed depth hoar. In the second p i t , continuous basal ice about 3 cm thick was present, and the ground was not frozen. The depth hoar had been altered by meltwater i n t h i s p i t , and ice layers in the snowpack were more pronounced than i n the f i r s t p i t . These observations indicate that meltwater had been deflected to the depression by the sloping stratigraphy of the snowpack (see chapter 3), and basal i c e had formed where i t had reached the ground. Elsewhere in the McGillivray Pass region, at lower elevations, basal i c e of 10 cm or more i n thickness was observed melting out as the snow disappeared. Apparently i n the winter of 1976-77, lower ground temperatures were reached due to the lack of snow in the early part of the winter, and the formation of basal i c e was favoured by t h i s freezing. A p i t dug during a f i n a l v i s i t i n March, 1978 revealed frozen ground, and a snowpack which was below 0°C for the lower half of i t s 2 m depth. No basal ice was observed, and i t was apparent that meltwater had not yet penetrated through the snowpack, although seme surface melting had occurred. (Some basal i c e was noticed along roads at lower elevations.) Temperature and p r e c i p i t a t i o n were s l i g h t l y above normal during the preceeding two months. from these observations i n three years of widely d i f f e r i n g snowpack conditions, i t can be concluded that frozen ground during the winter and the formation of an impermeable layer of 49 basal i c e i n the spring are usual at t h i s s i t e . These conditions are apparently common in alpine and subalpine locations throughout t h i s region. 2.7 REGIONAL REPRESENTATIVENESS OF ABLATION AT THE STUDY SITE Fig. 2,5 shows the average snow water eguivalent cf the study watershed over the snowmelt season, and also the record from the snow pillow at Mission Ridge, and the snow courses at McGillivray Pass and Tenguille Lake. Considerable variation in the snowmelt rates between the di f f e r e n t locations i s noticeable, e s p e c i a l l y during the period from May 14 to June 14. The factors which would be expected tc affect the snowmelt rates at di f f e r e n t s i t e s in the same region and at about the same elevation are: 1) aspect and exposure 2) persistent l o c a l cloud formation 3) albedo of the snow surface 4) presence of forest cover 5) presence of an advective s i t u a t i o n . Differences i n snowmelt rates between north and south facing slopes near the study s i t e were noticeable, but at actual snow course s i t e s the differences i n aspect are s l i g h t , since they are generally on f l a t or s l i g h t l y north-facing slopes. Local cloud formation might be important i n some l o c a t i o n s , but t h i s factor i s impossible to evaluate without r a d i a t i o n measurements or frequent weather observations. Albedo differences may be very important i n explaining the difference i n melt rates at the study s i t e and at the 50 McGillivray Pass snow course. In May and early June, s l i g h t differences i n the freezing l e v e l often resulted i n fresh snow f a l l i n g at the study s i t e but not at the snow course, which i s about 120 m lower in elevation. The albedo of fresh snow was t y p i c a l l y about 0,85, while that of snow after about a week of melting was about 0.65; thus, the older snow could absorb at least twice as much solar radiation as the fresh snow. The presence of more fresh snow at the study s i t e therefore could have led to s i g n i f i c a n t l y lower melt rates during late May and early June, when the s i t e was subject to frequent l i g h t snowfalls. The presence of a fo r e s t cover at or very close to a s i t e would be expected to raise the a i r temperature i n the v i c i n i t y , due to increased absorption of solar radiation by the darker forest area, as compared with unforested, snow covered areas. This would cause increased snowmelt from long-wave radiation and from turbulent heat transfer. The immediate v i c i n i t y of the McGillivray Pass snow course i s more heavily forested than that of the Tenguille Lake snow course, while the study s i t e i s almost completely alpine, These differences could explain some of the differences i n observed snowmelt at these three s i t e s , (A comparison with the Mission Bidge snow pillow s i t e i s not possible because the writer has not v i s i t e d t h i s s i t e . ) An advective s i t u a t i o n favouring high snowmelt rates would be expected tc occur when the s i t e i s near large areas of fore s t , snow-free areas, bodies of water, or other features which would produce higher a i r temperatures than those over the s i t e . The study s i t e i s r e l a t i v e l y free from such influences. 51 while the McGillivray Pass snow course i s close to large areas of forest and to areas which are snow-free r e l a t i v e l y early due to the shallower snow cover i n t h i s area. From examination of s a t e l l i t e photos, i t appears that the Tenguille Lake snow course would be l e s s affected by such influences cn a large scale than would the McGillivray Pass snow course. The Mission Ridge instrument s i t e , however, i s i n a location very subject to advective influences, being i n a small sub-alpine area completely surrounded by forests at a lower elevation, and also being close tc two large lakes, one of which does not freeze i n winter. On the basis of t h i s crude examination of surrounding snow courses, i t can ten t a t i v e l y be concluded that the melt rates observed at the study s i t e are probably t y p i c a l of large alpine areas, while areas of s i m i l a r elevation and snowfall but which are closer to forested areas, or large bodies of water, would probably experience higher melt rates and e a r l i e r depletion of the snow cover. 2.8 SUMMARY The accumulation and ablation of snow i n the watershed during the snowmelt season was measured using methods which are a composite of several techniques used i n gl a c i e r mass balance studies and in snow surveys. To overcome the problems of s p a t i a l v a r i a b i l i t y , d i f f e r e n t sampling networks were established for the measurement of density, depth changes, and t o t a l snow depth, in increasing order of the sampling density required.,More detailed sampling was done at one s i t e i n order to measure ablation at a point on a daily basis. 53 CHAPTER 3 WATER MOVEMENT IN THE SNOWPACK The t i m i n g and shape of the hydrograph at the o u t l e t c f a watershed i n response to a snowmelt i n p u t are a f f e c t e d by the processes of water movement through the snowpack, and by the processes of water movement through or over the s o i l and through the stream channel network. In a very s m a l l watershed such as the one under study, the e f f e c t of the stream channel network i s minimal. S u r f a c e and s o i l r u n o f f processes have been s t u d i e d e x t e n s i v e l y ( f o r a review of t h e o r e t i c a l work, see Freeze, 1974) ; i n p a r t i c u l a r , r u n o f f processes d u r i n g snowmelt have been s t u d i e d e x p e r i m e n t a l l y by Dunne and Black (1971), and by Dunne, P r i c e , and Colbeck (1976). These processes w i l l be d i s c u s s e d i n chapter 4. A deep snowpack i s of c o n s i d e r a b l e importance i n d e l a y i n g the response of the stream hydrograph and i n p r o v i d i n g a r e s e r v o i r f o r the t r a n s i e n t s torage of meltwater. The theory o f water movement i n snow has become w e l l developed i n recent years (f o r a review, see Colbeck (1977) , but t h e r e i s a need f o r f i e l d s t u d i e s which provide t e s t s of the theory under d i f f e r e n t environmental c o n d i t i o n s , p a r t i c u l a r l y a t the watershed s c a l e . In t h i s c h a p t e r , the theory i s reviewed, and examined c r i t i c a l l y i n terms o f i t s a p p l i c a b i l i t y to d e s c r i b i n g the response o f the stream t o snowmelt i n the study watershed. In order to apply t h i s theory to a p a r t i c u l a r environment, i t i s necessary to c o l l e c t experimental data which determine c e r t a i n parameters i n the model; the extent of v a r i a t i o n o f these parameters from one environment t o another, and over time and space w i t h i n the environment under study, should a l s o be 54 determined. An attempt i s made here to do t h i s , and the success of the theory i n describing flow at the watershed scale i s also examined, i n terms of the data requirements and of possible s i m p l i f i c a t i o n s to the model, 3.1 THEORY AND PREVIOUS STUDIES Gerdel (1945) observed that the process of meltwater drainage i n a "r i p e " snowpack (one which i s isothermal at 0°C and has been subjected to the passage of meltwater) i s similar to drainage in coarse sand, Colbeck (1972) and iankiewicz (1976) treated "mature" snow (snow which has been ripe for some time and in which density and grain s i z e are no longer increasing rapidly) as a r i g i d porous medium i n which water movement i s governed by Darcy's law for unsaturated flow, , Snow d i f f e r s from sand i n that the water flowing through i t is the same substance as the porous medium i t s e l f , and phase changes can i n t e r f e r e with the process of water flow . Even i n an isothermal melting snowpack, the snow i s undergoing meltwater metamorphism, which tends to decrease the porosity and increase the grain s i z e ; t h i s metamorphism i s ultimately caused by phase changes at a very small scale (Hakahama, 1968; Muller, 1971). If a deep snowpack has been subjected to meltwater passage for some time (in the order of several weeks), the snow i s reduced to rounded, coarse (1 to 2 mm) grains, and further metamorphism proceeds very slowly. Thus, over the course of an experiment l a s t i n g for several days, a mature snowpack can be considered to be a r i g i d porous medium (Sankiewicz, 1976). The texture of mature snow i s remarkably s i m i l a r from one environment to 55 another; however, inhoraogeneities such as ice layers and ice glands {vertical icy columns i n the snow), which have been formed during snow deposition and by meltwater movement while the snow was colder than 0°C, can be an important influence on meltwater movement (Gerdel, 1954; Smith, 1974). These ichcntogeneities vary greatly between different environments and dif f e r e n t years, and cause meltwater i n most natural snowpacks to behave d i f f e r e n t l y than would be predicted by a model of a homcgenecus porous medium; thi s s i t u a t i o n i s analogous to that caused by natural inhomogeneities i n s o i l s , Darcy's law for the flow of water in an unsaturated porous medium can be expressed in one-dimensional form as: where V i s the volume flux of water in the downward di r e c t i o n , z i s the height above a datum, K i s the unsaturated hydraulic conductivity (a variable which depends on l i g u i d water content or on c a p i l l a r y pressure), and h c i s the c a p i l l a r y pressure head {which i s always negative for an unsaturated medium, in d i c a t i n g that the pore water i s under tension and that water w i l l tend to flow from a more saturated to a less saturated region). In t h i s chapter, the notation and units of Hankiewicz (1976) are used; h c has units of length, and K has units of vel o c i t y , as does V. The eguation of continuity (Colbeck, 1972) i s given by: where B i s the volumetric l i g u i d water content. .Combining egs, 3,1 and 3,2, one obtains: (3.1) &Z ot (3.2) {3.3) 56 If K and 8 arc known functions of h c, then eq. 3.3 can be solved for h c at any point ( z , t ) . This has been accomplished usinq numerical methods f o r the problem of i n f i l t r a t i o n into s o i l (Freeze, 1969). Colbeck (1972) assumed that for steady or decreasing flow, the c a p i l l a r y pressure gradient term i n eg.,3.1 i s n e g l i g i b l e ; t h i s gravity drainage assumption was supported with experimental evidence by Wankiewicz (1976). In this circumstance, eg. 3.1 becomes: V = K . (3.4) For the l i g u i d water content found in snow under most natural conditions, the relationships between hydraulic conductivity, c a p i l l a r y pressure, and l i g u i d water content can be expressed as power laws (Wankiewicz, 1976). I t i s convenient to use the " e f f e c t i v e saturation", S*, instead of the l i g u i d water content, B : e-e- t where <f> i s the porosity and Q\ i s the " i r r e d u c i b l e water content", or the water content which would be held by c a p i l l a r y and surface forces i f the snow were allowed to drain for a prolonged period. The denominator of eg. 3.5 i s known as the "e f f e c t i v e porosity", 0e . The power law r e l a t i o n s for hydraulic conductivity under drainage conditions are: K = K SS* £ (3.6a) K = K s(-^d) (3.6b) where K s i s the saturated hydraulic conductivity and h bj i s the a i r entry c a p i l l a r y pressure for the boundary drying curve 57 {which i s approximately the height of the c a p i l l a r y fringe above a water table), I t follows that: s . . ( ^ ) X where A . = V £ , Sankiewicz (1976, p. 48} suggests values of about 3.5 for £ , 4 for X , and 14 for T\; Colbeck and Davidson ( 1973) used £=3, (Colbeck*s a n a l y t i c solution of the flow equations requires that be an integer.) Hankiewicz*s re s u l t s suggest that h y i s about -3 to -4 cm. Since egs. 3.6 apply only at low leve l s of S*, the values of Ks and hy actually used are obtained from intercepts of plots of K and h c , or of V and U v (see e^. 3.7 below), and may not be related to values of Ks and h ^ measured under saturated conditions. Several measurements of the permeability of snow to a i r or kerosene have been reported in the l i t e r a t u r e (eg. Shimizu, 1970, and de Quervain, 1972); from these, the saturated hydraulic conductivity can be calculated, knowing the v i s c o s i t i e s of the f l u i d s involved. The values of Ks which r e s u l t range from about 1 to 7 cm/sec for coarse-grained (1 to 2 mm) snow. Indirect determinations of K5 from observations cf flow at low l i q u i d water contents (Colbeck and Davidson, 1973) indicate values of about 0.1 to 0.2 cm/sec. Schematic diagrams of the conductivity and c a p i l l a r y pressure r e l a t i o n s are shown i n f i g . 3.1. The c o n d u c t i v i t y - c a p i l l a r y pressure relationship f o r s o i l s generally shows hysteresis, with any observed wetting cr drying curve forming a curve contained within the boundary wetting and drying curves for that s o i l . Wankiewicz (1976) found t h i s phenomenon to occur in snow as well. The hysteresis effect i s such that the water content and conductivity w i l l be higher for a given c a p i l l a r y pressure during drying than during wetting. This i s due largely to surface tension e f f e c t s i n pores interconnected by smaller passages ( H i l l e l , 1971). The conductivity-water content r e l a t i o n i s believed to show much less hysteresis than the relations involving c a p i l l a r y pressure (Wankiewicz, 1976); both Colbeck and Wankiewicz assumed that 3.6a i s not affected by hysteresis. Ey assuming that c a p i l l a r y pressure gradients are neg l i g i b l e and by using eg. 3.6a, Colbeck (1972) was able to solve eq. 3.2 for the speed of a flux wave U v; This solution holds for steady and decreasing flows, and indicates that any value of a flux V i s propagated through the snow as a kinematic wave, which moves at a speed which depends on the magnitude of the flux i t s e l f . Thus, larger values of V overtake smaller values, and an i n i t i a l snowmelt wave (which might be roughly shaped as a sine curve) i s distorted with increasing depth to a shock front followed by a long recession. A schematic curve of t h i s behavior i s shown i n f i g . 3.2, Observed hydrographs of meltwater flow in g l a c i e r s and seasonal snowpacks do not show a perfectly sharp shock front as predicted by eg. 3.7; instead, the wave front i s somewhat attenuated. This i s due to the c a p i l l a r y pressure gradient term i n eg. 3.3, which Colbeck neglects i n his analysis, and to inhomogeneities i n the snow, which cause the meltwater wave to progress in a fingering flow pattern (Gerdel, 19 54; Wankiewicz, (3.7) 59 0 S* a . C a p i l l a r y t e n s i o n - w a t e r s a t u r a t i o n r e l a t i o n , s h o w i n g b . C o n d u c t i v i t y - w a t e r h y s t e r e s i s . ( A f t e r H i l l e l , 1 9 7 1 . ) s a t u r a t i o n r e l a t i o n . ( A f t e r C o l b e c k , 1 9 7 2 . ) F i g . 3 . 1 C o n d u c t i v i t y - c a p i l l a r y p r e s s u r e r e l a t i o n s . S u r f a c e . 0 time 2*r hrs F i g . 3 . 2 P r o p a g a t i o n o f a f l u x wave w i t h t i m e . ( A f t e r C o l b e c k , 1 9 7 2 . ) 1976) . Hankiewicz (1976) introduced the f r a c t i o n a l d erivative,to, of conductivity with respect to l i q u i d water content: to= J - M. - jL(Ml/i (3.8) K d 9 " ^ e \ K / This i s a convenient term because l i g u i d water content i s very d i f f i c u l t to measure precisely, but changes in l i q u i d water content can be determined by measuring changes i n density, a r e l a t i v e l y simple and precise measurement (assuming that, for the course of a short experiment, the skeleton of ice grains does not change i n density). As eg. 3. 8 indicates, CJ i s a slowly changing function of K. Measurement of (*) for a given snow layer (see Hankiewicz, 1976, and section 3,4 below) removes the need for measurement of the K (S*) r e l a t i o n s h i p of eg. 3.6a, and s i m p l i f i e s eq, 3.7 to: D v = UV (3.9) (assuming eq. 3.4 i s v a l i d ) . The above analysis i s val i d only for steady or decreasing flow. Colbeck (in Dunne et a l , 1976) gives an approximate formula for c a l c u l a t i n g the speed of the shock front. Op, for increasing flow, assuming that £=3: 0 F = = ^ V , 2 ' 3 • V,"3 V / 3 + V/' 3) (3.10) where V( and V 2 are the low and high flows bounding the shock front. This formula was applied by Dunne et a l (1976) to model the propagation of observed d a i l y snowmelt waves through a snowpack. Solution of eg.,3.3 by numerical methods might be an improvement over the use of egs. 3.7 and 3.10, because eg, 3,3 61 i s equally v a l i d for increasing and decreasing flows, and the gravity drainaqe assumption i s not necessary. However, eg. 3.3 requires that the c o n d u c t i v i t y - c a p i l l a r y pressure r e l a t i o n be known, as well as the conductivity-saturation r e l a t i o n ; this introduces a d d i t i o n a l data requirements into a model usinq t h i s approach. Colbeck (1974) extended his model to include meltwater flow through the saturated layer at the base of the snowpack. He suggested that flow through the saturated zone i s much faster (fay about 2 orders of magnitude) than flow through unsaturated snow. Dunne et a l (1976) included flow through the saturated zone i n t h e i r model of the generation of snowmelt runoff on h i l l slopes. However, the model of saturated flew occurring i n a layer of uniform thickness i s probably too s i m p l i s t i c to be applied under most conditions; flow at the base of the snowpack tends to become highly channelized. Basal flow can occur only when the ground i s frozen or saturated, or i s covered by a layer of basal ice. Smith (1974) and Langham (1974) found that saturated flow can also occur over dense and continuous i c e layers within the snowpack, Colbeck (1975) also extended his theory to two-dimensional flow in a layered in c l i n e d snowpack. This modification takes i n t c account the reduction i n the e f f e c t i v e hydraulic conductivity perpendicular to the s t r a t i f i c a t i o n i n the snowpack, and describes the deflection of the flow from the v e r t i c a l i n an inclined snowpack. 62 3.2 INSTRUMENTATION Meltwater movement i n the snowpack at the study s i t e was studied quantitatively using instrumentation developed by Wankiewicz (1976) for studies in deep Coast Mountain snowpacks. Porous cup tensicmeters were used to measure c a p i l l a r y pressure, and a large melt pan was used as a lysimeter to measure flux rates. These instruments were i n s t a l l e d i n snow pits i n an approximately l e v e l area near the meteorological s i t e ; the pits were enclosed with a cover of plywood and aluminum sheets to exclude solar radiation and to minimize possible disturbances of melt patterns near the p i t . The f i r s t p i t was used u n t i l June 23, and i n s t a l l a t i o n s a f t e r t h i s date used a second p i t about 90 m away. The lysimeter consisted of a 1 m sguare pan of sheet metal with a 12 cm raised rim on three sides, and a drain i n one corner. It was i n s t a l l e d by cutting a s l i t i n an alcove notched into the snow p i t wall, and in s e r t i n g the lysimeter at a s l i g h t angle so that meltwater would flew to the drain. A tipping bucket gauge and an event recorder provided continuous measurement of the flux rate. The i n s t a l l a t i o n i s shown i n f i g . 3.3. Some delay i n the response of t h i s lysimeter i s expected because of the transient storage of water in the saturated layer at the surface of the lysimeter (Wankiewicz, 1976, p. 82). Wankiewicz also designed a tension lysimeter to overcome t h i s problem, but i t was not used i n t h i s study because i t s i n s t a l l a t i o n i s complicated.,The larger size of the sheet metal lysimeter i s an advantage because i t averages out horizontal inhemogeneities in the flow f i e l d to some extent. Despite i t s 63 large s i z e , the lysimeter (on i t s second i n s t a l l a t i o n ) over-read by a factor of about 1.5 times when the snow depth over the lysimeter was 70 cm and greater; after the snow depth was 45 cm or l e s s , the lysimeter volumes and the snowmelt determined by stakes were e s s e n t i a l l y egual. This indicates that i c e layers (see f i g . 2.4) or other s t r a t i g r a p h i c features deflected additional meltwater into the lysimeter. (The lysimeter was about 40 to 50 cm below the ice layers shown on the June 3 p r o f i l e in f i g . 2.4.) An early i n s t a l l a t i o n of the lysimeter from mid-May tc mid-June was unsuccessful because the lysimeter was not i n s t a l l e d with s u f f i c i e n t slope, and also because a thick, s o l i d i c e layer developed over i t s surface. This was possibly because the snow was not ripe at the time of i n s t a l l a t i o n (which could cause rapid metamorphism i n the presence of meltwater over the lysimeter; see Wakahama, 1968), and because heat may have been conducted from the snow by the metal lysimeter in the cold temperatures which prevailed during t h i s period. The second i n s t a l l a t i o n , from June 28 to July 18, was successful, although problems with the event recorder clock caused some loss of record. The event recorder trace was e l e c t r o n i c a l l y d i g i t i z e d and d i f f e r e n t i a t e d to produce a hydrograph of the meltwater f l u x . The design of the tensiometers i s discussed i n Wankiewicz (1976); a photograph i s shown i n f i g . 3.4. B a s i c a l l y , each tensiometer consisted of a porous cup at the end of a 45 cm by 1.3 cm support tube, connected by f l e x i b l e tubing to a water-f i l l e d manometer consisting of a 2 mm c a p i l l a r y tube. Each 64 Snow surface Cover / Lysimeter Ground surface Pi f ! Snow blocks n a Tipping bucket ,5««y* and event recorder F i g . 3.3a (above) Lysimeter i n s t a l l a t i o n . F i g . 3.3b ( r i g h t ) L y s i m e t e r and t i p p i n g bucket gauge. F i g . 3.4 ( l e f t ) Tensiometer and f u n n e l l y s i m e t e r i n s t a l l a t i o n . 65 tensiometer was inserted into the snow by d r i l l i n g a hole at a s l i g h t angle from the horizontal so that the cup was i n contact with the end of the hole, and was s l i g h t l y lower than the zero l e v e l of the manometer to prevent i t from loosening or f a l l i n g out. Normally, four tensiometers were placed i n a row at each of two le v e l s , i n an alcove recessed into the wall of the snow p i t . , The tensiometers were supported by a thin r i g i d s t i c k fixed to the snow wall to minimize drooping of the tensiometer tubes. A thin white p l a s t i c marker was inserted into the snow wall, and such droop as occurred was measured r e l a t i v e to t h i s marker. At the end of each experiment, the positions of the scale zeroes and of the cups were measured r e l a t i v e to the marker by using a water l e v e l (consisting of a transparent w a t e r - f i l l e d p l a s t i c tube), The positions of the cups were measured by removing the tensiometers and c a r e f u l l y cutting back the wall, without disturbing the reference marker, to expose the end of the hole where each cup had been positioned. Thus, the zero o f f s e t cf each tensiometer cup r e l a t i v e to the scale zero could be accurately measured. The c a p i l l a r y pressure, h c , at each tensiometer i s given by (after Wankiewicz, 1976, p. 74): h c = - h,- + h z • h^ (3.11) where i s the manometer reading { a negative number), hr i s the c a p i l l a r y r i s e i n the manometer tube (1.5 cm), h z i s the zero o f f s e t at the end of the experiment (positive i f the scale zero i s higher than the cup), and hi i s the observed droop at the time of the reading {positive r e l a t i v e to the manometer position at the end of the experiment). T y p i c a l l y h z was about 1 66 to 2 cm, and h«| was 0.3 to 0.5 cm over a period of about one week. If hm and hj are measured to a precision of ±0.1 cm, then he i s precise to ±0.14 cm; t h i s i s much less than the variation between adjacent tensiometers due to the inhomogeneity of c a p i l l a r y pressures in the snowpack. Eankiewicz•s tests indicate that the tensiometers respond very rapidly to changes in c a p i l l a r y pressure.; A crude lysimeter consisting of a 21 cm diameter funnel draining into a graduated cylinder was i n s t a l l e d at the l e v e l of each row cf tensiometers. These lysimeters were too small to accurately measure fl u x rates, but they gave an approximation of the timing and shape of the meltwater wave. A calorimeter of the type designed by Yosida (1960) was used to measure the l i g u i d water content of the snow adjacent to the tensiometers, i n an attempt to determine a r e l a t i o n s h i p between c a p i l l a r y pressure and l i g u i d water content. However, the accuracy of the calorimeter measurements i s i n doubt (see below). Also, since destructive sampling of the snow in the v i c i n i t y of the tensiometers was necessary, the number of samples which could be taken at one location was l i m i t e d , and sampling could be performed only during the l a s t day of a tensiometer i n s t a l l a t i o n . Two tensiometer experiments, consisting of two l e v e l s of four tensiometers each, were performed, during the periods June 17 to 22 and June 30 to July 8. An additional experiment, involving only four tensiometers at one l e v e l , was performed on July 14-15 i n conjunction with calorimeter measurements. On two occasions, readings were taken over a complete 24 hour period; otherwise, readings were taken during the day only. The experiments were hampered by the scarcity of warm sunny days which would produce high melt rates and a d i s t i n c t i v e diurnal melt pattern. 3.3 LIQUID WATEB CONTENT MEASUREMENTS Calorimeter measurements of l i g u i d water content were made on two occasions, taking samples over a 24-hour period i n an attempt to determine the h c (S*) and K(S*) relationships. A set of four samples was taken at each tensiometer l e v e l by using a clear p l a s t i c tube to extract horizontal cores of 70 cm3 from the snow between the tensiometers. The volume of each sample was controlled by cutting the core to a standard length before placing i t i n the calorimeter. This procedure was performed rapidly and c a r e f u l l y to ensure that neg l i g i b l e melting of the core occurred during the sampling operation. The procedure provided a density measurement for each calorimeter sample, which gives a check on the precision of the calorimeter r e s u l t s as well as an alternate means of calculating changes in l i g u i d water content. The density, p , and the l i g u i d water content by weight, S, were calculated as the mean of the four samples; these r e s u l t s are summarized i n table 3.1. The volumetric water content, 6, can be calculated from: 9 ~ (3 . 1 2 ) J w where j>w = 1. 00 0 gm/cm3. The e f f e c t i v e saturation, S*, can be calculated from eg. 3,5..This reguires an estimate of the irr e d u c i b l e water content 8 i , which i s d i f f i c u l t t c obtain, but 68 1±1 CALOBIMETEY RESULTS. DATE AND TIME 9 W 0 S* * V 3 (gm/cm3) (cm) (cm/hr; Exp, 1a (upper l e v e l ) ; 0 =0.48 June 21 1715 0.537 0, 185 0.099 0.1 53 -•8.5 0. 23 2145 0.546 0.162 0.088 0.129 -11.8 0.03 June 22 0915 0.528 0. 115 0.061 0.0 69 -12.6 0. 02 Exp. 1b (lower l e v e l ) ; 0 = 0.46 June 21 1745 0. 563 0. 148 0.083 0.123 -7.8 0. 29 2205 0.575 0. 194 0.112 0.191 -9.1 0.09 June 22 0940 0.550 0. 148 0.081 0.119 -11.3 0. 04 Exp. 2 (one l e v e l only); 0=0.44 July 14 1100 0.566 0. 150 0.085 0. 134 -10. 7 0.12 1310 0.587 0. 189 0.111 0. 198 -7.6 0. 28 1530 0.591 0. 248 0. 147 0.285 -7.3 0.34 1850 0.579 0.216 0. 125 0.232 -8. 2 0. 14 July 15 0955 0. 573 0. 192 0.110 0.195 0.08? 1430 0. 574 0.218 0.125 0.232 0. 31 Estimated standard e r r o r s : s(p) = 0.007 s(W) = 0.013 s{8) = 0.007 s(S*) * 0.03 Notes: A l l density and water content figures are the average of 4 samples. 1 Calculated using 0i=O.O3, and 0 as noted. 2 C a p i l l a r y pressures calculated using mean of 4 tensiometers (exp. 1a), or 2 tensicmeters (exp.,1b,2) 3 Flux rates for exp. 1 obtained from funnel lysimeters; approximately +50%. which must be somewhat less than the lowest values of 0 obtained. A one-way analysis of variance was performed on the calorimetry data to obtain an estimate of the variance within the four-sample measurement sets. Estimates of the standard errors of the values i n table 3,1, which are means of the four-sample sets, are shown i n the table. These standard errors are measures of precision, and do not indicate any bias which may be. present i n the measurements. The l i q u i d water contents measured are somewhat hiqher than most of those reported in the l i t e r a t u r e for coarse-qrained mature snow. Gerdel (1945), U.S. Army Corps of Engineers (1956, plate 8.7), Ambach and Howorka (1965), and Leaf (1966) report l i q u i d water contents of at most 12% by weiqht in ripe sprinq snow, althouqh Radok et a l (1961), Hathews and Mackay (1963), and de Quervain (1973) report a few values as hiqh as 20%. Rankiewicz (1976) had doubts about the accuracy of the measurements made with t h i s particular calorimeter. He used the r e l a t i o n dp = d 9 p w (3.13) as an approach to calculate changes in 9, instead of absolute values of 9. A scatter diaqram of p vs. 9 (fiq 3,5) suqqests that the measured l i q u i d water contents are too hiqh by a factor of 1.5 to 2 times, since eq, 3,13 implies that the slope of a l i n e throuqh a set of measurements at a point i n time should be 1.0. Such an error could conceivably arise from p a r t i a l meltinq of the sample before i t i s placed in the calorimeter, cr frcm addition of heat to the cold chamber of the calorimeter frcm the 70 ObO 0.51 0.57 Dehs'i+y, P . 0.5b 0-55 0.54-0.53 0.52 0-5I 0.50 —>"^> x ) © June 2 1 , upper row A June 2 1 , lower row X July I t - I S s(e) 0.05 00. 007 00t 0.01 0\0 OM 0-I2 OI3 0.|<r 0.I5 0.I6 Volumetric Water Content, 0 F i g . 3.5 C a l o r i m e t e r measurements : l i q u i d water content and d e n s i t y . l 1 r 0.W 0.20 .2 0.10 +• ? 0.08 oo 0.06 0.0 0.02 -1—i—i i i X X A A * ° A - i 1 1 — l — i i i i S(S«) * 0.03 5(M - OXtM Cy(V) = 0.12 for J W ; 0.05 for July X A T © A O June 21 i upper row A Jur,e 21 , lower row X July It-15 _i I i I i I - 6 - 8 -10 - 2 0 Capillory Pressure , h t (cm) 0-02 0-OV 0-06 0.08 0-10 Flux, V («»/J.r) 0-10 0H0 F i g . 3.6 C a p i l l a r y p r e s s u r e - f l u x s a t u r a t i o n r e l a t i o n s . 71 hands or from the surrounding i n s u l a t i o n . It could also a r i s e from an erroneous calorimeter constant. It i s not clear why such errors should r e s u l t in a proportional rather than an additive bias. Hence the existence of a bias i n the calorimeter measurements i s a l i k e l y p o s s i b i l i t y , but i s by no means certain. Since melting calorimetry involves determining the l i q u i d water content as a small difference between two large guantities, one of which i s subject to considerable error, the use of freezing calorimetry or centrifuging might be considered instead for more accurate measurements. Freezing calorimetry {Badok et a l , 1961) i s a more involved procedure and might be too inconvenient f o r routine f i e l d use. Centrifuging (La Chapelle, 1956) i s very simple, but i t i s prone to possible bias, and i t determines the guantity 8-0^, rather than 9 i t s e l f . 3.4 EXPERIMENTAL RESULTS: APPLICATION TO THE THEORY The parameters in the porous medium model which must te experimentally determined are the exponents £ and T\ i n egs. 3.6, and the term E.#€_1KS'^ i n eq. 3.7. The determination of CO as a function of K i s eguivalent to the determination of the l a t t e r term. Direct experimental measurements of Ks and £. in eg. 3.6a do not exist i n the l i t e r a t u r e , but Colbeck and Davidson (1973) produced i n d i r e c t experimental evidence which indicates a value of 3.0 to 3.5 f o r £. Their approach involved p l o t t i n g measured meltwater flux, V, against the kinematic wave speed, U v; t h e i r measurements were obtained using columns of homogeneous. 72 a r t i f i c i a l l y repacked snow, , From eq, 3.7, the slope of such a plot i s (£-1)/£. (A plot of Sharp's (1952) data for natural g l a c i e r snow, reported in Colbeck (1972), indicates a value of less than 2, although since these data are obtained from small funnel lysimeters, i t may not be r e l i a b l e . ) lysimeter data for three days with f a i r l y well-developed diurnal meltwater curves were used to obtain si m i l a r graphs. The surface melt curve was synthesized using methods discussed in chapter 6. A major uncertainty i n using t h i s method i s that the sheet-metal lysimeter can over-read due to deflection of the flow by ice layers. Therefore the lysimeter curves were adjusted sc that the t o t a l d a i l y volume of flow matched the observed surface melt as measured d i r e c t l y usinq ablation stakes,,The ca l c u l a t i o n of U v i s sensitive to t h i s s c a l i n q , so the r e l i a b i l i t y of t h i s method i s questionable. (For t h i s reason, data from the small funnel lysimeters i s not r e l i a b l e enough to apply in t h i s manner.) The meltwater curves are shown in f i q . 3.7, and the r e s u l t i n g plot of Dy vs. ,V i s shown i n fig.,3.8. The slope of about 0.9 implies that £2:10; t h i s i s much higher than Colbeck*s value. Such a high value has disturbing t h e o r e t i c a l implications, especially i f eg. 3,3 i s to be applied, since i t implies a correspondingly high value of l\r and K i s exceedingly sensitive to very small changes i n h c and 6 i f ?j and t are high. Direct plots of S* vs. V and h c are shown i n f i g . 3.6. Although the S* values are subject to considerable error, and hysteresis probably affects the plots as well, the trend of the points indicates that £ and A. are both about 3. However, t h i s 73 F i g . 3.7 Lysimeter flow and snowmelt for 3 days. Surface melt i s calculated from the energy balance (chapter 6). F i g . 3.8 Plot of U vs. V. 74 value of t implies that K5, estimated by extrapolating the V{S*) curve to the intercept S*=1, i s unreasonably low, less than 100 cm/sec. It i s possible that the measured S* values are too high, or that t i s greater than 3; however, a value as high as 10 for £ does not seem reasonable from t h i s plot. I t i s very l i k e l y that the sheet-metal lysimeter over-reads at very low flows on the drainage limb due to the release cf stored water from the saturated c a p i l l a r y fringe above the lysimeter surface. ,<9ankiewicz*s (1976, p. , 82-88) analysis of lysimeter response indicates that the delay of response at very low flows may be several hours. Also, water temporarily stored above ice layers or other i r r e g u l a r i t i e s may be released slowly, leading to a more delayed recession limb at low flows, and the large size of the lysimeter i t s e l f may serve to lengthen the recession over what would be observed at a point i n homogeneous snow. Colbeck and Davidson (1973) reported that minimum flows in t h e i r experiments i n repacked snow were consistently higher than those predicted by the model. If the recession limb i n f i g . 3.7 i s extended at low flows, a greater slope i n f i g . 3.8 w i l l r e s u l t ; thus, i t i s possible that the estimate of £. using f i g . 3.8 i s high. Also, since t h i s method i s based on the rate of meltwater passage through a considerable depth of heterogeneous snow, i t i s possible that values of £ and Ks obtained i n t h i s way might be very d i f f e r e n t from those obtained by d i r e c t conductivity and l i g u i d water content measurements i n a single snow layer, since they r e f l e c t the properties of two d i f f e r e n t flow processes. The c a p i l l a r y pressure-conductivity r e l a t i o n for the 75 drainage limb was plotted using tensiometer and lysimeter data (assuming that V=K); some of the plots are shown i n f i g . 3.9. The plots are very si m i l a r i n general appearance to those cf Wankiewicz (1976); that i s , they show the drainage limb as a scanning curve which appears to approach an assymptotic boundary drying curve. The range of c a p i l l a r y pressures i s also very sim i l a r to that measured by Wankiewicz. The apparent slope, 1\, of the boundary drying curve ranges from about 7 to 18 on these plots, and a l l the plots could be reasonably f i t by the value of 1\=14 used by Sankiewicz. The fluxes used i n f i g . 3,9b were obtained from the single sheet-metal lysimeter curve by using eg, 3,7 (with £=3, and 60 for the intercept term; see below) to reconstruct two flux curves at the two tensiometer l e v e l s . The upper l e v e l was 17 cm above the lysimeter, while the lower l e v e l was 40 cm below; therefore, the curve for the upper l e v e l i s probably more accurate. Funnel lysimeter data taken at the l e v e l of the tensiometers was used in f i g . 3.9a; the data was corrected for apparent over-read and under-read, although a bias in t h i s respect would a f f e c t only the intercept of the curve, not the slope. These re s u l t s confirm Wankiewicz's findings that the c o n d u c t i v i t y - c a p i l l a r y pressure r e l a t i o n i s easy to measure compared with the r e l a t i o n s involving l i g u i d water content, and they also indicate that the former r e l a t i o n does not vary a great deal between di f f e r e n t snow layers, or between the writer's study s i t e and Hankiewicz's Mt. Seymour study s i t e . Thus, a model based on eg. 3.3 should be feasible with respect to data reguirements, although the hysteresis i n the c a p i l l a r y pressure r e l a t i o n s and the large value of the exponent might 76 2 0 -15 T — i — i — i — i — r T 1 1—i—i—i—i—r J u h e 3 0 - J u l y 5 , upper row • J u n e 3 0 X J u l y 1.2,3 © J u l y 5" Juhe 30 - July 5, lower row o ©e J H 1 1—I I I I H h +4-® June 20-21 , upper row June 20-21 , lower row 5h j l i i i i i 0.00* J I I I 1 I—I I I 0.007 0.01 0-02 0.0* 0-07 0-10 Flux, V ( c * M J I L 0-20 0.V0 F i g . 3.9 Plot of the flux - c a p i l l a r y pressure r e l a t i o n . 77 cause some problems. The calculation of the f r a c t i o n a l derivative, CO, i s th e o r e t i c a l l y equivalent to the calcu l a t i o n of the parameters in eqs. 3.6a and 3.7, and the use of co provides a s l i q h t l y s i m p l i f i e d approach to modelling meltwater movement. The f r a c t i o n a l derivative can be calculated at a point by'measuring changes in l i g u i d water content and meltwater f l u x over time. By combininq eqs. 3.4, 3.8, and 3.13, a f i n i t e difference expression for CJ can be obtained (Wankiewicz, 1976, p. 157): Co = liUVi / V 2 ) p (3. 14) where « i s the average value of to over the range V| to Vj, ; this range may be quite large in order that a difference i n p can be resolved. The assumption i s made that V=K, although t h i s i s not s t r i c t l y true on the r i s i n g limb. Calculations of w using r e s u l t s from the calorimetry measurements are shown i n table 3.2. These calculations are very approximate; the standard error of the term P i - p i i s about 0.01 gm/cm3, which i s comparable to the magnitude of t h i s term in the calculations. This results i n a c o e f f i c i e n t of variation for co of about 100%. This large error i n the density term might be improved upon by taking density measurements independently of calorimeter measurements, using a much larger sampling tube. The cal c u l a t i o n s of 6J are plotted i n f i g . 3.10, along with measurements reported i n Wankiewicz (1976, p. 167); the values are quite variable, but considerinq the errors involved, they appear reasonable. fin alternative approach i s to calculate co from eq. 3.9, as the r a t i o between the kinematic wave speed Uv and the flux V. This miqht be expected to qive a di f f e r e n t r e s u l t , since the 78 c a l c u l a t i o n i s based on the movement of water through a layered snowpack instead of on the water retention properties of the snow at a single point. A l i n e based on f i g . 3.8 i s shown on f i g . 3.10; i t may be in error for low vaues of V, as discussed above, but i t indicates higher values of CO than those calculated by the f i r s t method for the same snow pit. The saturated hydraulic conductivity, , can t h e o r e t i c a l l y be calculated from the available data in several ways. One method i s to use the K<hc) or the K(S*) curves; however, t h i s i s impractical because the former r e l a t i o n i s very sen s i t i v e to the value of , and the l a t t e r r e l a t i o n depends on accurate measurements of S*. A somewhat i n d i r e c t method i s to use a graph of co vs. K. The slope of t h i s r e l a t i o n on a logarithmic scale i s ~1/£, and the intercept at K=1 cm/hr i s Lpt~ lK s (eg. 3.8). However, a c a l c u l a t i o n of K s by t h i s means i s very sensitive to the assumed value of £. I f i t i s assumed that £=3, the average position of the intercept i n f i g . 3,10 i s about 60, which corresponds to a value of Ks-640 cm/hr (0.18 cm/sec), i f 0e=O.43. However, considering the scatter of the measurements on f i g . 3.10, the intercept could range from 30 to 120, which would r e s u l t i n a range of two orders of magnitude for K s, since K$ i s proportional to the t h i r d power of the intercept. The intercept term can also be estimated from the wave front speed, as observed from the tensiometer records (see section 3.6), using eg. 3.10. The wave front speeds and accompanying c a l c u l a t i o n s are shown i n table 3,3, and give an average value for the intercept of about 100, which implies a somewhat higher value for Ks than was obtained from measurements of 60. I t i s apparent " i — i — i — i — i — i r A June 20-21 O July Hr-15 X Wahkiewicz, 1176} point taeasurewetl+S ^00 h 200 CA) 100 80 60 4-0 1 1 1 1—I—I I I i r •from Uv: V dliagrenn, f i 9 . 3.8 Colbeck an** Davidson, 1173 i i i i i i i i Wavtkiewicz; kinematic waves j I > I I i—i i I J L 0 . 0 2 0.0<f 0-06 0 0 8 O.IO 0.20 0.<r0 0.60 0.80 [.00 2-oo ^.00 F i g . 3.10 Plot of the f r a c t i o n a l derivative, CO, and conductivity. U5 80 TABLE 3. 2 CALCULATION OF THE FRACTIONAL DERIVATIVE. to i s calculated using GO = ^p^j^^ Pu to and K indicate mean values over the measurement i n t e r v a l . V and K are i n cm/hr; p i s in gm/cm3. DATE J une 21-2 2 (upper) June 21-22 (lower) July 14-15 July 14-15 July 14-15 July 14-15 Flow period Nature of flow 1715 -0915 drying 1745 -0940 drying 1100 -1310 1310 -1530 1530 -1850 setting wetting drying 1850 -0955 drying Flow at t| : V, (cm/hr) p, (qm/cm3) <e.) 0.23 0.537 (0.099) 0.29 0.563 (0.083) 0.12 0.566 (0.085) 0.28 0. 587 (0. 111) 0.34 0. 591 (0. 147) 0. 14 0.579 (0. 125) Flew at t 2 : (e2) K = JvTJn 0.02 0. 528 (0.061) 271 0.07 0.04 0.550 (0.081) 152 0. 11 0.28 0.587 (0.111) 40 0. 18 0. 34 0. 591 (0. 147) 49 0. 31 0. 14 0.579 (0. 125) 74 0. 22 0. 08 0.573 (0. 110) 93 0. 11 TABLE 3.J.3 OBSERVED WAVE FRONT SPEEDS. DATE OBSERVED UF MIN. FLOW MAX. FLOW INTERCEPT ABLATION (cm/hr) V, (cm/hr) V a (cm/hr) TERM (mm) June 18 29 0.04 0.73 120 17 June 20 24 0.04 0.73 98 13 June 21 31 0.04 0. 82 113 22 July 1 23 0.02 0.55 124 14 July 2 18 0.02 0. 55 100 11 July 5 22 0.03 0. 82 79 31 geometric mean = 10 4 Up i s obtained from tensiometer traces, and has an error cf about ±10 to 20%. The speeds for July 1-5 are more uncertain because of the response problem noted on p. 87. Maximum and minimum flews are about ±20% f o r June 18-21 (obtained from funnel lysimeters) and about ±10% for July 1-5 (from large lysimeter).. The intercept term, L0~l K$'/£ / i s calculated frcm Up using eg. 3.10. 0 e i s about 0.44 for June 18-20, and 0.42 f o r July 1-5. Notes: 1, 2. 3. 4. 81 that Ks cannot be uniquely determined for a natural snowpack using the methods described above. However, since the important parameter i n the porous medium model i s the intercept £ .0 e _ 1K s , /' £ , knowledge of Ks i t s e l f i s not essential. The term Kj as used in t h i s intercept bears l i t t l e , i f any, r e l a t i o n s h i p to the actual saturated hydraulic conductivity. Colbeck*s use of Shimizu's direct measurements of Ks in his model of unsaturated flow (eg. i n Dunne et al,1976) i s therefore questionable. 3.5 QUALITATIVE OBSERVATIONS OF ME LT W AT E B MOVEMENT The application of dye to the surface of the snow i s a useful technigue for obtaining q u a l i t a t i v e information on the nature of the flow patterns within the snowpack (see Wankiewicz, 1976). Dye tests were performed on several occasions i n order to observe the nature of the flow i n l e v e l snowpacks i n the v i c i n i t y of the lysimeter and tensiometer i n s t a l l a t i o n s , and to observe the effects of steep slopes, meltwater channels, and ice layers on meltwater flow. The dye was normally applied to an area of about 0.4 m2, some distance back from the edqe of a snow p i t . After an hour or two, the face of the p i t was cut back to expose the dye trace, which was then photoqraphed; t h i s was repeated several times as the melt wave progressed through the snow. A strong solution of powdered red dye was used, and was applied t h i n l y over the snow surface using a s p r i n k l e r made from a perforated can. The amount normally applied was about 0.5 l i t r e over about 0.4 m2; t h i s i s equivalent to about 1 to 1.5 mm of l i q u i d over the dyed area. This amount is small compared with natural melt over a period of several hours, but the darkening 82 of the snow probably causes melt rates to be at least doubled for an hour or so following application. A series of photos on June 28 ( f i g . 3,11a,b) shows the average position of the front of dyed water moving at a rate of about 40 cm/hr, which i s almost twice as fast as the speed of the natural wave fronts usually observed (see section 3.6). Dye tests on an approximately l e v e l snowpack showed that meltwater progressed in a fingering flow pattern, with cert a i n columns of snow being preferred paths of flow ( f i g . 3.11a). These flow paths did not d i f f e r in appearance from the surrounding snow i n any obvious way, and i t i s possible that water was diverted to these paths by the structure of icy layers above, and that the snow between these layers was f a i r l y homogeneous. Behind the front, the dyed water appeared to permeate the snow f a i r l y uniformly. The e f f e c t of i c y layers i n channelling the flow i s obvious i n f i g . 3.11a; most of these layers are not s o l i d i c e layers, and were not noticeable before the dye was applied. V e r t i c a l ice glands, as described by Gerdel (1954), were not present i n the study watershed, although they were commonly observed at higher elevation i n the region. Fig. 3.11c shows a dye test conducted on a steep slope, and shows the control which well-developed i c e layers exert on the flow pattern. The deflection of the flow from the v e r t i c a l i s s l i g h t but s t i l l apparent in other layers of the snowpack. Fi g . 3.11d shows a test conducted at a l a t e r date at the same s i t e , with s i m i l a r r e s u l t s . These tests suggest that the model of Colbeck (1975) would not accurately describe flow on slopes dominated by a few nearly impermeable ice layers, but i t might F i g . 3.11 Dye t e s t s . D a t e , a n d e l a p s e d t i m e a f t e r s t a r t o f t e s t a r e i n d i c a t e d . 84 c. July 2, 2.5 h r s . d. July 17, 3.3 h r s . F i g . 3.11 (cont.) 85 86 be useful i n approximating an average effect of slopes on the length of the flow path of meltwater. Fig, 3.11e shows a test which was conducted i n order to examine flow patterns in the large hollows which form ever stream channels and other topographic depressions. A prominent feature of the snowpack at t h i s test location i s the thick ice layers, which are generally better developed i n such depressions than elsewhere; t h i s i s probably due to deflection of meltwater by ice layers and other low-permeability stratigraphic l a y e r s , downslope towards the depression early i n the season while the snow was not yet ripe. This hypothesis i s supported by observations made in a p i t dug in flay 1977 (see section 2 . 6 ) , while the snowpack was in a p a r t i a l l y ripe condition. Fig. 3.11e shous the strong deflection of meltwater by ice layers towards the center of the depression. The configuration of the i c e layers suggests that the prominent hollow was not formed by subsidence of the entire snowpack. I t i s more l i k e l y that i t was formed by accumulations of d i r t which were ca r r i e d by the meltwater from the surface or lower layers and deposited i n the depression on icy layers, which acted as f i l t e r s . This d i r t accumulation can then cause increased absorption of solar radiation. Figs. 3.11f and g show a si m i l a r test at t h i s s i t e at a l a t e r date; the i c e layers which were prominent i n f i g . 3.11e have melted out, and those which remain do not exert as strong a deflection on flow. In summary, the dye tests show that i n f a i r l y l e v e l areas, the flow of meltwater i s distorted somewhat by i r r e g u l a r i t i e s in the snowpack, esp e c i a l l y by ice layers, but the di r e c t i o n cf 87 flow i s e s s e n t i a l l y v e r t i c a l and a one-dimensional flow model i s probably applicable over a scale of approximately one sguare meter or more. On steep slopes and along depressions, however, the flow of meltwater i s greatly influenced by ice layers., 3.6 EXPERIMENTAL RESULTS: APPLICATION TO HATERSHED RESPONSE Observations of flux rate and c a p i l l a r y pressure in the snowpack over the snowmelt season confirm the general nature of meltwater flow as predicted by the porous medium model. Combined with observations of surface melt and stream discharge, they provide seme information on the response of the watershed to snowmelt. The re s u l t s of tensiometer and funnel lysimeter readings for several days are shown in fig.,3.12. These curves c l e a r l y show the delay and d i s t o r t i o n of the diurnal melt wave with depth, as would be predicted by Colbeck's t h e o r e t i c a l analysis. They are comparable i n t h e i r general behavior to Hankiewicz*s (1976) curves of c a p i l l a r y pressure at various depths in a deeper and somewhat more heterogeneous snowpack on Mt. Seymour. The curves also indicate the v a r i a b i l i t y of the timing and magnitude of the c a p i l l a r y pressures amongst adjacent tensiometers, es p e c i a l l y i n the lower snow layers. The lack of response of tensiometer number 5 in experiment 1 could be due to poor contact between the cup and the snow, or to the cup being placed in a pocket of snow through which l i t t l e flow passes because of some deflecting i c e structure. The lower l e v e l of tensiometers i n experiment 2 show slowly responding c a p i l l a r y pressure curves, which lack the sharp wave front of the other F i g . 3.12 Tensiometer and funnel lysimeter record for several days. Instrument depth i s indicated. oo oo T 1 1 1 1 1 1 1 1 1 1 1 i r June 30 July I J u , y 5 F i g . 3.12 (cont.) 90 JUNE 28 JUNE 29 JUNE 30 JULY 1 JULY 2 21 JULY 3 JULY 4 JULY 5 JULY 6 JULY 7 F i g . 3.13 Lysimeter record for June 28 - July 18. Solar and net radiation are also shown. 91 SI JULY 13 JULY 14 JULY 15 JULY 16 JULY 17 F i g . 3.13 (cont. ) 92 curves. Excavation of these tensiometers showed that the cups had been placed on, or very near, the contact between a thick snow layer of t y p i c a l grain size and density, and an underlying layer of old depth hoar of a coarser, looser texture and hence a probably very d i f f e r e n t set of c a p i l l a r y pressure-conductivity-saturation relations. As wankiewicz (1976, p.58) showed, perturbations of the c a p i l l a r y pressure f i e l d are l i k e l y tc e x i s t near such a contact. The record of the large sheet-metal lysimeter for the period June 28 to July 18 i s shown in f i g , 3.13, along with the record of solar and net radiation for the same period. The depth of the lysimeter ranged from 88 cm at the beginning of the i n s t a l l a t i o n to 8 cm on the date of removal. On the l a s t two days, the melt t o t a l may have been affected s l i g h t l y by solar radiation reaching the metal surface. The record shows q u a l i t a t i v e l y several features of the propagation of diurnal meltwater waves which are predicted by Colbeck's model: the delay of the meltwater wave with depth, the damping of a complex melt input at the surface into a simple waveform with depth, and the increasing d i s t o r t i o n with depth of the melt wave into a shock front and a long recession limb. Since r a d i a t i o n accounts for most of the snowmelt (as w i l l be shown i n chapter 6), the radiation curves provide a good indication of the shape of the meltwater wave at the surface. However, the very i r r e g u l a r pattern of the surface melt wave on most days makes precise calculations of the speed of meltwater waves with depth impossible (except on a few "good" days, as shown above). Fig. 3.14 i s a set of diagrams showing the passage of the 93 meltwater wave throughout the entire system, from the surface to the stream gauge, f o r several days for which good records were obtained. The diagrams for the f i r s t three days, which show res u l t s from the f i r s t snow p i t i n s t a l l a t i o n , c l e a r l y show the compression of the r i s i n g limb with depth. They also show the attenuation of the r i s i n g limb of the stream hydrograph, which i s due to the variation of snowpack depth and flow c h a r a c t e r i s t i c s over the watershed. The f i r s t e f f e c t i s not as apparent i n the l a s t three diagrams, due to the above-mentioned problems with the lower row of tensiometers in the second installation..Rough estimates of the wave front speeds can be made from these diagrams; these range from about 17 to 30 cm/hr. The speeds for the f i r s t set of diagrams are somewhat greater, possibly because of differences i n snowpack stratigraphy between the two p i t s . This observation i s surpr i s i n g , because Gerdel (1954) and Colbeck (1977) suggest that the conductivity should increase with time as the snowpack becomes more mature and ice layers break down. Table 3.3 shows some estimates of wave front speeds made frcm the tensiometer records. These speeds are i n the range of 18 to 31 cm/hr, and are probably subject to an imprecision of about ±5 cm/hr. I f eg. 3.10 i s applied using, as a f i r s t approximation, values of E=3, 0e=O.43, Ks=640 cm/hr, V|=0.05 cm/hr, and V^=0.30 cm/hr, a speed of 0p=17 cm/hr i s obtained, which i s somewhat less than the observed speeds. As indicated in section 3.4, these r e s u l t s suggest that Ks i s somewhat higher than the above value, i f eg. 3.10 accurately describes the wave front speeds. 94 0000 1200 June 18 0000 1200 June 20 1200 June 21 1200 June 30 F i g . 3.14 Progress of the meltwater wave through the snowpack. The top l e v e l indicates temperature and solar radiation. The bottom l e v e l i s the stream hydrograph, and intermediate l e v e l s are tensiometers (T) and the lysimeter (L). The f i r s t point i n each p a i r indicates the beginning of the diurnal r i s e , and the second indicates the peak. A rectangle indicates an i n d e f i n i t e range over time, such as a range of response of several tensiometers. 95 Additional estimates were made from f i g . 3.7, using the computed suface - melt wave and the lysimeter record; these gave very approximate values of 0 15 cm/hr for both June 30 and July 5. A major d i f f i c u l t y i n using an energy balance based surface melt wave i s that a negative energy balance often occurs during the night, which must be made up i n the morning before meltwater i s released into the snowpack from the surface layers. This negative energy balance re s u l t s f i r s t in the freezing of the i r r e d u c i b l e water content of the surface snow layer, followed by a lowering of the snow temperature. It i s very d i f f i c u l t to observe or calculate the time ! i t takes for meltwater to s t a r t draining from the surface layers i n the morning. For the above ca l c u l a t i o n , the energy d e f i c i t area indicated on f i g ; 3.7 has been used as a rough guide. The wave front speed i s the p r i n c i p a l factor determining the a r r i v a l time of the meltwater wave at the base of the snowpack, given an average diurnal pattern of the surface melt. At the watershed scale, t h i s a r r i v a l time i s one of the p r i n c i p a l factors determining the time of the stream hydrograph peak, the other factors being the response time of water flowing under the snow t c the stream channel, and the response time of the channel network i t s e l f . In the study watershed, the l a s t factor i s believed to be i n s i g n i f i c a n t , although the second factor may be of some importance. As the snow depth becomes l e s s , the peak of the stream hydrograph arrives e a r l i e r ; by pl o t t i n g the time of the peak over the season, an estimate of the average wave front speed over the watershed can be made. Such a plot i s shown i n f i g . 3.15. A rough l i n e was drawn 96 through the points by eye, and by taking the difference in snow depth between two days near the beginning and end of the season, an estimate of 22 cm/hr was obtained, which i s i n good agreement with d i r e c t l y observed wave front speeds. This figure actually represents the delay i n the peak stream discharge per centimeter depth of snow. Part of thi s delay may be due to flow beneath the snow, although most of i t should be due to the movement of the melt wave through the snowpack; f i g . 3.14 indicates that the delay from the base of the snowpack to the stream i s minor. Fig. 3.15 also shows the time of the center of the hydrograph r i s e (taken as the discharge midway between the low point and the peak); t h i s i s analogous to the average a r r i v a l time of the wave front at the base of the snowpack. This plot shows a less orderly advance of time with decreasing snow depth, and indicates the complicating effect of the changing shape of the hydrograph over the season, as discussed i n chap. 4. The scatter in the points i s due to the variations i n timing of the dai l y energy input, and to the fa c t that the wave front speed also depends on the magnitude of the peak meltwater f l u x (eg. 3.10). 3.7 CONCLUSIONS AND RECOMMENDATIONS The re s u l t s shown in f i g . 3.8 and 3.10 indicate that there i s a certain degree of consistency i n the behavior of meltwater movement i n mature spring snow i n a number of d i f f e r e n t locations. However, the uncertainty in cal c u l a t i o n s of £., 60, and K$ indicate both that there i s considerable variation i n snow properties within a single snowpack, and that i t i s d i f f i c u l t or DeptK*222 c m 0 Time of Hyd(ro3fapK peak X Time of center of nyaVojnyiri Hit (at print owdvrty between hiinimuH) and maximum discKarje) X X 10 May 20 20 May 30 30 Jwn*1 <r0 50 June 21 60 July*} 70 J*/y 80 July 21 10 F i g . 3.15 Times of peak stream discharge. 38 impossible to c o l l e c t data which f i t the d e t a i l s of the porous medium model, using simple f i e l d methods. The major assumption made i n such a model i s that the snowpack can be defined i n terms of an equivalent porous medium {freeze, 1975), in which flow i s governed by the above equations using a single set of parameters, and which behaves i n a manner simi l a r to the r e a l , heterogeneous snowpack. Possibly the model i s too s i m p l i s t i c to describe accurately the flow i n a natural snowpack, and the v a r i a b i l i t y of snowpack c h a r a c t e r i s t i c s with depth and over an area may be too great to determine single values of the model parameters which can r e l i a b l y describe the flow over a watershed area. Since r e a l snowpacks, featuring i c e layers and glands and snow layers of di f f e r e n t texture, probably depart considerably from the ide a l behavior of the model, a better approach might be to simplify the model and introduce a certain l e v e l of empiricism. Such a s i m p l i f i c a t i o n might be to use a simple function, or a constant value, for the parameter t0„ Measurement of the wave front speed using tensiometers or lysimeters appears to be the most promising approach to determining t h i s parameter. Since the main application of such a model i s t o determine the delay of the meltwater hydrograph i n very deep snowpacks, a simpler, more empirical version should be adeguate. More detailed study i s useful for determining the v a r i a b i l i t y of the parameters describing the snowpack over d i f f e r e n t environments, and for understanding the assumptions which would be made in using a s i m p l i f i e d model. In terms of data requirements, a major need i s that of 99 r e l i a b l e l i g u i d water content measurements i n a variety of snow types. The simple melting-type calorimeter used in t h i s study does not appear to be adeguate for t h i s purpose. The e l e c t r i c a l capacitance method, used by Gerdel (1954), Ambach and Howorka (1965) and others, may be promising i f i t can be calibrated using a more accurate method such as freezing calorimetry. More sophisticated non-destructive methods, such as the isotope p r o f i l i n g snow gauge (Smith, 1974; Young, 1976) or microwave methods (Linlor et a l , 1974) might be useful in detailed studies of the movement of l i g u i d water i n snow. The simple instrumentation used i n this study appears to be adeguate for measuring c a p i l l a r y pressure and meltwater flux. The zero-tension lysimeter may not be fast enough i n i t s response at low flows to be used for detailed study, and the use of a number of tension lysimeters at each of several l e v e l s may be necessary to accurately measure the behavior of a meltwater wave. 100 CHAPTER 4 RUNOFF GENERATION The snowmelt hydrograph as recorded at the outlet of the watershed lags somewhat behind that observed near the bottom of the snowpack, and i s considerably attenuated ( f i g . 3.14). This response i s due to the processes of water movement through the ground or the saturated snow at the base of the snowpack, and through the network of permanent and temporary channels and ponds. No dir e c t measurements were made of processes operating between the snowpack i t s e l f and the stream gauge; indeed, such measurements would be very d i f f i c u l t , as they would reguire a great deal of excavation (see Dunne and Black, 1971) and destructive sampling of the s o i l . However, some inferences about these processes can be made from q u a l i t a t i v e observations of the snow-ground interface durinq breakup of the snowpack, and by observations of the recession c h a r a c t e r i s t i c s of the streamflow hydrographs. 4.1 PREVIOUS SOBK Studies of the response of streams to r a i n f a l l events are numerous in the hydrology and engineerinq l i t e r a t u r e , but physically based studies involving the response to snowmelt are scarce. The studies of the U.S. Army Corps of Engineers (1956), and Garstka et a l (1958) relate streamflow hydrographs to snowmelt in terms of c l i m a t o l o g i c a l inputs, but these studies were empirical i n t h e i r approach, and did not examine the intervening flow processes i n any d e t a i l . , Dunne and Black (1971) conducted a c a r e f u l l y designed experimental study of runoff processes on h i l l s l o p e plots i n 101 Vermont.,They emphasized the role of frozen ground beneath the snowpack i n producing overland flow from snowmelt, and found that the diurnal variation i n the snowmelt hydrograph was due almost e n t i r e l y to water supply via overland flow. Dunne et a l (1976) applied s i m i l a r methods to a study cf runoff processes at a subarctic s i t e in Labrador. They observed a s i m i l a r response to snowmelt, with almost a l l the runoff being produced as overland flow. They applied Colbeck's model of flow through unsaturated and saturated snow with considerable success. However, t h e i r use of a single parameter to describe flow along the base of the snowpack i s suspect (see discussion below), Woo and Slaymaker (1975) were able to re l a t e g u a l i t a t i v e l y changes in the timing and shape of the hydrograph i n a small subalpine watershed i n the Coast Mountains of B r i t i s h Columbia to the processes of water retention i n the snow and to the area of snow cover. Their study watershed i s at a lower elevation and in a more maritime environment than the writer's watershed; however, t h e i r r e s u l t s are relevant to the present study, since they are concerned with runoff frcm a deep mountain snowpack. 4.2 DISCHARGE MEASUREMENTS AND HYDROGRAPH SEPARATION A Stevens type F water l e v e l recorder was used to measure the water l e v e l behind a 90° V-nctch weir at the outlet of the watershed. The stage-discharge r e l a t i o n was established by s a l t -d i l u t i o n gauging (Church and Kellerhals, 1970), and by t o t a l retention gauging at very low flows. The rating curve i s shown in appendix 4. The precision of a single s a l t d i l u t i o n discharge measurement i s estimated to be about ±2%, considering the 102 sources of error discussed i n Church and Kellerhals (1970, p. 50) . The stage as extracted from the recorder chart i s precise to about ±1%. I f the rating curve through the points measured by s a l t d i l u t i o n i s considered to be a regression l i n e with stage as the independent variable, the 95% tolerance l i m i t s of the discharge average ±8% over the observed range. The portion of the curve at very low discharge i s somewhat less precise, but since the volume of water i s very small, the greater error i s not important i n terms of the o v e r a l l water balance. The rating curve i s believed to be without appreciable bias, since care was taken to correct for any sources of bias i n the stage and discharge measurements. Daily t o t a l discharge values are considerably more precise than the above figure of ±8%, since a d a i l y t o t a l i s calculated from the mean of a large number of stage observations. Continuous discharge measurements were obtained for the period from May 21 to Oct, 8, with the exception of Sept.,4 to 6; the discharge record i s shown in appendix 3. The stage record was d i g i t i z e d e l e c t r o n i c a l l y , and discharge was computed from the rating curve at approximately 50 to 100 points each day. In order to separate the r e s u l t i n g hydrograph into runoff generated on i n d i v i d u a l days, a separation method based on exponential recessions was used. This procedure i s i l l u s t r a t e d i n f i g . 4.1. A plot of the hydrograph was produced on a logarithmic scale, and an a r b i t r a r y base l e v e l was chosen which coincided approximately with the lowest discharge of the period of i n t e r e s t . The lower part of the recession limb of the hydrograph was extended i n a straight l i n e to t h i s base l e v e l . Since the 103 104 recession rate was never constant on a logarithmic scale, tut rather declined with decreasing flow, the slope of the lower part was used, h r e l a t i v e l y high rase l e v e l was used to avoid extrapolating the recession a long distance. The diagram was then transferred to a l i n e a r scale, and the daily runoff was calculated by measuring the separated hydrograph with a planimeter. The volume of flow below the base l e v e l was calculated over the time base determined by the intersections of the extended recessions with the base l e v e l ( f i g . 4.1); a r i s i n g trend i n the low flows resulted i n a time base longer than 24 hours, and conversely, a f a l l i n g trend resulted in a shorter time base. This method i s mathematically eguivalent to using no base l e v e l and extrapolating the recession limb to i n f i n i t y on the logarithmic plot ( i f the recessions are p a r a l l e l ; eg. Garstka et a l , 1958, p. 72) . I t i s assumed that a given discharge on the recession limb represents a unigue volume of water storage i n the watershed system, although t h i s i s not s t r i c t l y true, since the system does not appear to act as a set of l i n e a r reservoirs (see below). It i s also assumed that there i s no baseflow component which i s independent of the daily snowmelt inputs; t h i s assumption i s reasonable, since i f there was, i t would be i n the order of 1.0 1/sec, and t h i s would result i n variations of only about ±20 m3 in the calculated da i l y runoff t o t a l s , which were t y p i c a l l y about 1000 m3. The da i l y runoff t o t a l s calculated by t h i s method are summarized in appendix 2, along with the mean d a i l y discharges cn a 24-hour basis. 105 4.3 OBSERVATIONS OF RUNOFF PROCESSES The surface of the watershed can be idealized as a series of slopes extending from l o c a l drainage divides to permanent or temporary channels. In a great deal of the study watershed, these slopes are f a i r l y short due to the hummocky nature of the t e r r a i n . I f a slope i s impermeable to the i n f i l t r a t i o n of water due to saturated s o i l , frozen s o i l , or a basal ice layer, then meltwater frcm the snowpack w i l l flow over the surface of the slope, i n a manner s i m i l a r to overland flow except that the water must move through the pores of the overlying snow. Colbeck (1974) treated t h i s as saturated Darcian flow over a smooth boundary, with the shape and timing of the flow hydrograph at the base of the slope depending on the length and angle of the slope and the saturated hydraulic conductivity of the snow. This model was applied with seme success by Dunne et a l (1976). In the study watershed, i t i s reasonable to assume that most cf the meltwater flows over an impermeable surface, as described above, rather than i n f i l t r a t i n g into the s o i l . Basal ice was observed to cover about 75% of the watershed, and considerable areas i n depressions and at the base of slopes were saturated at the time the snow disappeared. Also, most of the watershed i s underlain at a shallow depth by a compact t i l l of very low permeability. Some areas of the watershed, however, especially those with coarse s o i l s developed on colluvium or t a l u s , are guite permeable and do not become saturated. Also, some areas do not become covered with basal i c e , e s p e c i a l l y those with early snow d r i f t i n g or with thick vegetation. Therefore, meltwater probably i n f i l t r a t e s into unsaturated s o i l . 106 without flowing over the surface, in about 10 to 20% of the watershed. Map c of appendix 1 shows the d i s t r i b u t i o n of s o i l and drainage c h a r a c t e r i s t i c s over the watershed. The period of breakup of the snow cover, from about July 22 to August 10, provided an opportunity to observe the flow cf water at the base of the snowpack. During this time, the basal ice layer was s t i l l intact over most of the watershed as i t melted out at the edge of snow patches. Although at t h i s time, much of the basal ice layer was porous and soft (possibly due to radiation penetration during the l a s t few days of melt, but also possibly due to prolonged contact with meltwater), there was a layer of saturated snow above i t , which indicates a substantial amount of water was flowing over the ice. Also at th i s time, overland flow was observed below many snow patches, due to saturated s o i l ; t h i s condition existed mainly i n areas of low slope, i n depressions leading to temporary ponds or streams, and in ccncave areas of slopes. Thus, i n many areas lacking basal i c e , or in which the basal i c e had become permeable or had broken down, the saturated s o i l below s t i l l resulted in overland flow. This condition of saturated s o i l was probably due l a r g e l y to the fine texture, and hence low permeability, of the s o i l below the organic layer (see ch. 7), and to the compact t i l l underlying the s e l l at a shallow depth. Photographs of overland flow are shown in f i g . 4.2. The flow was obviously turbulent, and was channelized both on a micrc-scale around f l a t - l y i n g meadow vegetion, and on a l o c a l scale due to small undulations i n the topography. This l a t t e r condition resulted i n a network of small temporary channels 107 108 flowing over the mat of dead vegetation. By inference, the flow of water through the base of the snowpack, over the basal ice or saturated ground, must have been s i m i l a r l y l o c a l i z e d into channels or concentrations of flow. Thus, i t i s very unlikely that flow under the snow can be described as a uniform sheet, as in the model of Colbeck (1974) . Bather, most of the flow i s probably i n concentrated flow paths which would develop a higher saturated conductivity than the surrounding snow, or i n channels eroded into the basal i c e , i n which turbulent flew would occur. ; Also, considerable flow probably takes place i n the mat of dead vegetation between the s o i l and the basal i c e or snow; t h i s mat would have a higher conductivity than the snow due to i t s high porosity and coarse texture. The hydrographs reported in Dunne et a l (1976) show a noticeably faster response than was predicted by Colbeck's model; i t i s l i k e l y that t h i s i s because much of the flow over the surface occurred in preferred flow zones of high conductivity, or even as turbulent flow i n temporary channels. As the snow cover broke up, a number of temporary bodies of standing water were observed in the central, hummocky region of the watershed ( f i g . 4.3). Some of these ponds drained quite quickly, presumably through the loose A-horizon of the s o i l , or thrcugh the pockets of f l u v i a l material which are common i n depressional areas. These ponds thus could contribute to the declining limb of the daily hydrograph, along with water released from the saturated s o i l areas and from saturated snow at the base of the snowpack. Some ponds took several weeks or longer to drain; these contributed to the longer recession of 109 the hydrograph in mid-August. 4.4 HYDFOGSAPH ANALYSIS From examining the hydrograph of stream flow over the season (appendix 3), i t i s apparent that the shape, as well as the timing, of the d a i l y hydrograph changes over the season. There i s a tendency for both the r i s i n g limb and the recession limb to become steeper, and for the hydrograph to become more peaked for a given volume of runoff. Some inferences about the shape of the r i s i n g limb and the peak of the daily hydrograph can be made from the seasonal hydrograph. The attenuation of the r i s i n g l i m b (as pointed out i n chapter 3, f i g . 3. 14) i s large l y due to the variation over the watershed i n the time at which the wetting front reaches the base of the snowpack. As the snowpack becomes shallower, these variations i n tr a v e l time diminish as the ov e r a l l t r a v e l time becomes le s s ; also, the snowpack becomes more homogeneous with increasing maturity, thus further diminishing the v a r i a b i l i t y . , Thus, the response of the watershed system to snowmelt becomes more rapid, and the r i s i n g limb becomes shorter. As the a r r i v a l cf water at the base of the snowpack becomes more synchronous over the watershed, the hydrograph peak becomes shorter in time; thus, there i s a tendency for peak flows tc be higher late in the season. An increase in the saturated hydraulic conductivity of the snow and basal i c e at the ground surface with time (see below) may also produce a more rapid r i s e of the hydrograph, by decreasing the t r a v e l time of water in unsaturated flow along 110 slopes. Figure 4.4, which shows the times of the beginning and end of the hydrograph r i s e , i l l u s t r a t e s the shortening of the r i s i n g limb over the season. This diagram i s similar to f i g . 3. 15, which was used to estimate the speed of the meltwater wave through the snowpack. The e a r l i e r a r r i v a l of the meltwater wave at the stream gauge l a t e r i n the season i s due partly to increasing rates of flow at the base of the snowpack, as well as the shallower snow depth. I t i s d i f f i c u l t to estimate the r e l a t i v e importance of these two e f f e c t s , although f i g . ,3.14 suggests that the former e f f e c t i s l e s s important., The recession limbs of a l l the daily hydroqraphs are shown on a logarithmic scale i n f i g . 4.5. To construct t h i s diagram, the season was divided into three periods, based on the appearance of the o v e r a l l seasonal hydrograph. This diagram i s sim i l a r to the one given i n Woo and Slaymaker (1975) for .snowmelt hydrographs at M i l l e r Creek. ,From f i g . 4. 5 i t i s apparent that the recession rate from the peak becomes more rapid as the season progresses, and also that the recession curve becomes more concave upwards, also, e a r l i e r i n the season, the recession curves are e s s e n t i a l l y p a r a l l e l , while l a t e r in the season, they show considerable variation in shape from day to day. This behavior was also noticed by Woo and Slaymaker. The recession limb of the hydrograph, following the cessation of snowmelt for the day, i s the res u l t of the release of water from storage i n the watershed, A high proportion of t h i s storage i s i n the snowpack, and the release of water from unsaturated storage i n the snowpack dominates the hydrograph at 2<h r- / 18 £ 12 0 v. Ax X Peak discharge # lf0 or less clou4 cover R 1.0 mm or more rair> R * U * R R R * * * * R I 30 June'? June If 50 June T\ 60 July? 70 Ju/y II # * R RR 80 July 21 F i g . 4.4 Times of peak and low flows. 112 50 30 June 15 - July 2 July <t- 22 July 23 - Auj- 3 16 0 . 8 16 Hours offer peak 16 2f F i g . 4.5 Stream hydrograph r e c e s s i o n limbs f o r the snowmelt season. i.o 0.6 o.cm-0.02L 0.01 June 28 - July 6 ysime+er depth : 57+.88 cm July 10- \if lys'mte+er deptd: 33*o38cin 16 0 Houi-J af+er peak it-F i g . 4.6 Lysimeter r e c e s s i o n limbs. (Note: the v e r t i c a l s c a l e i s twice t h a t o f f i g . 4.5.) 113 higher flows. Later in the season, as the storage capacity of the snowpack i s depleted at an e a r l i e r time, the l a t e r part of the recession curve i s dominated by the release of water ficm the saturated zone at the base of the snowpack, and from storage i n the s o i l and in transient ponds and channels. According to c l a s s i c a l l i n e a r reservoir theory (eg., see U.S. Army Corps of Engineers, 1956, p. 118), the recession limb of a hydrograph can be described as a sum cf two or more exponential recessions, each recession representing a l i n e a r release of water from storage from one component of the watershed system. The rate of release of water from each reservoir i s d i r e c t l y proportional to the amount of water remaining in storage, and the r e s u l t i s a recession of the form: - t / t * 9 = g 0« <"'1> where g 0 i s the discharge at t=0, and t* i s the recession constant, or the time i t takes g to drop to e - 1 of <g0. However, i t i s l i k e l y that the two components of the d a i l y recession limb mentioned above are non-linear. The equations governing the release of water from the snowpack (egs. 3.2 and 3.3) cannot be solved a n a l y t i c a l l y f o r discharge as a function of time for any r e a l i s t i c boundary conditions (although Colbeck solved eg. 3.2 for the speed of a flux wave as a function of discharge). However, the lysimeter observations, as well as a numerical solution of eg. 3.3 (see below) strongly suggest that water i s released from a snowpack i n a non-linear manner. The release of water from saturated storage at the base of the snowpack i s also l i k e l y to be non-linear, since water i s fed in t o t h i s zone continously as the unsaturated snowpack drains; 114 t h i s i s unlike the s i t u a t i o n following a rainstorm, i n which the supply of wafer i s terminated at the end of the storm. The storage capacity i s greater, and the recession i s more attenuated, for a deep snowpack than for a shallow snowpack ( f i g . 3 . 2 ) , so the recession of the re s u l t i n g stream hydrograph i s slower e a r l i e r i n the season. Also, a very deep snowpack d i s t o r t s the shape of the snowmelt input at the surface and produces a meltwater wave which i s s i m i l a r i n shape for widely varying shapes of the surface snowmelt input. In a shallow snowpack, the meltwater wave produced w i l l bear more resemblance to the o r i g i n a l shape of the snowmelt or r a i n f a l l input, and thus the shape of the recession curve i s much more variable l a t e r i n the season. This increase in v a r i a b i l i t y over the season i s noticeable on the hydrograph i n appendix 3. After about July 25 , discontinuous snow cover also allowed the stream to respond d i r e c t l y to r a i n f a l l and evaporation> thus introducing more v a r i a b i l i t y into the hydrograph shape. As the season progresses, the flow network through the saturated snow and basal ice at the base of the snowpack becomes better developed, and flow over the ground becomes more rapid (Colbeck, 1977). The release of water from storage at the base of the snowpack therefore should become more rapid as the season progresses; t h i s would contribute to the more rapid recession in the early and middle parts of the recession curves. However, release of water from the s o i l would not become more rapid, and therefore the l a t e r part of the recession curve would not change appreciably, A gradual breakdown i n the basal i c e layer l a t e r i n the season might cause more meltwater to enter the s o i l , and 1 15 t h i s could actually cause the l a t e r part of the recession curve tc become les s rapid, as the proportion of the watershed contributing surface runoff decreases. The concavity of the recessions i n f i g . 4.5 i s equivalent t c an increasing value of the recession "constant", t * , with decreasing discharge. The recession constants for the season are l i s t e d i n table 4.1; these were calculated from the slopes of the hydrographs on a logarithmic scale at their intersections with the given discharge values. (A number of recessions at low flows af t e r the snowmelt season are also shown.) Since the logarithmic recessions are concave upwards, the values of t * are greater for lower discharge values. The table shows a d e f i n i t e trend towards decreasing values of t * at the higher discharge value as the season progresses, and also a s l i g h t tendency towards increasing values of t * at the lower discharge value; t h i s i s a q u a n t i f i c a t i o n of the behavior of the recessions noted above i n f i g . 4.5, The slower recession rate i n the lower part of the hydrograph l a t e r in the season may be due to increased storage of meltwater i n the s o i l , or i t may be simply due to the temporal shortening of the hydrograph peak as the snowpack becomes thinner and more mature. Secessions of the lysimeter discharge record f o r several days are shown i n f i g . 4.6; note that these recessions as well are concave upwards on a logarithmic scale. They are s i m i l a r i n general appearance to the stream hydrographs i n f i g . 4.5, except that the recessions are f a s t e r , with a t * in the lower portions of about 9 to 11 hours. These recession curves suggest that the water released from the snowpack does not follow an exponential 116 decay, as i n eg. 4.1. A numerical solution of eg. 3.3 was calculated, using a method developed by Freeze (1969) for the problem of i n f i l t r a t i o n into s o i l s ; the boundary condition used was that of a constant input of meltwater which was terminated abruptly, allowing the snowpack to drain. This solution produces recession curves very s i m i l a r to those i n f i g . 4.6; the recession curves are concave upwards on a logarithmic scale, and are steeper {i.e. with lower values of t*) for shallower snow depths. These re s u l t s suggest that the curvature of the recessions of f i g . 4.5, and the faster recession rates l a t e r in the season, are at lea s t partly due to the properties of unsaturated flow through the snowpack. •  One approach to the problem of examining the recession c h a r a c t e r i s t i c s of the different components of the watershed system i s to derive an integrated hydrograph from information on recessions at various flows throughout the season. An example of t h i s approach i s found i n the D.S. Army Corps of Engineers {1956, p.119 and plate 2-11), i n which such synthesized hydrographs are used to compare q u a l i t a t i v e l y the recession c h a r a c t e r i s t i c s of d i f f e r e n t watersheds. The standard method of hydrograph separations ( l i n s l e y , Kohler, and Paulhus, 1975, p.228) was not used, since the snowmelt hydrographs appear to be dominated by the non-linear release of water. (This does not compromise the hydrograph separations used to determine d a i l y runoff t o t a l s i n section 4.1, since for the short extrapolations used, the l i n e a r recessions are not greatly d i f f e r e n t from the hydrograph derived below; also the l i n e a r recessions are much 117 IABLE 4 X1 HYDROGRAPH RECESSION CHARACTERISTICS. Recession "constants" (or slope of the recession curves) , in hr/log cycle, are tabulated for several flow l e v e l s . E indicates rain > 1.0 mm; * indicates cloud cover < 1/10. Missing days indicate no melt, or complex or rainstorm-dominated hydrograph. , t * at flows: t * at flows: DATE 15.8 10.0 6.3 DATE 15. 8 10. 0 6. 3 1/sec 1/sec 1/sec 1/S€C 1/sec 1/sec June 15 26 R July 9 30 33 16 26 26 10 14 27 17 28 28 * 11 22 34 18 30 30 12 26 34 19 28 31 13 21 B 20 30 14 14 31 21 22 33 15 16 34 * 22 29 34 16 20 30 * 23 56 17 16 29 * 24 18 13 29 * 25 19 20 26 29 20 19 29 B 27 18 25 * 21 23 29 28 18 31 22 19 29 29 31 23 30 30 34 24 15 30 July 1 34 25 9 33 * 2 37 26 16 43 3 R 27 6 13 47 * 4 18 36 R 28 9 B 5 19 28 * 29 36 B 6 26 31 30 7 40 fi 7 R 31 6 18 42 8 21 27 R OTHER RECESSION DATA: May 21 t*=78 hr at 1.8 1/sec May 23 t*=129 hr at 1.4 1/sec May 27 t*=23 hr at 6.3 1/sec (rain on snow) t*=138 hr at 1,5 1/sec June 10 t*=52 hr at 3.6 1/sec Aug 10-14 t**80 hr, from 2 to 5 1/sec Bainstorm recessions: Aug 9 t*=53 hr at 6 1/sec (includes snowmelt) Aug 22 t*=143 hr at 1 1/sec Aug 28-31 t*=88 hr at ~1 1/sec (for 3 days; high evaporation) Sept 7-10 t*=127 hr at ~.8 1/sec (for 4 days) Sept 21-26 t*«300 hr at ~. 2 1/sec (long period of clear weather) 118 F i g . 4.7 Synthesized recession hydrograph derived from recession data. The recession curve i s obtained by integrating the curve through the data in the top figure. 119 easier to use for routine applications.) Several recessions cf two or more days in length occurred following r a i n f a l l events i n the late summer, and several s i m i l a r long recessions occurred early i n the snowmelt season duritg cold periods. These provide data at low flows for the release of water from s o i l moisture and surface depression storage, and the values of t * obtained are shown i n table 4.1. These data are plotted on f i g . 4.7, along with the average values of the snowmelt recession constants l i s t e d in table 4.1. A rough curve r e l a t i n g the recession constant to the discharge can be drawn, and t h i s curve can then be integrated tc give a synthesized recession hydrograph for the entire range of observed flows ( f i g . 4.7b). This hydrograph i s approximate, considering the scatter i n f i g . 4.7a, and i t i s probably quite variable in the upper part, since the changing properties cf the snowpack produce recessions of varying shapes at high flows. However, the lower part of the curve, below about 5 1/sec, i s probably a good representation of the hydrograph which would resul t i f the watershed were allowed to drain f o r a prolonged period following snowmelt or r a i n f a l l . / The lower part of the curve, representing flow a f t e r the snowmelt season, may act as a series of linear reservoirs. Unfortunately, rainstorm recessions at discharges comparable to those during snowmelt were not obtained, and information on the recession c h a r a c t e r i s t i c s of the snow-free watershed i s limited. An i l l u s t r a t i o n of the importance of a slow recession from snowmelt i s given by the peak flow event of the season, which occurred on July 24. The hydrograph of t h i s event, along with 120 the temperature and radiation records for the same time, i s shown i n f i g . 4.8. Although more runoff was produced on July 23 than on July 24, i t resulted i n a f a i r l y low peak flow because i t was spread over the day, and was b u i l t on a very low recession limb from the preceding day. Much of the melt was l a t e in the day (presumably due to warm temperatures combined with strong winds, although t h i s cannot be v e r i f i e d as the s i t e was not v i s i t e d on t h i s day) , and considerable melt occurred due to warm temperatures during the night, as can be seen on both the hydrograph and the temperature record. This resulted i n an unusually high recession flow on the following morning, and although the runoff produced on July 24 was less i n volume, i t produced a high peak flow because i t was b u i l t on a high recession limb. Also the narrow hydrograph peak, t y p i c a l of days dominated by radiation melt, contributed to the r e l a t i v e l y high peak flow. This role of the recession limb can also be seen by examining periods of high runoff on the seasonal hydrograph i n appendix 3. A long period of high-runoff days r e s u l t s i n increasing peak flows for several days, as each day»s runoff builds on the recession of the previous day. This phenomenon, which was also noted by 8oo and Slaymaker (1975), occurs because during high runoff periods, considerable water remains i n storage at the base of the snowpack and in the s o i l for longer than 24 hours. 4.5 CONCLUSIONS Although quantitative information of flow processes 122 occurring under the snowpack and i n the channel network i s lacking, some conclusions on these processes and on the response of the watershed to snowmelt can be made from analysis of the hydrcgraphs and from gu a l i t a t i v e observations. 1. Most of the area of the study watershed (at least 75%) contributes surface runoff under the snow to the stream channel. This runoff moves through saturated snow and basal i c e , through the vegetation mat beneath the snow, and through temporary channels. Surface runoff occurs because of the prevalence cf a basal ice layer, and because much of the s o i l beneath the snow i s saturated during the snowmelt period., 2. As the season progresses and the snow becomes shallower, the delay i n runoff due to unsaturated flow through the snowpack becomes le s s . For t h i s reason, and also because the flow paths beneath the snow become better developed, the d a i l y hydrograph becomes more peaked and the r i s i n g limb becomes steeper. 3. The recession limb of the daily hydrograph for the f i r s t few hours after the peak i s dominated by the release of water frcm the unsaturated zone of the snowpack. After the f i r s t few hours, i t i s dominated by the release of water from saturated snow, saturated s o i l , and ponded water at the base of the snowpack. 4. The release of meltwater from the snowpack and from the s o i l does not follow an exponential recession and cannot be described by l i n e a r reservoir theory. Bather, the watershed releases water from snowmelt i n a non-linear manner, dominated by Darcian flow through the snowpack and the s o i l . 123 CHAPTER 5 THE WATER BALANCE 5.1 THE WATER BALANCE EQUATION A central problem in hydrology i s to determine, for a watershed of interest, the proportion of water from a snowmelt or r a i n f a l l event which enters the stream as surface runoff, i s stored i n the watershed for release l a t e r in the season, and i s l o s t to evaporation., For any hydrological system, the water balance can be expressed simply as: inputs - outputs = change i n storage. (5.1) For the watershed under study, i t w i l l be assumed that there i s no movement of water across the surface watershed divides. P r e c i p i t a t i o n (P) i s considered to be the only input. It can occur as r a i n or snow. The outputs are runoff (Q), and evaporation (E). I t i s assumed that a l l the runoff i s surface runoff through the stream channel, and that there i s no groundwater runoff beneath the channel; t h i s i s a reasonable assumption considering the nearly impermeable t i l l which underlies most of the watershed. The evaporation term can be negative, i n the case of an input of water through condensation. The storage term i s divided into two components: the change i n storage of s o i l water and groundwater, AS (which i s positive for an increase in storage), and ablation, the negative of the change of storage i n the form of snow. (Ablation i s defined as the loss of snow i n a l l phases from the watershed, and has units of length..The snowmelt volume, M, as defined i n chapter 2 i s used in the water balance c a l c u l a t i o n s ; this i s the product of 124 ablation and the snow-covered area.) Since the snowmelt season i s the period of i n t e r e s t , i t i s convenient to define ablation as a positive term; i n t h i s case, accumulation of snow i s treated as a negative value of ablation. The water balance eguation for the watershed i s then: Q = P • H - E - AS (5.2) with a l l terms having units of volume. During the early part of the season, runoff was low, and the accumulation and ablation of snow were nearly equal. Freguent fresh snow made the c a l c u l a t i o n of the actual accumulation and ablation over the watershed d i f f i c u l t , as discussed i n chapter 2. Therefore, the snowmelt period i s considered to begin on June 14. 5.2 ABLATION, RUNOFF, AND PRECIPITATION CALCULATIONS The calculations of ablation and surface runoff have been described i n chapters 2 and 4, respectively. After July 24, some of the stake locations were bare, and an increasing amount of estimation was necessary i n the c a l c u l a t i o n of ablation. These calculations are summarized i n table 5.1. U n t i l July 31, the ablation was simply calculated from the remaining stakes in each region. From July 31 to August 8, the estimate of ablation i s very approximate; i t was made with the aid of a cumulative mass curve of net solar radiation against ablation. Also, since the s i t e was not v i s i t e d for 6 consecutive days during t h i s period, the time d i s t r i b u t i o n of the area of snow cover i s not known; therefore the c a l c u l a t i o n of the snowmelt volume from eq. 2.2 i s very approximate. The 125 T A B L E 5^ .1 SNOWMELT VOLUME E S T I M A T E S . E g . 2 . 2 i s u s e d t o c a l c u l a t e s n o w m e l t v o l u m e s d u r i n g t h e p e r i o d o f p a r t i a l snow c o v e r . D a t a a r e t a b u l a t e d by r e g i o n , as f o l l o w s : 128 A b l a t i o n (mm) a t c o n t r i b u t i n g s t a k e s 1800 S n o w m e l t v o l u m e (m 3 ) f r o m e g . 2 . 2 99% Snow c o v e r a t e n d o f p e r i o d . B r a c k e t e d f i g u r e s i n d i c a t e e s t i m a t e d a b l a t i o n , f r o m s t a k e s i n o t h e r r e g i o n s ( b e f o r e A u g . 2 ) , o r f r o m a d o u b l e - m a s s p l o t c f a b l a t i o n a n d s o l a r r a d i a t i o n ( a f t e r A u g . 2 ) . PERIOD LAYS 1 2A 2B 3 T O T A L VOLUME J u l y 14 -17 4 128 139 124 131 1800 1240 €40 1450 513 0 99% 98% 99% 99% J u l y 18-23 6 187 189 182 191 2540 1620 900 2030 7090 95% 91% 93% 93% J u l y 2 4 - 2 7 4 118 124 110 112 1520 970 510 1100 4100 89% 82% 85% 85% J u l y 2 8 - 3 0 3 9 4 (93) 86 112 106 0 (640) 350 1000 3050 71% 71% 7 4% 76% J y . 3 1 - A u . 1 2 (73) (73) 62 84 (630) (420) 210 660 1920 52% 56% 60% 66% A u g . 2 -8 7 (25) <25) (25) (25) (900) (700) (400) (1200) (3200) 1% 1% 5% 22% E r r o r s i n t o t a l v o l u m e f o r e a c h p e r i o d : Up t o J u l y 30 - ± 5 t o 10% J u l y 3 1 - A u g . 1 - a b o u t +15% A u g . 2-8 - a b o u t ± 3 0 % . 126 e r r o r i n the snowmelt volume f o r the p e r i o d from June 14 t c J u l y 30 i s estimated at about ±5% (chapter 2), and t h e e r r o r f o r the p e r i o d J u l y 31 to Aug. 8 i s probably about ±20%. The e r r o r i n the r u n o f f t o t a l s i s much l e s s than ±5%. The t o t a l a b l a t i o n i n the watershed over the p e r i o d from June 14 to J u l y 30 i s 5% g r e a t e r than that measured by the small s u r f a c e stakes a t the m e t e o r o l o g i c a l s i t e . T h i s d i f f e r e n c e i s p o s s i b l y w i t h i n experimental e r r o r , but i t c o u l d a l s o be due to g r e a t e r c o n v e c t i v e melt i n those areas of the watershed which have g r e a t e r s l o p e and exposure t o wind, as w e l l as g r e a t e r long-wave r a d i a t i o n melt i n areas of t r e e cover. The s u r f a c e r u n o f f f o r each p e r i o d of measurement corresponding to the a b l a t i o n stake readings was c a l c u l a t e d using hydrograph s e p a r a t i o n s , as d i s c u s s e d i n chap 4. The p r e c i p i t a t i o n f o r each p e r i o d was measured with two r a i n gauges. 5.3 EVAPORATION ESTIMATES The e s t i m a t i o n of e v a p o r a t i o n over a watershed by e m p i r i c a l methods i s a very approximate procedure. I f d e t a i l e d m i c r c m e t e o r o l o g i c a l measurements are a v a i l a b l e , more accurate c a l c u l a t i o n s can be made. However, t h i s i s i m p r a c t i c a l f o r most s t u d i e s , s i n c e such measurements are very l a b o u r - i n t e n s i v e and r e g u i r e f a v o u r a b l e weather c o n d i t i o n s ; a l s o , i t i s d i f f i c u l t t o extend measurements taken at a p o i n t t o an e n t i r e watershed. S e v e r a l energy balance approaches which cam be used to e s timate e v a p o r a t i o n are d i s c u s s e d i n chapter 6. Of the many e m p i r i c a l or p a r t l y e m p i r i c a l approaches a v a i l a b l e f o r the e s t i m a t i o n of evaporation, o n l y the 127 aerodynamic approach i s suitable for both snow and vegetated surfaces. This i s e s s e n t i a l l y the approach used by Light (1941); the basic eguation he used i s a form of eg. 6.7b, i n which evaporation i s a function of wind speed, the vapour pressure gradient between the surface and the measurement height, and the roughness length of the surface. The equations used for the water balance estimates are: for snow: E = 0.175 u (6.1 mb - e) (5.3a) and for vegetation: E = 0,63 u (e s - e) (5.3b) where E i s evaporation i n mm/day, u i s wind speed i n ra/sec, e i s the vapour pressure in mb, and e s i s the saturation vapour pressure at the a i r temperature. (It i s assumed that the surface temperature i s the same as the a i r temperature as measured i n the instrument screen, and that the vegetation surface i s freel y evaporating.) Vapour pressures f o r every day are available from the thermohygrograph record. Hind speed i s not available every day; for missing days, the average speed for a l l observed days, 1.3 m/sec, i s used. The constant term has units of mm sec (m day mb) - 1; the value of 0.175 for a snow surface i s eguivalent to a value of b = 5.0 J m—3mb_i i n eg. 6.11. I t i s concluded i n chapter 6 that a value of 5.0 or l e s s for b i s appropriate at the meteorological s i t e ; a high value i s used for these estimates, since a large part of the watershed has surfaces with greater large-scale roughness, slope, and exposure to wind than the meteorological s i t e . During the period of "complete" snow cover, trees covered approximately 3% of the watershed area. Therefore, the average 128 evaporation was calculated on the basis of 97% coverage by snow and 3% coverage by vegetation; t h i s proportion was changed as the snow cover decreased l a t e r i n the season. Since there i s no known means of calculating the evaporation from an i s o l a t e d clump of trees, e s p e c i a l l y i n alpine regions, t h i s method i s exceedingly crude. The evaporation estimates are probably subject to an error of at l e a s t ±100%, but since f o r the period from June 14 to July 30, evaporation accounts f o r only 0.4% of the water balance, t h i s error i s acceptable. The d a i l y evaporation estimates are shown i n table 5.2. 5.4 RATER BALANCE RESULTS The components of the water balance for each measurement period of the snowmelt season are summarized i n table 5.3. I t i s assumed that the storage term, AS, i n eg..5.2 i s zero. This assumption i s inherent i n the use of runoff volumes calculated frcm hydrograph separations, since the separation procedure i s equivalent to removing the effect of watershed storage changes frcm the daily discharge t o t a l s . Because of the non-linearity of the hydrograph recessions, as discussed i n chapter 4, t h i s assumption i s not s t r i c t l y correct, but errors due to storage changes are probably quite small. Because of the greater error i n the snowmelt volume a f t e r July 30, the period from June 14 to July 30 i s used to assess the accuracy of the water balance. The t o t a l volumes for t h i s period are: IhilS 5XJ2 EVAPORATION ESTIMATES. D a i l y evaporation estimates frcm aerodynamic formula. U n i t s are mm/day; t o t a l volume i s i n m'/day; averaqe before J u l y 20 i s tased on 3% t r e e cover. EATE SNOW VEG. AVERAGE TOTAL VOLUME 35 June 14 -0.02 1.13 0.01 0. 36 June 15 -0. 23 0.80 -C.20 -8. 37 June 16 -0.05 3.93 0.07 3. 38 June 17 0.21 3.72 C.32 12. 39 June 18 -0.07 2.17 -0.00 -0. 40 June 19 -0.00 1.99 C.C6 2. 41 June 20 0. 13 1.54 0.17 7. 42 June 21 0. 10 2.42 C. 17 7. 43 June 22 0.27 2.49 0.33 13. 44 June 23 0. 14 1. 36 0.17 7, 4 5 June 24 0. 18 0.63 0. 20 8. 46 June 25 0.13 1.53 C.47 18. 47 June 26 0.02 0.30 0.03 1. 48 June 27 0.14 3. 10 0.23 9. 49 June 28 0.08 4. 60 C.22 9. 50 June 29 -0. 16 2.47 -0.08 - 3 . 51 June 30 0.05 1.97 0. 10 4. £2 J u l y 1 0.04 0.91 0.07 3. 53 J u l y 2 0. 18 1.69 C.23 9. 54 J u l y 3 -0.00 1.88 C.06 2. 55 J u l y 4 0.07 3. 11 C. 16 6. 56 J u l y 5 0.08 2.86 C.17 7. 57 J u l y 6 -0.34 2.22 -0.27 -10. 58 J u l y 7 -0.16 0.38 -C. 14 - 6 . £9 J u l y 8 -0.15 2.75 -0.07 - 3 . 60 J u l y 9 0.05 1.62 C. 10 4. 61 J u l y 10 0.23 2. C.29 11. 62 J u l y 11 0.10 1.80 0.16 6. . 63 J u l y 12 -0.02 1.92 0.04 1. 64 J u l y 13 -0.05 0.85 -0.02 -1. 65 J u l y 14 -0.02 1. 82 C.C4 2. 66 J u l y 15 0.02 3.99 0.14 6. 67 J u l y 16 0.04 4. 14 0. 16 6. 68 J u l y 17 -0.03 3.87 0.09 4. 69 J u l y 18 -0.03 3.64 0.08 3. 70 J u l y 19 -0. 27 2.75 -C. 18 -7. 71 J u l y 20 -0.32 1.52 -0.25 -10. 4 72 J u l y 21 -0.20 0.93 -C. 15 - 6 . 4 73 J u l y 22 -0.18 1.34 -0. 10 -4. . 5 74 J u l y 23 -0.27 2.69 -0.09 - -4. 6 75 J u l y 24 -0. 25 4.93 C. 11 4. 7 76 J u l y 25 0.05 4.57 0.41 16. 8 77 J u l y 26 0.06 3.28 0.38 15. 10 78 J u l y 27 0. 18 4.84 C.74 29. 12 79 J u l y 28 -0.22 1. 17 COO 0. 16 80 J u l y 29 -0.34 0.87 -0. 10 - 4 . 20 81 J u l y 30 -0.39 1.59 0.09 3. 24 82 J u l y 31 -0.21 2.58 C.E3 25. 30 83 Aug 1 -0. 36 3.28 C.S5 37. 36 84 Auq 2 -0. 75 1.39 0.19 8. 44 85 Aug 3 -0.80 1.99 0.71 28. 54 86 Aug 4 -0.84 1.38 0.58 23. 64 87 Auq 5 -0.80 1.29 C.73 29. 73 88 Aug 6 -0.80 2. 47 1.65 73. 81 89 Auq 7 -0.84 1.31 1.03 41. 87 90 Aug 8 -0.77 1.31 1.14 45. 92 % OF WATERSHED BARE 130 1MLS I i i WATEB BALANCE SUMMARY. A l l figures are i n m3. Q M P E M+P-E PERIOD BAYS Streamflow Snowmelt Precip* Evap. Total generated volume June 14-19 6 5400 3950 560 10 4500 June 20-25 6 3880 2960 400 50 3310 Jn.26-Jy.3 8 7460 6510 180 30 6660 July 4-8 5 6840 5800 750 -1 0 6550 July 9-13 5 4510 4360 70 20 4410 July 14-17 4 5690 5130 0 20 5110 July 18-23 6 8260 70 90 590 -3 0 7710 July 24-27 4 4770 4100 0 60 4040 July 28-30 3 3700 3050 570 0 3630 Jy.31-Au.8 9 7940 (5120) 1520 310 (6340) Notes: 1. M for July 31 - Aug. 8 i s approximate. with an error of about ±20%. / 2. Periods correspond to stake measurement periods (table 2. 3) . 131 Cumulative observed runoff (l03m3) F i g . 5.1 Cumulative mass curve of water balance data. 132 Q 50500 rn3 M P E 42900 B3 3100 m3 M + P-E 200 rn3 45800 m3. These t o t a l s show that the measured runoff over the snowmelt period i s 10% greater than the t o t a l of snowmelt, p r e c i p i t a t i o n , and evaporation. The figures in table 5.3 are plotted in f i g . 5. 1 as a cumulative mass curve; t h i s shows that the 10% discrepancy i s consistent over the season. The discrepancy i s greater than can be explained by the errors i n the measured components of the water balance. I t i s unlikel y that the discharge measurements are biased (see section 4.2), and the p r e c i p i t a t i o n and evaporation tot a l s are too small for errors to be s i g n i f i c a n t . The most probable explanation i s a flux of groundwater across the watershed boundaries. The upper 25% of the watershed i s underlain by colluvium, s t a b i l i z e d t a l u s , and fractured bedrock as well as t i l l , and a long h i l l s l o p e of s i m i l a r geology extends up the ridge above the apparent watershed divide. I t i s possible that groundwater from the slope above moves into the watershed, and that the watershed therefore discharges runoff from snowmelt over an area somewhat greater than the apparent watershed area, An independent check can be made on the above water balance calculations by using the t o t a l snow volume measured at the beginning of the season, on Hay 23. August 26 was taken as a rather arb i t r a r y date for the end of the snowmelt season. On t h i s date, a few small snow patches remained, but the discharge was lower than on May 23, i n d i c a t i n g some loss of water from s o i l and groundwater storage. (Hydrograph separations were not 133 used for t h i s longer period.) The water balance t o t a l s for t h i s period are, neglecting evaporation: t o t a l discharge : 667 00 m3 snow water eguivalent, May 23 : 48000 m3 t o t a l p r e c i p i t a t i o n : 10100 m3 5 8100 m3. These t o t a l s indicate that 15% more runoff occurred over the entire season than can be accounted for by snowmelt and p r e c i p i t a t i o n , even neglecting evaporation. The error inherent i n t h i s estimate i s greater than that in the f i r s t c a l c u l a t i o n , but the result i s b a s i c a l l y i n agreement. In p a r t i c u l a r , the independent measurement of the t o t a l snow volume indicates that there i s no appreciable bias i n the snowmelt t o t a l . Frcm the above analysis, i t can be concluded that i n the study watershed, v i r t u a l l y a l l the water produced from snowmelt i s discharged as surface runoff, without appreciable losses to groundwater or evaporation. The method of determining ablation over the watershed by means of a stake network, combined with p r e c i p i t a t i o n gauge observations, i s capable of determining t h i s runoff with an acceptable degree of accuracy. The problem of groundwater flux across the watershed divide apparently caused a s i g n i f i c a n t error in t h i s watershed, even though the study watershed was c a r e f u l l y chosen to avoid such problems. In most small watersheds i n mountainous areas, the problem i s l i k e l y to be considerably greater. 134 C H A P T E E 6 T H E E N E R G Y B A L A N C E AND T H E E S T I M A T I O N O F S N O W M E L T A n a l t e r n a t i v e t o t h e d i r e c t m e a s u r e m e n t o f s n o w m e l t i s i t s e s t i m a t i o n b y e n e r g y b a l a n c e m e t h o d s . T h i s a p p r o a c h i s c o m m o n l y u s e d i n w a t e r s h e d r u n o f f m o d e l s w h i c h b a s e s n o w m e l t e s t i m a t e s o n c l i m a t i c p a r a m e t e r s . I n t h e p r e s e n t s t u d y , b a s i c c l i m a t e m e a s u r e m e n t s w e r e t a k e n t h r o u g h o u t t h e s n o w m e l t s e a s o n , w i t h d e t a i l e d p r o f i l e m e a s u r e m e n t s t a k e n o n s i x d a y s . T h e p u r p o s e o f t h e s e m e a s u r e m e n t s w a s t o d e t e r m i n e t h e r e l a t i v e i m p o r t a n c e o f r a d i a t i v e a n d t u r b u l e n t e n e r g y t r a n s f e r , a n d t o p r o v i d e a b a s i s u p o n w h i c h t o d e v e l o p s i m p l e m e t h o d s b y w h i c h t h e s e e n e r g y t r a n s f e r s c a n b e e s t i m a t e d . P r e v i o u s w o r k o n t h e e n e r g y b a l a n c e a p p r o a c h t o s n o w m e l t f a l l s i n t o t w o m a i n c a t e g o r i e s . T h e f i r s t i s t h a t o f d e t a i l e d p r o f i l e o r e d d y c o r r e l a t i o n s t u d i e s , u s u a l l y o n g l a c i e r s , i n v o l v i n g e l a b o r a t e i n s t r u m e n t a t i o n , a n d w i t h r e s u l t s u s u a l l y b a s e d o n o n l y a f e w d a y s o f " g o o d " m e a s u r e m e n t s a t a s i n g l e p o i n t . T h e s e c o n d c a t e g o r y i s t h a t o f e m p i r i c a l l y - b a s e d s t u d i e s o f t h e m e l t o f s e a s o n a l s n o w p a c k s , w i t h t h e a i m o f o b t a i n i n g r e s u l t s w h i c h c a n b e u s e d t o p r e d i c t s n o w m e l t r u n o f f o n a w a t e r s h e d s c a l e . A s t u d y o f t h e f i r s t t y p e i s t h a t o f M u n r c ( 1 9 7 5 ) , w h i c h p r e s e n t s c a l c u l a t i o n s o f e n e r g y t r a n s f e r o v e r m e l t i n g i c e o n t h e P e y t o G l a c i e r i n A l b e r t a w h i c h a r e p r o b a b l y h i g h l y a c c u r a t e . T h e r e h a v e b e e n many s i m i l a r s t u d i e s o n g l a c i e r s , b e g i n n i n g w i t h t h a t o f S v e r d r u p ( 1 9 3 6 ) i n S p i t s b e r g e n . , ( F o r a r e v i e w , s e e P a t e r s o n , 1 9 6 9 . ) E x a m p l e s o f s u c h s t u d i e s o n s e a s o n a l s n o w a r e f o u n d i n G r a n g e r ( 1 9 7 7 ) , a n d M c K a y a n d T h u r t e l l ( 1 9 7 8 ) , I n t h e s e c o n d c a t e g o r y , A n d e r s o n ( 1 9 7 6 ) 135 developed a computer simulation model of snowmelt using a theoretically-based energy balance approach combined with empirical methods. Kuzmin (1961) discusses methods used for predicting snowmelt i n watersheds i n the Soviet Onion, using both th e o r e t i c a l and empirical approaches..Somewhat more empirical i s the work of the O.S. Army Corps of Engineers (1956); t h e i r r e s u l t s , however, are based on an extensive set of f i e l d measurements. wendler and Is.hi.kava (1974) attempted to extend point energy balance measurements on the McCall Glacier in Alaska to estimate the water balance of the entire watershed of the gl a c i e r . The energy balance eguation for a land surface i s normally written as; Q* = Q H • QE • Q & (6.1a) where Q* i s net r a d i a t i o n , QH i s sensible heat f l u x , QE i s the latent heat flux cf evaporation, and Q<j. i s s o i l heat f l u x , for a melting snow surface, Q & i s zero, but an addit i o n a l latent term i s reguired. This i s QM, the energy used for snowmelt. I t i s also convenient to change the sign of Q H and Q E from the conventional form, so that a l l sources of energy for the snow surface are positive. The energy balance for a melting snow surface can then be written: Q M = Q* + Q H + Qf . (6. Ib) An additional term for the introduction of heat by r a i n f a l l can be included; however, i n t h i s study, i t proved to be i n s i g n i f i c a n t compared to other sources of energy. I f melt at the base of the snowpack i s negligible (as was the case i n t h i s 136 study; see section 2.6), and i f the snowpack i s isothermal at 0°C, eg. 6.1b also represents the energy balance for the entire thickness of the snowpack. 6.1 INSTRUMENTATION AND OBSERVATIONS Snowmelt at the meteorological s i t e was measured by four small stakes, with an additional eight stakes i n the near v i c i n i t y (chapter 2), The average l i g u i d water content of the snow i s believed to be about 8% by weight (chapter 3), so the melt term of eg. 6.1b can be calculated from; Q M = 0.92Lf A (6.2) where A i s the ablation in kg m - 2 s e c - 1 (numerically equivalent to mm/sec), and Lf i s the latent heat of fusion, 3.33x10s J/kg. The factor 0.92 i s commonly c a l l e d "thermal q u a l i t y " of the snow. Accurate measurements of l i g u i d water content are d i f f i c u l t to make, and variations i n l i g u i d water content with time are a potential source of error i n melt c a l c u l a t i o n s . Snowmelt was measured on a daily basis only; the determination of snowmelt over shorter periods i s not feasible using stake methods (see chapter 2). Ablation was calculted using an average density curve; thus, errors are introduced due to short-term changes i n subsurface density, as discussed fcy LaChapelle (1959). However, these errors tend to cancel out over periods of several days. Net radiation was measured with a Middleton net radiometer, and solar radiation was measured with two Middleton solarimeters ( f i q . 6.1). Data were recorded on three Rustrak m i l l i v o l t recorders, powered by alkaline batteries. Some problems were 1 3 7 6.1 Radiometers : net radiometer on r i g h t , and two solarimeters for incoming and r e f l e c t e d solar radiation on l e f t . 6.2 Temperature and wind p r o f i l e i n s t a l l a t i o n : psych-rometers, anemometers, and thermocouple probes. The radiometer i n s t a l l a t i o n i s i n the background. 138 encountered with d r i f t i n g of the recorder zeroes due tc battery voltage drops and r e s i s t o r s e n s i t i v i t y during cold weather. , Freguent checks of the instruments and recorders were made with a micro-voltmeter, and the recorders and batteries were kept i n a covered metal box i n the snow to minimize temperature fluctuations. The c a l i b r a t i o n s of the instruments and recorders were checked at the beginning and end of the f i e l d season. The error of the radiat i o n measurements i s roughly estimated at ±5% for solar radiation, and ±10% for net radiation, This includes the inherent imprecision of the instruments (Latimer, 1972), the uncertainty of f i e l d c a l i b r a t i o n s , and the imprecision of the integration of the chart trace, over periods of an hour or longer. Complete net radiation records were obtained for 20 days during the snowmelt period, with p a r t i a l records f o r 12 additional days. Complete records of incoming solar r a d i a t i o n were obtained for 43 days, ft Kahlsico bimetallic actinograph was alsc operated as a back-up instrument; a nearly complete record was obtained for the f i e l d season. Albedo was determined from several d a i l y t o t a l s of r e f l e c t e d solar r a d i a t i o n , together with many spot measurements. From these, a curve of albedo f o r the season was drawn ( f i g . 6.3), The albedo ranged from 0.83 a f t e r fresh snowfalls to 0.54 at the end of the snowmelt season. Temperature and r e l a t i v e humidity were measured throughout the f i e l d season with a Weathermeasure thermchygrograph, which was freguently checked against Assmann psychrometer readings. The instrument was i n a Stevenson screen, and the instrument height varied from 0.5 to 1.1 m as the snow melted. Temperature 139 p r o f i l e s were obtained with unventilated thermocouple probes (see f i g . 6.2) at three lev e l s ( t y p i c a l l y about 0.4, 1.0, and 1.8 IB) . . Two Assmann psychrometers were also used to measure temperature and vapour pressure gradients. However, tests showed that the two psychrometers could d i f f e r by about 0.6°C and 0.7 mb during calm, sunny weather, so the psychrometer readings were used to calculate mean a i r temperature and vapour pressure only, and were not used to calculate gradients. There was no consistent systematic difference between the psychrometer and thermocouple probe temperatures. Thermocouple and/or psychrometer readings were normally taken over 10 minute periods at cne hour i n t e r v a l s during detailed observations. Hind was measured at three l e v e l s with Casella sensitive anemometers. Due to t h e i r high power reguirements, only 10-minute measurements of wind were taken at each observation; no continuous wind run measurements were taken. Appendix 2 gives a summary of climate data, and indicates the dates of detailed meteorological observations. 6.2 EADIATIOH MODELLING Complete records of net radiation are d i f f i c u l t to obtain because net radiometers reguire considerable atention; furthermore, net radiometers are not as precise as solarimeters. Therefore, i f continuous records over an entire season are wanted, i t i s desirable to model the long-wave portion of the radiation balance i n terms of more eas i l y measured parameters. The radiation balance of a surface can be written: 140 Q* = K* • L* = K| (1-<x) + Li - 14 (6.3) where K* i s net s o l a r r a d i a t i o n , L* i s net long-wave r a d i a t i o n , and <* i s the s u r f a c e albedo. The symbols I and t i n d i c a t e the incoming and outgoing components, r e s p e c t i v e l y . j T h e long-wave r a d i a t i o n emitted by a s u r f a c e i s ; where £. i s the s u r f a c e e m i s s i v i t y , T i s temperature i n K, and <r i s the Stefan-Boltzmann constant, 5.67x10 _ a H m_2K-*. .'For a melting snow s u r f a c e , i f £, i s taken as 0.95, I t i s constant at 300 «/m2. The u s u a l approach to modelling long-wave r a d i a t i o n ( S e l l e r s , 1965; Monteith, 1973) i s to determine the e f f e c t i v e atmospheric e m i s s i v i t y under c l e a r - s k y c o n d i t i o n s as a f u n c t i o n of a i r temperature and vapour p r e s s u r e , and to t r e a t c l o u d -covered sky as a departure from t h i s model. Since only two c l e a r - s k y days o c c u r r e d during the p e r i o d of r e c o r d , a more e m p i r i c a l approach was taken, using d a i l y a i r temperature, vapour pressure, c l o u d cover, and incoming s o l a r r a d i a t i o n as independent v a r i a b l e s i n a stepwise m u l t i p l e r e g r e s s i o n . Weather o b s e r v a t i o n s were taken a t the time of each p r o f i l e measurement, and at l e a s t four times a day on a l l days. Cloud cover was observed a c c o r d i n g to the method which was used on g l a c i e r s observed i n Canada during t h e I n t e r n a t i o n a l H y d r o l o g i c Decade. The c l o u d cover was broken down i n t o low, medium, and high l a y e r s , and each was assigned an o p a c i t y value i n tenths. For example, a t y p i c a l o b s e r v a t i o n might be : 9/10 : 5/10L8 4/10M4. A cloud number, Cn, was then c a l c u l a t e d as f o l l o w s : L t = £ < T T » (6.4) 141 Cn = C L0 L • 0.7C M0 M + 0.36C HO H (6.5) where C i s coverage i n tenths, 0 i s opacity i n tenths, and the factors 0.7 and 0.36 were a r b i t r a r i l y chosen to account f o r the lower radiative temperatures of the medium and high cloud layers. Thus, Cn for the above example i s 0.51. For a d a i l y cloud cover index, the mean of the cloud numbers taken during the day was used. The cloud cover in tenths other than c i r r u s was also used i n the regression, but the calculated cloud number gave much better results. The best predictive eguations, using daily averages f o r 19 days, were: L* = 14.0 " 0.162Ki r*=0.68 s.e.=9.4 (6.6a) L* = -47.0 + 50.9Cn r*=0.65 s.e. = 9.7 (6.6b) with units of H/m*. Air temperature and vapour pressure proved to be insignigicant in the multiple regression model. Eg. 6.6a, which i s not physically based, works egually as well as eg. 6.6b because Cn and K| were highly correlated, with r2=0.85 (r=-0,92). Eg. 6.6a, of course, can only be used for daily averages, and i s only applicable for the months of June and July, from which the data sample was taken. It was decided to use eg. 6.6a f o r estimating d a i l y Q*, since K| was measured every day, while some days had only a small number of cloud observations, or had cloud observations which were not evenly distributed throughout the daylight hours. ;Eg.,6,6b was used for estimates of Q* for shorter time periods. Both eguaticns have the l i m i t a t i o n that no account i s taken of sky conditions at night. Estimated and measured daily average Q* are shown in f i g . 142 -i 1 1 r -i 1 1 1 1 1 r ~\ 1 1 r OA • 0.8-0.7 • 0.6 • !0.5-• o.t-• Point Kitasurt»iei>+s witti iwcro»olt»««t«ir ©Daily averaae, from daily titals of Kt«4 Kt S- Snowfall R: Raih-WI S SSSS R I I INI I s ss I II R SS R I II l l S S R I I I RR RR RRR R R O i — I III I I 5 10 IS" 20 25 30 3S »0 Its SO SS 60 65 10 75 80 85 M«y20 Moy30 T U M I Ju»eH Ju»«29 Jul/1 , July 19 Tul,21 F i g . 6.3 Graph of albedo for the season. F i g . 6.4 Plot of estimated and measured Q*. 113 6.4, and the data used to obtain egs. 6,6 are given i n appendix 5. The error of measured daily values of Q* i s estimated as ±7 M/m2, while that of estimated Q* i s about ±14 W/m2.1 The highest and lowest measured d a i l y values of L<J. correspond to e f f e c t i v e r a d i a t i v e sky temperatures of ~3°C and -18°C, respectively. The l a t t e r temperature i s higher than expected for clear skies; perhaps th i s could be accounted for partly by the surrounding valley walls, but i t could also indicate a systematic positive error i n the measurement of Q*. 6.3 AEBGDYNAMIC ESTIMATES OF TUBBULENT FLUXES Since on the average during t h i s study, radiation accounted for about 90% of melt, Q H and QE are small compared to the error in the term QM~Q*. Therefore an aerodynamic approach, rather than a Bowen r a t i o approach, must be used to estimate Q H and QE. Also, since Q H and QE are r e l a t i v e l y small compared to Q*, for the purposes of this study they do not need to be modeled with any great accuracy. However, i n other environments they may be r e l a t i v e l y more important, so i t i s desirable t c develop methods to estimate them as accurately as possible. The aerodynamic approach to the c a l c u l a t i o n of energy transfer for use i n snowmelt models i s discussed i n Kuzmin (1961) and Anderson (1976), It i s worthwhile to examine t h i s approach in some d e t a i l , i n order to assess i t s usefulness for modelling snowmelt, especially with regard to data reguirements ^Calculated from: s 2 (Q*) = s 2{K*) * s 2 (L*) • 2 cov. (K*,L*) (Freese, 1962). The error of Q* i s reduced over that of L* (confidence l i m i t s about ±20 H/m2 for the la t t e r ) because K* and L* are negatively correlated. 144 and to the complications which arise under strongly stable temperature p r o f i l e s . A s i m p l i f i e d , empirical version of the aercdyna&vic model i s also discussed by the above authors, and i t w i l l be examined below as an alternative to the more physically based model. The basic aerodynamic eguations for energy transfer under neutral conditions, using measurements at two l e v e l s z and z , are: o - pCbkZATAu (6.7a) (In z 2/z, ) 2 Q _ p c p k 2Ae AU (6.7b) y(ln z 2/z, ) * where pep i s the volumetric heat capacity of the a i r , k i s von Karman's constant, 0.40, T i s a i r temperature, e i s vapour pressure, u i s wind speed, and J i s the psychrometric constant. These eguations are developed in several texts (for example. S e l l e r s , 1965; Munn, 1966). Over snow, a bulk approach (Munro, 1975; Anderson, 1976) i s desirable, because the surface temperature and vapour pressure are known exactly, and the temperature and vapour pressure gradients above a convenient height are often too small to measure accurately. Inversion conditions invariably occur over melting sncw; under stable conditions, eg, 6 . 7 must be modified by a s t a b i l i t y correction f (Bi), where Ri i s the Richardson number (Dyer, 1974; Munro, 1975; Anderson, 1976). 2 The bulk aerodynamic eguation f o r a single reference l e v e l z then becomes: 2Mcre precisely, the s t a b i l i t y correction is a function of z/L, where L i s the Mcnin-Obukhov s t a b i l i t y length. However, in practice, z/L i s calculated as a function of Ri. 145 n - / > C p k 2 A T u 2 (6.8) (in z/z 0) z where z 0 i s the roughness length, at which u i s approximately zero. QE i s then calculated from the Bowen Ratio, B=QH/QE-JfAT/Ae, where & i s approximately 0.53 mb/°C at an elevation of 1900 m. Several ways of c a l c u l a t i n g the Richardson number e x i s t : 5 i = T W ( 6 * 9 a ) B i 8 = f ^ z (6.9c) Eg. 6.9a i s the d e f i n i t i v e form, where 8 i s potential temperature ( S e l l e r s , 1965, and others). Eg. 6.9b, where zhl i s the geometric mean of z, and z 2 , fellows from 6,9a i f the substitution e>z=zd(lnz) i s made. It i s v a l i d i f lev e l s z, and z% are net too f a r apart; a r a t i o z 2/z, of from 2 to 4 i s common. In eg. 6.9c, Rig i s known as the "bulk" Richardson number (Anderson, 1976). From the above, i t i s apparent that Bi i s not constant with height. However, conservation of mass and energy require that on the average, Q H and QE do not vary with height. Continuity of eg. 6.8 with height i s maintained because, under non-neutral conditions, the temperature and wind p r o f i l e s depart from the neutral logarithmic p r o f i l e ; i . e . du/d|lnz) and ^8/o(lnz) are not constant with height. Under non-neutral conditions, measurements at a large number of l e v e l s (about 6) are reguired to accurately determine Ri, Q^ , and Qg. Munro (197 5) found that QH and QE could be accurately measured using the bulk approach, with Bi being calculated from detailed 146 p r o f i l e s . Under stable conditions, Ri i s positive, while under neutral conditons i t i s approximately zero. Richardson numbers cal c u l a t d from the various forms of eg. 6.9 varied greatly, due tc the non-neutral p r o f i l e and the low accuracy of the measured gradients . Eg. 6.9b, evaluated from z=1 m to z 0# was chosen somewhat a r b i t r a r i l y for the purposes cf computation. 3 This resulted i n Ri>0,2 for about 10% of the measurements. Ri=0.2 i s an average value for the M c r i t i c a l n Richardson number, above which turbulent transfer ceases (Oke, 1970; Webb, 1965; Munro, 1975; Anderson, 1976). The s t a b i l i t y correction f(Ri) i s taken as (after Dyer, 1974; see also Anderson, 1976): f (Ri) = (1 - 5Ri) 2. (6. 10) Examples of measured wind and temperature p r o f i l e s over 10-minute periods are shown in f i g . 6.5. A t o t a l of 31 three-level p r o f i l e s were measured, as well as a number of 2-level p r o f i l e s . On the average, they indicate a roughness length ZQ of about 10 mm, although t h i s varies widely from p r o f i l e to p r o f i l e . Due to the smoothness of snow, the extrapolated distance from the lowest measurement l e v e l to z 0 i s large; furthermore, the apparent value of z 0 w i l l depend on the degree of s t a b i l i t y , with the extrapolated p r o f i l e giving an overestimate of z0 under stable conditions (Munro, 1975). Taking t h i s into account, and considering values of z0 measured i n other studies (table 6.1), a value of z„=5 mm was chosen for purposes of computation. (This cannot be considered a '•measured" value of z 0 , since the 3E<js. 6,9b and 6,9c are i d e n t i c a l i n form, d i f f e r i n g only by a factor which, i n e f f e c t , r e f l e c t s the heights at which the Richardson numbers are computed. 147 TABLE BOUGH NESS LENGTHS 07EB SNOW. Some values of z 0 as reported i n the l i t e r a t u r e . : SOUBCJ z 0 imm) COMMENTS Price and Dunne, 1976 5 Melting seasonal snow. Fohn,1973 5 Suncupped gl a c i e r snow. Munro, 1975 0.07 Glacier ice (his procedure i s guestionable). ,, O.07 Quoted; snow-covered lake ice, 0.12 Quoted; Antarctic snow., Kuzmin, 1961 0.5 Smooth snow. 6 Shallow snow with protruding stubble. , Anderson, 1976 1.5 to 5 Melting seasonal snow. 2 .3 Quoted from Sverdrup; melting g l a c i e r snow. Wendler and Weller, 1974 2.4 Glacier i c e . 0.9 Glacier snow. 148 5.0 2.0 0 LO Wind speed (w/sec) 3-0 2-0-1.0 -0-5 0-2 O.I aos 0.02 0.01 -| r June 17 June 18 8 to 10 12 (°C) F i g . 6.5 Examples of wind and temperature p r o f i l e s . L i n e s are f i t by eye. 149 F i g . 6.5 (cont.) 150 roughness length i s defined in terms of a wind p r o f i l e under neutral conditions, which were never observed i n t h i s study.) A noticeable feature of the temperature and wind p r o f i l e s i s that the temperature gradients are r e l a t i v e l y much less steep than the wind gradients; i . e . the average position of the z-axis intercept (sometimes c a l l e d z H) i s three tc four orders of magnitude less than z 0 (assuming that at z H , T=0°C). Furthermore, both wind and temperature p r o f i l e s are substantially l i n e a r with respect to log z i n the measured range (about 0.3 to 2.0 m). This suggests near-neutral p r o f i l e s in t h i s range, overlying a layer close to the snow surface i n which the temperature gradient i s very steep; in t h i s lower layer, turbulent transfer i s therefore probably strongly damped by the extreme s t a b i l i t y of the temperature p r o f i l e . F i g . 6,5 i s f a i r l y t y p i c a l of p r o f i l e conditions. Complex temperature s t r a t i f i c a t i o n ( i .e. reversals of the lapse rate within the measurement layer) was never observed, although complex wind s t r a t i f i c a t i o n occurred on some occasions, possibly indicating katabatic drainage. The fetch was les s than i d e a l , with clumps of trees and topographic r e l i e f features situated within 50 m of the s i t e i n some di r e c t i o n s ; however, since the surrounding area was completely snow-covered during the measurements (except f o r scattered clumps of tre e s ) , a s i g n i f i c a n t advective s i t u a t i o n did not exist. Observed wind speeds at t h i s s i t e were much lower than those commonly reported from studies on g l a c i e r s ; wind speed r a r e l y exceeded 2 m/sec, and averaged 1.3 m/sec. During the 10-minute wind observation periods, i t was noted that sporadic 151 gusts of wind, la s t i n g a few seconds to about a minute, often occurred. It i s possible that most of the turbulent transfer under such conditions takes place during these gusts, which probably are eddies set up by large roughness elements upwind, such as trees or topographic obstacles. This suggests that under conditions of low wind speed and l e s s - t h a n - i n f i n i t e fetch, turbulent transfer does not take place i n the l a t e r a l l y and temporally homogeneous manner assumed by the aerodynamic model. Fig. 6,6 shows an example of the v a r i a b i l i t y of wind speed over a one-hour period. This graph suggests that 10-minute wind averages, which were used in t h i s study, are not s u f f i c i e n t to represent the average wind speed over one-hour periods, and that continuous wind run should be recorded i n a study of t h i s type. Secondly, the v a r i a b i l i t y of wind speed suggests that, since eg, 6.8 i s non-linear, aerodynamic flux estimates using 10-minute average wind speed and temperature may be biased, probably on the side of underestimating the flux, Aerodynamic estimates of Q H and QE were calculated from eg. 6.9 for each p r o f i l e measurement, using a reference height cf 1 m. Average 10-minute wind speed, and average 10-minute temperature and vapour pressure frcm psychrometer readings were used, standardized to 1m using z 0=5 mm and ZH=10~ 3 mm. Results for several days are shown on f i g . 6.7, along with hourly estimates of net radiation, calculated from eg. 6.6b. P r o f i l e measurements were normally taken for 10-minute periods at the half-hour, i n order to compare as well as possible with hourly radiation t o t a l s . Actual measured net radiation i s also shewn on f i g . 6,7 where available. On July 16 and 17, the 1 m* lysimeter 152 T 1 1 1 r Time (biin-) Stai-tinj 1300, July 16 F i g . 6.6 V a r i a b i l i t y of wind speed over time, July 16. 153 <K»r-300 200 5loo 50 -e-Q« — QH — 0E equation) QH — o£ (from ewplHcol equation ) 0800 June 7 June 8 July 5 tool 300 200 < 3 100 0 50 Q X QM (measured Wi+li lysimetti-) 0600 1600 0000 080O July 6 July 16 NT OOOO 0800 July 17 F i g . 6.7 Energy balance calculations for several days. (The lysimeter melt shown for July 16-17 lags s l i g h t l y behind the surface melt, due to the 15 to 20 cm thickness of snow above the lysimeter.) was close enough to the snow surface (about 20 cm) to measure melt continuously without excessive time lag or flow divergence due t o i c e layers. Melt rates frcm the lysimeter are indicated on f i g . 6.7; they support the contention that net radiatio n accounts for almost a l l the snow K e l t . , &n alternative to using the physically-based aerodynamic formulae i s to use empirical wind functions. This approach i s att r a c t i v e because of the uncertainties introduced into the bulk aerodynamic eguations by non-logarithmic p r o f i l e s and the guesswork involved i n c a l c u l a t i n g the Bichardson number. Empirical wind functions have been based on lysimeter studies of evaporation and condensation over snow, and also on energy balance studies, c a l c u l a t i n g parameters to take into account average surface and s t a b i l i t y conditions. The eguations are of the form: QE = f (u)Ae (6. 11a) f (u) = a + bu (6.11b) where a and b are empirical constants, and a is usually taken to be zero. I t then follows that: Q H = iff (u)AT . (6. 11c) If a=0, t h i s eguation i s eguivalent to eg. 6.8, the only difference being that the terms calculated from wind p r o f i l e data are replaced by the empirical constant b. Anderson (1976) quotes several values of b frcm the l i t e r a t u r e and from his own res u l t s , ranging from 5.0 to 10.5 J m~3mb~-1. Kuzmin (1961) gives calculated values of b, incorporating empirically-determined s t a b i l i t y corrections, of frcm 4.1 to 8.1, depending on z 0. He also gives average 155 experimental r e s u l t s from lysimeter studies of b=4.7 and a=5,8, i n units compatible with the above. . for the purposes of comparison, QH and QE were calculated frcm eg. 6.11, using a=0 and b=5.95, the value obtained by the U.S. Army Corps of Engineers, guoted by Anderson. The values of Q and Q so obtained are shown on f i g . 6.7. This method i s equivalent to using a constant s t a b i l i t y correction i n eg. 6.8, instead of computing a Bichardson number for each p r o f i l e measurement. Because of the d i f f i c u l t y i n c a l c u l a t i n g the Bichardson number from simple observations, t h i s approach i s preferable for hydrological studies, provided that a suitable average set of constants can be estimated for the environment i n guestion. The actual values of a and b depend on the exposure, vegetation, and r e l i e f c h a r a c t e r i s t i c s of the s i t e , on surface roughness, and on the reference height. The l a s t two factors are accounted for i n the formulae given by Kuzmin.• f i g . ,6.7 shows that the empirical approach gives very similar results to the more detailed aerodynamic ca l c u l a t i o n s . The main difference i s that the fluctuations over the day are smoothed; t h i s i s due to the use of a constant value instead of the highly variable f{Bi) i n eg. 6.8. Once the empirical constants have been calibrated f o r a given l o c a t i o n , t h i s approach i s preferable for c a l c u l a t i n g daily averages of Q H and Q^ , because of the reduced data reguirements. 6.4 DAILY MELT TOTALS In an attempt to extend climate-based melt estimates to the entire snowmelt season, daily energy balance t o t a l s were 156 calculated using net radiation estimated on a d a i l y basis (Q* e ) from measured solar radiation and eg. 6.6a, and using d a i l y screen temperature and vapour pressure. A computation based on dai l y averages i s preferred over hourly computations for a long-term energy balance, because of the simpler data reguirements, and because i t f a c i l i t a t e s comparison with d a i l y snowmelt measurements. However, there are several problems associated with using d a i l y averages: 1. Night-time sky conditions a f f e c t i n g long-wave radiation are not known. Also, since negative net radiation at night often causes freezing of the surface snow, the da i l y energy balance should i d e a l l y be taken from sunset to sunset, instead of from midnight to midnight. Errors due to these factors tend to cancel out over periods of several days. 2. Daily wind run was not measured; daily average wind was taken to be the average of spot measurements taken during the day. Since winds tended to be calmer at night, the daily wind averages may be biased. (If wind run had been a v a i l a b l e , separate day and night calculations would have been an improvement). 3. Screen temperatures and vapour pressures were s l i g h t l y d i f f e r e n t than those measured with the Assmann psychrometers; the average differences were 0.8°C and 0.6 mb lower than the psychrometers, respectively. Corrections were not made, since the differences are small, and there i s no reason to suppose the psychrometer readings are more accurate. Complete meteorological records are available for 32 days out of the 51 day snowmelt period. This period was used to 157 compute a value for b i n egs. 6.11 (assuming a=0), by taking the turbulent energy balance terms as a residual of observed melt and estimated net radiat i o n . As a f i r s t step, d a i l y sensible and latent heat fluxes were calculated from eg. 6.8, using no s t a b i l i t y c orrection; these are referred to as QH* and QE-», The average values for the 32 day period are: Q M : 83.6 W/mz (7.22 MJ m-2day-*) Q% : 76.4 w/m2 (6. 60 MJ a -aday-i) QH'+QE': * * . 5 w/mz (3.84 BJ m-zday-i) Thus, energy from radiation accounts for 91% of the observed melt, and on the basis of the mean values, the eguation for melt i s : Q M = Q*e + 0.16(Q H» • Q E») (6.12) which i s eguivalent to an average s t a b i l i t y correction f a c t o r i n eg. 6.8 of 0.16. This corresponds to a value of b=1.9 J m- 3mb-» in egs. 6.11. Since both Q*e and Q M are possibly subject to an unknown bias, with that of Q*e being perhaps ±5%, the uncertainty i n t h i s factor i s high, and b could range from, very roughly, 0.5 to 3.5 J m—3mb_1. A correlation analysis on the data used i n the above calculations produced the interesting result that the highest correlation for i s with temperature, r 2-0.63, while the co r r e l a t i o n between Q M and Q*e i s r 2=0.51. This r e s u l t i s somewhat paradoxical, i n that 91% of the energy reguired for melt i s accounted for by Q*e. The energy balance for the entire 51 day melt period (June 7 and 8, and June 14 to August 1) was computed using egs. 6.11, with the above value for b. Actinograph records were used tc f i l l i n 9 missing days of solar radiation, and the o v e r a l l 158 average wind speed of 1.3 m/sec was used for 14 days with no wind record. Since the period i s e s s e n t i a l l y continuous, errors i n the measured snowmelt are minimal. The data set i s tabulated in appendix 6. The t o t a l calculated energy balance for the 51 day period i s shown i n table 6.2. On the average, net radiation accounts for 91% of the t o t a l melt energy, sensible heat flux accounts for 9%, and latent heat flux averages zero over the period. Over the t o t a l period, the error i n Q M i s due to the error i n estimating the l i q u i d water content; t h i s may be about ±4%. The error i n Q*e , as estimated e a r l i e r i n this chapter, i s about ±20% on a daily basis; i f a 10% error i s inherent i n the measurement of Q*, and the remainder i s due to the error of estimate, the error i n the average Q*e over the period would be about ±12%. ,Q H was calculated, i n ef f e c t , as a residual of Q M and Q*e ; thus, i t s error i s approximately ±100%. for 30 of the 51 days, runoff t o t a l s from hydrograph separations are available. An energy eguivalent of the snowmelt runoff, QM(n) # was calculated from eg. ..6.2, using a l i g u i d water content of 8%, as before, and by assuming a 10% larger watershed area to account for the discrepancy in the water balance observed in chapter 5. I t i s d i f f i c u l t to assign an error to Q M ( P J » b u t i t i s probably s l i g h t l y greater than the error i n QM . The results of this c a l c u l a t i o n are plotted on f i g . 6.8, and are summarized i n table 6.2. Although the agreement of o v e r a l l t o t a l s i s good, i t i s apparent frcm f i g . 6.8 that the agreement of calculated melt with QM and QM(R) i s poor f o r some days of high snowmelt runoff. The days of poorest agreement are days on 159 TAELE 6j_2 ENEBGY BALANCE SOMMABY. K* 97.4 (8.42) L*c -25.3 (-2.19) Q*e 72.1 (6.23) QH 7.2 (0.62) QI 0.3 (0.03) 7.5 (0.65) A. Summary of the average daily radiation and energy balances for the 51-day snowmelt period. (Figures are in W/m2, with MJ m-zday - 1 i n brackets.) Net solar radiation Net long-wave radiation Total net radiation Sensible heat flux latent heat flux Total turbulent flux Calculated melt energy Q M(calc.) =Q*+QH+Q£ 79.6 (6.88) Observed snowmelt 82.3 (7.11) B. Summary of average daily runoff and energy balances for 30 days, i n W/m2 (and MJ m-2day-2) . Observed snowmelt QM 89.0 (7.69) Calculated melt energy Q r t(calc.) 88.8 (7,67) Energy equivalent of observed runoff Q-M(R) 91.5 (7.91) 160 Calculated welt energy , (W/W) F i g . 6.8 Plot of calculated d a i l y melt vs. observed melt and the watershed runoff energy equivalent. 161 which high convective melt was observed; the f a i l u r e to explain these high convective melt events may be due to the lack of adequate wind data. The value of b=1,9 J m-3mb_* calculated above i s considerably lower than the values reported i n the l i t e r a t u r e . This may, at least p a r t l y , be a result of the lack of wind data at night; the daily averages are probably biased towards the higher daytime speeds. A positive bias in Q*e, i f i t e x i s t s , would also contribute to a low value of b. The energy balance t o t a l s i n table 6.2 suggest a s l i g h t l y higher value for b, about 2.6 J m_3mb-i, which i s within the range for b mentioned above., However, since the turbulent fluxes are a small residual between large values of and Q*e , the error attached to b i s high, and i t can be safely concluded only that b i s a value less than about 5 J m~3mb-1. The energy balance estimates of melt at the meteorological s i t e are probably reasonably representative of the ent i r e watershed, since the t o t a l area i s small and the t e r r a i n i s not excessively variable. The t o t a l seasonal ablation over the watershed (see chap. 2) was about 5% greater than the t o t a l ablation at the s i t e , although t h i s discrepancy disappears i f the sloping area of the watershed i s used, instead of the map area. Areas of greater slope i n the watershed would be expected to have a s l i g h t l y lower proportion of melt due to r a d i a t i o n , because of the northerly aspect, and a s l i g h t l y higher proportion of melt due to turbulent transfer, because of greater exposure to wind. 6.5 DISCUSSION The main conclusions which can be reached from the energy balance results are: 1. About 90% of the melt over the snowmelt period can be accounted for by net radiation. This proportion i s higher than that reported i n most s i m i l a r studies on glaciers (Patersom, 1969). The proportion of turbulent transfer i s small because of low temperatures and wind speeds during the snowmelt period. 2. Sensible and latent heat fluxes are important only on a few warm, windy days. Latent heat flux averaged close to zero, as evaporation and condensation roughly balanced over the season. 3. Bulk turbulent transfer estimates based on a semi-empirical wind function are preferable to the more detailed aerodynamic method, since overly elaborate p r o f i l e methods are necessary to apply the l a t t e r method accurately. U, I t i s f e a s i b l e to model net rad i a t i o n with acceptable accuracy, using measured solar r a d i a t i o n and cloud observations. The p o s s i b i l i t y of a systematic overestimate of net radiation in t h i s study ex i s t s , and t h i s may have biased the c a l c u l a t i o n of the turbulent transfer terms. 5. Eesides an estimate of net r a d i a t i o n , the e s s e n t i a l information needed to estimate snowmelt i s a continuous record of temperature, humidity, and wind. A breakdown of the calculations into separate day and night periods would be an improvement over calculations on a daily basis. 163 CHAPTER 7 THE LATE SEASON HATES BALANCE A determination of the water balance of the watershed for the remainder of the summer following snowmelt i s useful i n evaluating the importance of the l a t e season release of snowmelt water from storage i n s o i l moisture and groundwater reservoirs. As discussed in chapter 5, the water balance eguation for any period can be written: Q = P + M - E - A S <5.2) with units of volume. In the late season, M i s the runoff contribution from the ablation of small lin g e r i n g snow patches. Fie l d work at the study watershed was sporadic after Aug. 2, by which date about half of the watershed area was snow-free. However, stream stage, solar r a d i a t i o n , temperature, r e l a t i v e humidity, and p r e c i p i t a t i o n were recorded during most of the period from Aug. 2 to Oct. 8, with a few interruptions due to instrument f a i l u r e . Therefore, i t i s possible to make rough estimates of the components of the water balance during t h i s period. 7.1 SOIL MOISTURE AND GROUNDWATEE DEPLETION S o i l moisture samples were taken regularly from f i v e test locations for the gravimetric determination of s o i l moisture. , Two locations near the meteorological s i t e were sampled more frequently than the other three locations, which were at three of the snow course points. Sampling from the B-horizon began as scon as the s i t e s were snow-free.,Samples were also taken from the A-horizon, beginning with samples taken beneath the snow using the Mt. Rose snow sampler. However, the A-horizon i s very 164 high i n organic material, and the water content of a sample proved to be determined mainly by the organic content; therefore, the A-horizon samples could not be used to determine s o i l moisture changes over time. The B-horizon samples were taken from about 15 cm deep i n shallow p i t s , with successive samples being taken as close together as was p r a c t i c a l . The s o i l at a l l the sample locations i s derived from t i l l , although s o i l s derived from c o l l u v i a l and f l u v i a l deposits cover part of the watershed. Grain size analyses were performed cn samples from a l l f i v e locations. These analyses, along with one ad d i t i o n a l sample from the underlying t i l l , are given i n table 7,1, They indicate a composition of about 20% gravel, 25% sand, and 55% s i l t and clay, A sketch map dividing the watershed into four broad s o i l drainage and vegetation categories was drawn to aid i n the interpretation of s o i l moisture and evaporation data; t h i s map i s shown i n appendix 1, The s o i l s covering about 10% of the watershed area remained saturated throughout the summer, and a further 60% was at or near saturation at the time snowmelt was complete. A shallow p i t was dug near the meteorological s i t e at a location where the water table was near the surface, to provide an index of water table flu c t u a t i o n . A record was also kept of the water l e v e l in a small pond which had no surface outlet a f t e r i t stepped receiving surface runoff from snowmelt. The r e s u l t s of these observations and of the s o i l moisture measurements are shown in f i g , 7.1. It i s obvious that the sampling density of s o i l moisture 165 TABLE T.J SOIL ANALYSES. Notes: 1. Analyses were performed using sieving and hydrometer techniques. 2. The r e s u l t s are expressed as percentages of dry mineral material under 2 mm i n size. 3. A l l samples, except the t i l l sample, are from the B-horizon. For locations, see appendix 1. The t i l l sample was taken from t i l l exposed at the stream gauge i n s t a l l a t i o n . SAMPLE FRACTION A B 4b 5b 9b TILL clay (<4yu) 12 14 17 14 16 15 s i l t 53 52 55 59 55 82 sand (63ju-2mm) 35 34 28 27 25 3 100 100 100 100 100 100 gravel (>2mm) 21 30 18 35 23 1 organic material {from hydrogen peroxide treatment) 4 4 6 5 5 0 (from ashing at 350°C) 10 10 15 13 14 1 bulk density (gm/cm3) 0. 79 0.82 0.70 0.73 1.3 porosity 0. 68 0.67 0.70 0.70 0. 50 166 T—r- 1 1 1 B horizon soil tnois+ure * All point* Measured 0 Mean of finis A «>MI 0 3 1 0 0 •t-Jt S 0.70 3 0.60 J 050 O.«t0i-10 liJ" .o 0 5-.J im 1, , r f f l n 0 ,n - Ground j « r f « e I o 30 V 20 10 G-rouriidvo+ei' level i n p i t hear rneteorofoaical S i t e I- 8otto>» of pit Approximate hioh k«ter level 80 70 60 5 0 <«[-30 20 10 Pondi wafer level (Pond «r ea * 120 w.1) V 80 <?0 100 110 120 (30 tW 150 July 21 A « « 8 A«j. 18 Auj.28 Sept. 7 Sept 17 S«pt.27 Ott.7 F i g . 7.1 S o i l moisture and groundwater l e v e l s for August, September, and early October. 167 and groundwater observation sites must be many times greater than was used i n t h i s study i f the re s u l t s are to represent any more than an approximate index of water los s . However, an approximation of the storage changes represented by the range of th i s data was made as follows. For a s o i l with a bulk density of 0.76 gm/cm3 and a porosity of 0=0.69 (the average of the f i v e s i t e s ) , and for an average depth cf 40 cm, a drop in the water content by weight, , from 0.79 tc 0.58 would represent a loss of water of about 60 mm, or 2400 ra3 from the entire watershed. I f the groundwater l e v e l were to drop by 30 cm i n a s i m i l a r s o i l , r e s u l t i n g i n a drop of the volumetric water content from p to about 0,150, the re s u l t i n g loss of water would be about 50 mm, or 2000 m3. (In t i l l with 0=0.5, t h i s r e s u l t would be about 1500 m3.) Thus, over the period from Aug. 1 to Oct. 11, the storage change due to the release of water from s o i l moisture and groundwater appears to be i n the order of 4000 m3. Because of the inadequacies of sampling, th i s must be considered an order of magnitude estimate only. 7.2 EVAPORATION ESTIMATES The aerodynamic approach to the estimation of evaporation, as used in chapter 5, requires wind and vapour pressure data, as do other semi-empirical approaches such as that of Penman (1956). These methods cannot be used here because wind data was not c o l l e c t e d , except for a few days, durinq the late summer and f a l l . Stewart and Rouse (1976) tested a model for evaporation 168 from tundra surfaces based on radiation data; t h i s model has the advantage that i t was developed i n an environment si m i l a r tc that of the present study area. This model i s based on the equilibrium evporation model of P r i e s t l y and Taylor (1972). Stewart and Rouse found that evaporation from a tundra surface cculd be described by the equation: Q E = « X ~ ( Q * - Q ) (7 .1) where s i s the slope of the saturation vapour pressure curve at the ambient a i r temperature, & i s the psychrometric constant, and i s an empirical constant depending on vegetation type and moisture supply. ( Q * , Q E , and Q$ are as defined in eg. 6.1a; note that the sign conventions are different from those used in the rest of chapter 6.) For poten t i a l evaporation from f r e e l y transpiring plants with no s o i l moisture l i m i t a t i o n s , o*. was found by P r i e s t l y and Taylor (1972) to be 1.26. Rouse et a l (1977) found that t h i s value was applicable for several di f f e r e n t environments, and they give ether values of oc ranging down to about 0.95 for r e l a t i v e l y dry lichen-heath tundra.. E s s e n t i a l l y , t h i s model provides a means of p a r t i t i o n i n g the energy available at the surface between Q H and Q E, which i s equivalent to computing the Bowen ra t i o . (For example, at 15°C, i f ot = 1.18# the guantity c*s/ (s + fr) =0.80, which corresponds t c a Bowen Ratio of 0.25.) For one-day periods, Q S can be assumed to be approximately zero. (This i s not s t r i c t l y true; on sunny, hot days following cool, cloudy days, QQ. w i l l be po s i t i v e , and for the reverse s i t u a t i o n , Q & w i l l be negative. Over periods of a week or longer, however, t h i s assumption i s not unreasonable.) 169 Stewart and House (1976) successfully calculated evaporation on a da i l y basis from t h i s formula, assuming that Q&=0 and using values of Q* modelled using incoming solar radiation. For the present study, eg. 6.6a was used to model L|; this i s somewhat les s than i d e a l , since eg. 6.6a i s based on data collected i n June and July, when the days are longer than in August and September. This might r e s u l t i n a s l i g h t bias towards an overestimate of Q*.,Lt was calculated using a l i n e a r approximation to eg. 6.4, assuming that mean da i l y a i r temperature, T, and surface temperature are equal. The albedo at the meteorological s i t e was 0.20, and the re s u l t i n g eguation used for estimating daily net radiation i s : Q*e = 0.638K4, + 14.0 - 4.76T (7. 2) with units of 8/m2. This equation i s very similar to the one given in Stewart and Rouse (1976) for low-elevation tundra near Hudson Bay.* A value of <*=1.26 was used for the 70% of the watershed area which has ample s o i l moisture (see map in appendix 1), and c<=1.00 was used for the remainder; t h i s results in an average of cx=1,18 f o r the watershed. The thermohygrograph was not operating after Sept. 16, so for the period u n t i l Oct. 5, the mean a i r temperature for the f i r s t half of September, 6°G, was used. (Temperature records f o r Shalalth, Pemberton, and Lajoie Dam indicate that the mean *Stewart and Rouse give two eguations, for half-hourly periods, for a dry tundra ridge and a wet meadow, respectively: (Q*-QG) = -60 * 0.634Ki, and (Q*-QG) = -32 + 0.7365KJ,, with units of W/m2. This suggests that net radiation i s f a i r l y conservative over tundra surfaces with s i m i l a r albedo, i n d i f f e r e n t locations. 170 temperature for t h i s period was within 1°C of the mean temperature for the f i r s t half of September.) Since s/ts + Jf) and It are slowly changing functions of T, t h i s approximation i s acceptable over periods of a week or more. Also, actinograph data i s missing for 5 days; for these days, K4- was estimated using a simple regression with the nearest radiation s t a t i o n , Vancouver, This gives an unreliable estimate f o r any given day, but f o r longer periods, i t should not introduce any major error, (Radiation and p r e c i p i t a t i o n records for September and early October indicate that weather patterns were s i m i l a r at Vancouver and at the site.) The net radiation and evaporation estimates are summarized in table 7.2. Net radiat i o n was measured d i r e c t l y for only one day, Aug. 31, but for t h i s day, the agreement between the measured and modelled figures i s very close (115 and 118 H/m2, r e s p e c t i v e l y ) . As a check cn the evaporation c a l c u l a t i o n s , a Weather-Measure evaporimeter was i n s t a l l e d at the meteorological s i t e . This instrument measures the evaporation from a disk of f i l t e r paper connected by a wick to a reservoir of water. It was placed in a screen which protected the instrument from dire c t solar radiation and r a i n , but which had open sides to allow free c i r c u l a t i o n of a i r . The daily readings from the evaporimeter, i n arbitrary units, are included in table 7.2, and are plotted against the evaporation estimates as a double mass curve in f i g . 7.2. This curve shows some differences, as would be expected, since eg. 7.1 i s based almost e n t i r e l y on radiation, and the evaporimeter i s influenced by wind, temperature, and vapour 171 ls.2 LATE SEASON E V A P O B A T I O N . Evaporation i s calculated from eq. 7.1. Evapcrimeter readings are in ar b i t r a r y units, *E* indicates estimate based cn Vancouver radiation data. CALCULATED EVAPOR- CALCULATED EVAPOR-15 ATE Q* EVAPORATION IMETER DATE Q* EVAPORATION IMETER {S/m2) (mm/day) READING <W/m2) (mm/day) BEADING Aug 1 58 1.4 1.8 Sept 3 9 0. 2 0. 4 2 21 0.5 1.0 4 11 0.2 0.6 3 70 1.7 1.3 5 36 0.7 0.5 ii 40 1.0 1.0 6 70 1. 3 5 48 1. 1 1.0 7 125 2.4 6 119 3.0 2.0 8 134 2. 8 7 38 0.9 0. 8 9 110 2.6 8 68 1.6 1.2 10 93 2. 2 9 81 1.9 1. 1 11 71 1.6 10 133 3.4 2.3 12 61 1.3 11 71 1.7 1.6 13 33 0.7 12 115 2.7 2.5 14 64 1. 4 13 46 1.0 0. 7 15 109 2.5 14 98 2.1 1.3 16 89 2. 1 15 104 2.3 1.9 17 44 1.0 16 13 0.3 0.3 18 99 2. 2 17 38 0.8 0. 4 19 104 2.3 18 29 0.6 1,6 20 94 2. 1 19 38 0.8 0.3 21 97 2.1 20 127 2.6 1.1 22 17 E 0. 4 21 81 1.7 1.3 23 31 E 0.7 22 33 0.7 0.5 24 55 E 1.2 23 51 1.1 0. 8 25 92 E 2.0 24 101 2.2 1.4 26 80 1.8 25 58 1.2 0. 6 27 89 2.0 26 76 1.5 0.4 28 54 1.2 27 22 0.5 0.4 29 67 1.5 28 15 0.3 0.5 30 81 1. 8 29 91 2.2 3.3 Oct 1 50 1.1 30 115 2.8 3.5 2 54 1.2 31 118 2.9 2.3 3 61 E 1.3 Sept 1 94 2.2 1.3 4 41 0. 9 2 50 1. 1 0. 8 5 51 1.1 172 F i g . 7.2 Plot of calculated evaporation vs. evaporimeter data. The dashed l i n e i s f i t by eye. 173 pressure. However, the agreement between the two methods i s guite good over f a i r l y long periods. From f i g . 7.2, a conversion factor of 1.21 mm/day per evaporimeter unit was obtained by f i t t i n g a straight l i n e by eye to the data. 7.3 THE WATER EALANCE Pre c i p i t a t i o n was measured with a recording tipping-bucket rain gauge after Aug. 1, as well as by the two storage gauges used a l l season. The snowmelt volume after Aug. 1 was estimated by calcu l a t i n g an average snow cover for each period of int e r e s t frcn the snow cover depletion curve, and by using rough estimates of ablation, which was not measured d i r e c t l y with stakes (see chapter 5). The season was divided into several periods of varying length, based on the a v a i l a b i l i t y of data and on the appearance of the seasonal hydrograph (appendix 3). The water balance t o t a l s for each period are tabulated i n table 7.3. For each period, the discharge was summed on a daily basis, rather than using hydrograph separations as i n chapter 5; thus, a drop i n discharge from the beginning to the end of the period indicates a l o s s of water from storage i n s o i l moisture or groundwater. The storage term, AS, was calculated as a residual from eg. 5.2. The errors i n the terms of the water balance eguation are indicated i n table 7.3. Over the period frcm Aug. 9 to Oct. 5, the t o t a l loss of water from storage was about 4300 m3, with an error of estimate of about ±15 tc 20%. An additional 2000 m3 (± at least 60%) was released during the period of p a r t i a l snow cover frcm July 31 to Aug. 8; the error of thi s estimate i s high 174 TflELJ 7.J LATE SEASON WATER BALANCE SUMMARY. , PERIOD DAYS Q M P E S error discharge snowmelt precip. evap, residual of S Jy.31-Au.1 2 1990 1920 80 60 -50 Aug. 2-8 7 6350 3200 1440 210 -1920 ±60% Aug. 9-15 7 1900 390 320 57 C -1760 ±15% Au. 16-S.3 19 1880 10 1930 1000 -940 ±35% Sept. 4-6 3 missing 0 1120 90 ( + 680) ±50% S. 6-Oct.5 29 860 0 430 1860 -2290 ±20% Notes: 1. A l l data are in m 3. 2. AS f o r Sept. 4-6 i s estimat ed from hydrograph separations. Errors (over periods of one week or more): Q - +5% M - ±35% P - ±10% E - ±2 5% TABLE 7.4 WATER BALANCE OF RAINSTORMS. DATE TOTAL SURFACE CF STORM RAINFALL RUNOFF1 RUNOFF2 REMARKS (mm) (%) (%) Aug. 8 13.7 83 19 10% snow covered Aug. , 16 7. 5 86 14 Aug. 19 18.1 91 13 Aug. 22 5. 5 113 14 Aug. 27 10.0 69 13 Sept. 4-6 28. 4 ? 7 discharge record incomplete Notes: 1 Calculated as Q/(P-E), where E i s the evaporation during the discharge period. 2 calculated as (storm runoff)/P 175 because of the imprecise estimates of snowmelt volume during t h i s period. The t o t a l of about 6000 m3 i s somewhat higher than the very rough estimate of 4000 m3 made above f o r the release of water from storage. Part of the discrepancy could be due to an overestimate of evaporation, but t h i s would be unlikely to account for mere than about 500 m3. An underestimate of the amount of water released from groundwater and s o i l moisture storage i s more l i k e l y ; there may be reservoirs of water i n boggy depressional areas or in pockets of f l u v i a l or c o l l u v i a l material which are larger and more active than the s o i l reservoirs which were sampled. This late season release of about 6000 m3 of water derived from snowmelt i s small compared with the t o t a l snowmelt volume for the season of 48,000 m3. The main significance of this release i s the maintenance of late-season streamflow during periods when evaporation exceeds pr e c i p i t a t i o n . I t may also be s i g n i f i c a n t early i n the snowmelt season of the following year, since the water lost from storage in the summer must be replenished either by autumn rains or snowmelt the following spring, or both. In 1976, the volume of wafer l o s t from storage i s eguivalent to about 8 days of strong melting. A v i s i t to the s i t e in October, 1977, following a winter of low snow accumulation and a hot, dry summer, showed that the water l e v e l s i n streams, ponds, and swampy areas throughout the region were much lower than at the same time in 1976. (The stream was s t i l l flowing i n the study watershed.) This suggests that i n longer, d r i e r summers, a much greater volume of water might be released from storage than was observed during the 176 study season, 7.4 STBEAM BESPONSE TO PBECIPITATION AND OTHEB EVENTS An examination of the response of the stream hydrograph to rainstorm events i s useful for int e r p r e t i n g the role of the channel and surface flow network in the response of the hydrograph to snowmelt events. In p a r t i c u l a r , the response time of the stream to a rainstorm, and the proportion of water frcm a storm reaching the stream as d i r e c t surface runoff (or stormflow; see f i g . 7.3), are of i n t e r e s t . A comparison of the water l e v e l recorder and the r a i n gauge charts shows that the response of the stream to a rain input i s e s s e n t i a l l y instantaneous, within the l i m i t s of resolution of the r a i n gauge. (One t i p corresponds to 0.35 mm of r a i n , and the time resolution of the chart i s about ±0.25 hr.) Therefore, the response time of the channel network was neglected i n interpreting the movement of water through the snowpack-watershed system in chapter 4, Six d i s t i n c t rainstorms occurred during August and September. The volume of runoff generated by each of these storms was calculated as the volume under the hydrograph from the beginning of the r i s i n g limb to the point where the recession limb reached the same discharge as the sta r t i n g point (see f i g . 7.3); t h i s procedure assumes that storage changes are zero between two points of egual discharge on the hydrograph. (The assumption i s true i f the watershed behaves as a l i n e a r reservoir.) The volume of surface runoff was determined by drawing a rather arbitrary l i n e separating i t from recession 177 Auj.27 Auj.28 Au3. 21 Auo.30 Aug- 31 Sept. I Sept.2 a. Storm of Aug. 27. Note the diurnal f l u c t u a t i o n in the recession limb, discussed i n section 7.4. 0™ UJ CO 0 ° S+ormf low Partly Showmelt Record incomplete. \ (Recession flow, Sept. ^ - 6 (2(0 r« 3 ; A S » + 6 8 0 m ^ ) ^ . - , I Rainfall I 2 .^8 mm jm Ll (+ 3.6 ww vie. Snow on Sept. 50 6 ) Recession flow, Sept. 7-11 (280m J; E=W0m 3 ; A S * -680 m 3, from t^.S-l) Sept. 3 Sept. 4- Sept. 5 Sept.6 Sept. 7 Sept. 8 Sept."? Sept. 10 Sept. II b. Storm of Sept. 4-6; estimation of AS for the period of incomplete hydrograph record. F i g . 7.3 Hydrograph separation procedure for rainstorms. F i g . 7.4 Hydrograph for the period Sept. 12 to Oct. 9. The figure i s a photocopy of the stage recorder trace. 178 flow ( f i g . 7.3; after Linsley, Kchler, and Paulhus, 1975, p.., 230) . The hydrograph of the biggest rainstorm, on Sept. 4 to 6, i s incomplete because of instrument f a i l u r e . The change i n storage for t h i s period was estimated by c a l c u l a t i n g the change in storage represented by the recession portion of the hydrograph ( f i g . 7.3b), using eg..5.2; i f , by the above assumption, the net change of storage over the period of flow from the storm i s zero, the storage component f o r the missing period can be calculated. The water balance components of six storms are summarized in table 7.4..The discrepancies between the observed p r e c i p i t a t i o n and the calculated sum of discharge and evaporation are probably due partly to inaccurate estimates of evaporation (which f o r these short periods are probably subject to an error of at least ±50%), and partly due to the i n v a l i d i t y of the l i n e a r reservoir assumption. A discrepancy could also be caused by possible bias in the p r e c i p i t a t i o n measurements. An i n t e r e s t i n g feature of the data i n table 7.4 i s the consistency of the proportion of surface runoff from each storm; the figure of 13 to 14% agrees f a i r l y well with the 10% of the watershed area mapped as saturated ground (appendix 1).,(The higher proportion of surface runoff for the storm of Aug. 8 could be because a greater area of the watershed was saturated, since the watershed was s t i l l p a r t i a l l y snow-covered.) The concept of p a r t i a l source area contributions to rainstorm runoff i s discussed i n Dunne and Black (1970). An interesting feature of the hydrograph i n August and 179 September i s the diurnal variation during periods of low flow. This consists of a r i s e of discharge during the night and a f a i r l y abrupt drop during mid-day. The variation i n discharge above and below the "average" hydrograph for each cycle (figs. 7.3 and 7.4) t y p i c a l l y amounts to about 2.3 m3, or about 0.6 mm of water over the 101 of the watershed which i s mapped as saturated ground. It i s possible that some of the diurnal variation may be due to the f a l l of dew in this area which contributes d i r e c t l y to streamflow. However, an approximate aerodynamic estimate of condensation (using eg. 5.3b) suggests a dew f a l l during the night in the order of 0.1 mm. Therefore, dew i s not l i k e l y to account for a substantial amount of the diurnal v a r i a t i o n , although cn some days there are small peaks i n the hydrograph i n mid-morning which may be due to the melting of f r o s t , ft more l i k e l y explanation i s that the r i s e and f a l l of the stream i s controlled by the transpiration of plants in the wet area bordering the stream channels. Since the s o i l i s shallow and i s underlain by a nearly impermeable t i l l , much of the flow cf groundwater to the stream must pass through the root zone of these plants. The lowering of the water table adjacent tc the stream channel during the day, and i t s r i s e during the night, could account for the diurnal variation in discharge. This fluctuation i n the l o c a l water table would be caused by the interception of water by the plants during the day when transpiration rates are high. Considering the evaporation rates i n table 7.2, evapotranspiration from the saturated portion of the watershed could feasibly account for the diurnal variation observed. 180 7.5 SUMMARY The water balance of the watershed during August and September indicates that an amount of water egual to about 12% of the t o t a l snowmelt volume i s released from storage i n the ground i n the l a t e season, following snowmelt. This proportion may be greater i n most years, when the summer i s longer and drier than i n 1976. The water balance was calculated from d i r e c t measurement of discharge and p r e c i p i t a t i o n , and from clima t o l o g i c a l estimates of evaporation. Evaporation i s estimated to account f o r about 60% of th i s water released from storage. S o i l moisture measurements produced an estimate of the release of water from storage which was somewhat lower than that r e s u l t i n g from the water balance c a l c u l a t i o n . However, the s o i l moisture measurements are extremely crude, considering the d i v e r s i t y of s o i l and drainage conditions within the watershed. The response of the watershed to rainstorm events i s very rapid. The assumption made in e a r l i e r chapters that the response time of the channel network to snowmelt i s ne g l i g i b l e compared with other delays i n the system i s v a l i d . 181 CHAPTER 8 CONCLUSIONS In the preceding chapters, the hydrology of a small alpine watershed during the spring and summer has been studied by examining, in seme d e t a i l , each of the components of the atmosphere-snow-soil-stream system. As a r e s u l t , an understanding has been gained of the response of the watershed as a whole to snowmelt, which might be applicable to the development of physically based models of snowmelt runoff. Snow ablation was measured using networks of ablation stakes and density measurement points; standard procedures from glaciology and snow survey practice were used to establish these networks and c o l l e c t data. Measurement of density p r o f i l e s in snow pi t s was found to be the most accurate and precise method cf determining snow density, although the snow sampler density measurements have the advantage that samples can be taken over a wide area at any given time. The snow sampler can be calib r a t e d against snow p i t measurements to give acceptably accurate density measurements. The network of ablation stakes used in the study watershed was barely adeguate to sample ablation rates; a higher density of stakes would be necessary i n a more rugged or more heavily forested l o c a t i o n , and a higher density should be used during the period of p a r t i a l snow cover. Measurement of meltwater flux rates and c a p i l l a r y pressure in the snowpack confirmed the general behaviour of meltwater movement as predicted by existing theory (Colbeck, 1977). Although the simple f i e l d instrumentation developed by wanJciewicz (1976) was adeguate for these measurements, the v a r i a b i l i t y of snow properties within the snowpack was found to 182 be great. Therefore, i t i s probably not fe a s i b l e to apply a detailed model based on th i s theory to predict water movement on a watershed scale. Analysis of hydrographs and observations of the snow-ground interface showed that about 75% of the surface area of the study watershed contributed runoff to the stream channel by flow over the ground surface. This compares with a surface runoff contributing area of about 10 to 15% during rainstorms when the watershed was snow-free. A well-developed layer of ice at the base cf the snowpack, and saturation of the s o i l , contributed to t h i s high proportion of d i r e c t runoff. The basal ice i s t y p i c a l of regions with a climate s u f f i c i e n t l y cold that the ground freezes under the snow i n winter, and the saturated s o i l i s probably t y p i c a l of t i l l - c o v e r e d areas, but not cf areas covered by more permeable surface material. Increasing channelization of flow beneath the snowpack and the decreasing depth of snow cover leads to a progressively more rapid and peaked hydrograph response as the season progresses. It was concluded that the shape of the recession limb of the diurnal snowmelt hydrographs could not be adeguately described by l i n e a r reservoir theory. Hater balance computations showed that v i r t u a l l y a l l of the water produced from ablation of the snowpack was released as stream runoff. Evaporation proved to be a very small component of the water balance, and was important only late in the summer when large areas of the watershed were snow-free. Approximately 10 to 15% of the snowmelt water generated was stored i n the s o i l during the snowmelt season and released as stream runoff l a t e r in the summer and autumn. 183 Energy balance measurements during the snowmelt season showed that i n the study watershed i n 1976, about 90% of the energy reguired for snowmelt was supplied by r a d i a t i o n . This propcrticn would be considerably less in locations more exposed to wind, and i n forested areas, but i t i s probably t y p i c a l of valley bottom sub-alpine and alpine locations. The simple f i e l d instrumentation used in this study was not adeguate to precisely measure the turbulent components of the energy balance over snow, and i t was concluded that empirical turbulent transfer formulae are more appropriate for studies i n which elaborate p r o f i l e measurements are not feasible. I t was concluded that net radiation over snow can be modelled with acceptable accuracy on a daily basis using measured incoming and reflected solar radiation, and that cloud cover observations are also useful i n such a model. As a r e s u l t of t h i s study, seme recommendations can be made regarding data reguirements and research p r i o r i t i e s for further studies of snowmelt hydrology. For studying the movement of meltwater i n deep snowpacks, more emphasis should be given to the measurement of the l i g u i d water content cf snow, and the development of r e l i a b l e instrumentation for t h i s measurement, work i s needed on the application of the theory of meltwater movement to deep snowpacks on a watershed scale, simplifying the model to reduce data reguirements. Also, considerable t h e o r e t i c a l and f i e l d work i s needed on processes occurring at the snow-ground interface, and on the role of the thermal and moisture status of the s o i l i n generating runoff hydrographs. Existing models of the energy balance of melting snow are 184 adequate to calculate ablation from f a i r l y l e v e l , unforested snow areas. The esse n t i a l data requirements to apply these models are solar radiation, snow surface albedo, a i r temperature and humidity, and wind. Net radiatio n data are necessary to develop net radiation models for a variety of environments. Considerable work i s needed on extendinq the ex i s t i n g energy balance models to forested areas, watersheds of complex topography, and areas of p a r t i a l snow cover. 185 BEEERENCES Ambach, W. and F. Howorka, 1966. Avalanche a c t i v i t y and free water content of snow at Obergurgl. Int. Ass. S c i . Hydrcl., Pub, no. 69 (International Symposium on S c i e n t i f i c Aspects of Snow and Ice Avalanches, 1965, Davos), pp. 65-72. Anderson, E.A., 1976. A Point Energy and Mass Balance Model of a Snow Cover. NOAA Technical Report NWS 19. U.S. Dept. of Commerce, National Oceanic and Atmospheric Administration, National Weather Service. 150 p. Bartos, L.R. and P.A. Rechard, 1974. Ablation c h a r a c t e r i s t i c s of an alpine snowfield i n summer. In H.L. Santeford and J.I. Smith (eds.), Advanced concepts and Technigues i n the Study of Snow and Ice Resources. U.S., Nat. Acad. S c i . , Washington, pp. 90-98. B r i t i s h Columbia, Dept. of Environment, Water Investigations Br. Snow Survey B u l l e t i n , 1976. B r i t i s h Columbia, Dept. of Lands, Forests, and Water Resources, Water Investigations Br., 1975. Summary of Snow Survey Measurements in B r i t i s h Columbia, 1935-1975. 342 p. Cairnes, C.E., 1937. Geology and Mineral Deposits of Bridge River Mining Camp, B r i t i s h Columbia. Geol. Surv, Can.,Mem. 213. 140 p. Canada, Dept. of Environment, Atmospheric Environment Service. Monthly Record: Meteorological Observations i n Canada, 1976. Church, fl. and R. K e l l e r h a l s , 1970. Stream Gauging Techniques for Remote Areas Using Portable Equipment. Canada, Dept. of Energy, Mines, and Resources, Inland Waters Br., Tech. E u l l . no. 25. 89 p. ,• Cclbeck, S.C., 1972. A theory of water percolation i n snow. J. Gl a c i o l . 11(63), pp. 369-385. Cclbeck, S.C., 1974. On predicting water runoff frcm a snow cover. In H.L. Santeford and J.L. Smith, op. c i t . , pp. 55-66. Colbeck, S.C., 1975. A theory for water movement through a layered snowpack. Water Resources Res. 11(2), pp. 261-266, , Colbeck, S.C, 1977. Short-term forecasting of water run-off from snow and i c e . J . G l a c i o l . 19 (81), pp. 571-587. Cclbeck, S.C. And G. Davidson, 1973, Water percolation through homogeneous snow. Int. Ass. S c i , Hydrol,, Pub. no, 107 (The Role of Ice and Snow in Hydrology: Proceedings of the Banff Symposia, Sept. 1972), pp. 242-257. De Quervain, M.R., 1973. Snow structure, heat, and mass f l u x 186 through snow. Int. Ass. S c i . Hydrol., Pub. no. 107 (The Bole of Ice and Snow i n Hydrology: Proceedings of the Banff Symposia, Sept. 1972), pp. 203-226. Dunne, T. and R.D. Black, 1970. P a r t i a l area contributions to storm runoff i n a small New England watershed, water Resources Res. 6(5) , pp. 1296-1311. Dunne, T, and R.D. Black, 1971, Bunoff processes during snowmelt. Hater Resources Res, 7(5) , pp. 1160-1 172. Dunne, T., A.G. Price, and S.C. Colbeck, 1976. The generation of runoff from subarctic snowpacks, Hater Resources Res, 12(4), pp. 677-685. Dyer, A.J., 1974. A review of f l u x - p r o f i l e relationships. Boundary Layer Meteorol. 7(3) , pp. 363-372. Fohn, P.M.B., 1973. Short-term snow melt and ablation derived from heat- and mass-balance measurements. J, G l a c i o l . 12 (65) , pp. 275-289. Freese, F. , 1962. Elementary Forest Sampling. U.S. Dept. of Agriculture, Forest Service, Agriculture Handbook no. 232. 51 p. ,. Freeze, R.A., 1969. The mechanism of natural groundwater recharge and discharge, 1. One-dimensional, v e r t i c a l , unsteady, unsaturated flow above a recharging or discharging groundwater flow system. Hater Resources Res. ,5(1), pp. 153-171. Freeze, R.A.# 1974. Streamflow generation. Rev, Geophys. Space Phys, 12(4), pp. 627-647. Freeze, B. A. , 1975, A stochastic-conceptual analysis of one-dimensional groundwater flow i n non-uniform homogeneous media. Hater Resources Bes. 11(5), pp. 725-741, Garstka, H.U., L.D. Love, B.C. Goodell, and F.A. Bertie, 1S58. Factors Affecting Snowmelt and Streamflow. U.S. Dept. of the Interior, Bureau of Beclamation/U.S, Dept. of Agriculture, Forest Service, Denver, Cclo.,189 p. Gerdel, B.H., 1945. The dynamics of l i g u i d water i n deep snowpacks. Trans. Am. Geophys. Union 26, pp. 83-90. Gerdel, B.H., 1954. The transmission of water through snow. Trans. Am, Geophys. Union 35, pp. 475-485. Granger, R.J., 1977. Energy Exchange during Melt of a P r a i r i e Snowcover. Unpublished M,Sc, Thesis, Univ. of Saskatchewan, Saskatoon, Sask, 122 p. H i l l e l , D,, 1971. S o i l and Hater: Physical P r i n c i p l e s and Processes. Academic Press, New York. 288 p. 187 Kuz*min, P.P., 1961. Melting of Snow Cover. U.S.S.R. State Hydrological I n s t i t u t e , Leningrad. (Israel Program for S c i e n t i f i c Translations, Jerusalem, 1972.) 2 90 p. LaChapelle, E.R., 1956. The c e n t r i f u g a l separation of free water from melting snow. J . G l a c i o l . 2(20), pp. ,769-771. LaChapelle, E.R. , 1959, Errors i n ablation measurements from settlement and sub-surface melting. J. G l a c i o l . , 3 (26) , pp. 458-467. Langham, E.J., 1974, The occurrence and movement of l i g u i d water i n the snowpack.. In H,L, Santeford and J.L. Smith, op. c i t , , pp. 67-75, Latimer, J,R., 1972. Radiation Measurement. Canada, Nat.,Res. Counc, Can. Nat, Com. I, H. D. , I.F.Y.G.L. Tech. Manual Ser. , no. 2. 53 p. Leaf, C., 1966, Free water content of snowpacks i n subalpine areas, Proc. Western Snow Conf., 34, pp.17-24. Light, P., 1941, Analysis of high rates of snow-melting. Trans. Am, Geophys, Union 22, pp. 195-205. L i n l o r , W.I., M.F. Meier, and J.L. Smith, 1974. Microwave p r o f i l i n g of snowpack free-water content. In H. L. Santeford and J.L. Smith, op. c i t , , pp, 729-736, Linsley, R.K., M.A. Kohler, and J.L,H,,Paulhus, 1975..Hydrology for Engineers (2nd ed.). McGraw-Hill, New York. 482 p. Male, D.H. and D.M, Gray, 1975. Problems i n developing a physically based snowmelt model. Can. J . Civ. Eng. 2(4), pp.474-488. Mathews, W.H. and J.R. Mackay, 1963. Snowcreep studies, Mt. Seymour, B.C.: preliminary f i e l d investigations. Geogr. Bull. (Ottawa) 20, pp. 58-75. McKay, B.C. and G.W. T h u r t e l l , 1S78, Measurement of energy fluxes involved i n the energy balance of a snow cover, J. Appl. Heteorol. 17(3), pp. 339-349. Montieth, J.L., 1973. Princip l e s of Environmental Physics. Edward Arnold, London. 241 p. Muller, F. , 1971. Snowpack Metamorphism. In Runoff from Snow and Ice: Hydrology Symposium no. ,8. Canada, Nat. Res. Counc, Subcom. on Hydrology, Vol.,2, pp. 33-50. Munn, B.E., 1966, Descriptive Micrometeorology, Academic Press, New York. 244 p. Munro, D.S., 1975. Energy Exchange on a Melting Glacier. Unpublished Ph.D. Thesis, McMaster Univ., Hamilton, Ont, 182 188 P. Oke, T.R., 1970. Turbulent transport near the ground i n stable conditions. J. Appl. Meteorol. 9(5), pp. 778-786, Ostrem, G, and A. Stanley, 1969. Glacier Mass Balance Measurements: A Manual for F i e l d and Office Work. Canada, Dept. of Energy, Mines, and Resources/Norwegian Water Resources and E l e c t r i c i t y Board. 119 p. , Parratt, L.G., 1961. Probability and Experimental Errors i n Science. John Wiley and Sons, Mew York. 255 p. Paterson, W.S.B., 1969, The Physics of Glaciers. Pergamon Press, Oxford. 250 p. Penman, H.L., 1956. Estimating evaporation.,Trans.,Am. Geophys, Onion 37(1), pp. 43-50. Price, A.G. and T. Dunne, 1976. Energy balance computations of snowmelt i n a subarctic area, l a t e r Resources Res. 12(4), pp. , 686-694. P r i e s t l y , C. H. B. and R.J. Taylor, 1972. On the assessment of surface heat f l u x and evaporation using large-scale parameters. Monthly Weather Rev., 100(2), pp. 81-92. Radok, 0., S.K. Stephens, and K.L, Sutherland, 1961. On the calorimetric determination of snow guality. Int. Ass. S c i . Hydrol., Pub. no. 54 (General Assembly of H e l s i n k i , 196C, Commission of Snow and I c e ) , pp. 132-135. Rouse, I.E., P. F. M i l l s , and R.B. Stewart, 1977. Evaporation i n high latitudes. Water Resources Res. 13(6), pp. 909-914. Santeford, H.L..and J.L. Smith (eds.), 1974. Advanced Concepts and Technigues in the Study of Snow and Ice Resources. 0.S., Nat. Acad. Sci. , Washington. 789 p. , S e l l e r s , W.D., 1965. Physical Climatology. Univ. of Chicago Press, Chicago. 272 p. Shimizu, H., 1970, Air Permeability of Deposited Snow. Contrib. from Inst, Low Temperature S c i . , Hokkaido Univ., Ser. A, no. 22, pp. 1-32. Smith, J.L., 1974. Hydrology of warm snowpacks and th e i r e f f e c t s upon water de l i v e r y ; some new concepts. In H. L. Santeford and J.L. Smith, op. c i t . , pp. 76-89. Snedecor, G.W. and W.G. Cochran, 1967, S t a t i s t i c a l Methods (6th ed.)-. Iowa State Univ. Press, Ames, Iowa. 592 p. Stewart, R.B. and W.R, Rouse, 1976. Simple models for calcula t i n g evaporation from dry and wet tundra surfaces. A r c t i c and Alpine Res. 8(3), pp. 263-274. , 189 Sverdrup, H.U., 1936, The eddy conductivity of the a i r over a smooth snow f i e l d , Geofysiske Publikasjoner 11(7), pp. 1-69. U.S. Dept. of Agriculture, S o i l Conservation Service, 1972. Snow Survey and Water Supply Forecasting. S.C.S. National Engineering Handbook, Section 22. 225 p. U.S. Army Corps of Engineers, 1956. Snow Hydrology: Summary Beport of the Snow Investigations. U.S. Army, Corps of Engineers, North P a c i f i c Div. , Portland, Ore. 4 37 p. Wakahama, G., 1968. The metamorphism of wet snow. Int.,Ass, S c i . Hydro!., Pub. no..79 (General Assembly of Bern, 1967, Commission of Snow and Ice), pp. 370-379. Wankiewicz, A.C,, 1976, Water Percolation within a Deep Snowpack: F i e l d Investigations at a Site on Mt, Seymour, B r i t i s h Columbia. Unpublished Ph.D. Thesis, Univ. of B r i t i s h Columbia. 177 p.. Webb, E.K., 1965, A e r i a l microclimate. In A g r i c u l t u r a l Meteorology. Am, Meteorcl, S o c , Meteorol. Monog. 6(28), pp. 27-58. Wendler, G. and N. Ishikawa, 1974. The combined heat, i c e , and water balance of McCall Glacier, Alaska. J. G l a c i o l . 13(68), pp. 227-241. Wendler, G. and G. Weller, 1974. A heat-balance study on McCall Glacier, Brooks Bange, Alaska: a contribution to the I.H.D. J. G l a c i o l . 13(67), pp. 13-26. Woo, M.K. and H.O. Slaymaker, 1975. Alpine streamflow response tc variable snowpack thickness and extent. Geogr, Ann. 57A (3-4), pp. 201-212., Work, B, A., H.J. Stockwell, T.G. Freeman, and B.T, Beaumont, 1965. Accuracy of F i e l d Snow Surveys: Western United States, including Alaska. U.S. Army, Cold Beg, Bes, and Eng. Lab., Tech. Bep. no. 163. 43 p. Yosida, Z., 1960. A calorimeter for measuring the free water content of wet snow. J. G l a c i o l , 3 (27), pp. 574-576. Young, G.J., 1974. A s t r a t i f i e d sampling design for snow surveys based on t e r r a i n shape. Proc. Western Snow Conf., 42, pp. 14-22. Young, G.J., 1976, A portable p r o f i l i n g snow gauge - re s u l t s of f i e l d tests on g l a c i e r s . Proc. Western Snow Conf., 44, pp. 7-11. 190 APPENDICES 1. Maps a. Topographic map fc. Snow cover map c. Vegetation and s o i l s map 2. Climate data summary 3. Seasonal hydrograph and plot of climate data 4. Stage - discharge r e l a t i o n 5. Data used for radiation modelling 6. Energy and water balance summary 191 100 m 192 100 m 193 N C. VEGETATION AND DRAINAGE Depressions; saturated soil. Sedq.es and grasses. •Wei I-developed soil, at«ple moisture Supply, moderately well drained. Herbaceous plants and arasses. Similar to b; on steeper slopes, Wiainly stakil/ied talus. Subtly ket+tr drained-Rocky, well-drained areas; ridje crests a*J talus. Thin soil; heather, lichens-(J|^A) Tree - covered areas SCALE 100 m o *•** APPENDIX 2 **** CLIMATE DATA SUHHABI »**» 0 o o o o o o U w in I - BEAN IAILY SCBEEN TEHPEBATUBE, °C VP - DEAR DAILY SCBEEH VAPCUB PBESSUBE, HB. SAX - IAILY RAXIHUH SCBEEN TEHPEBATUBE, °C HIM - DAILI BINIHUH SCBEEH TEHPEBATUBE, °C K - SCIAB BAEIATION FBOH KIPP, B/H« K(ACI)- SCLAB BADIATION FBOH ACTINOGBAPH, H/H* Q* - NET BADIAT10B. B/H* ALB - ALBEDO BIND - AVEBAGE HIND SPEED FBOH SPOT HEASOBBHENTS, H/SEC CI - CLOUD BUHBEB (EFFECTIVE COVBB AND OPACITY) C - CICOD C0V1B IN TENTHS PPT - PHECIPITATION IN HH; TYPE PCILOHS: B=B AIN S=SMO« T=MIXED Z=CUHULATIVB H - INDICATES HICBCHET HEASUEEHEN1S AVAILABLE A - SUCH ABLATION AT HET SITE IN HH. BATEB EQUIVILANT Q - DAILY STBEAH DISCUABGE IN CUBIC HBTEBS PEAK - PEAK EISCHABGE IN LITBES/SEC. BUN - BUBOFF GEBEBAIED, CUBIC HE1EBS t - EEECEIT SNOB COVEB DATE T VP HAX HIN K K (ACT) Q* ALB BIND CN c PPT H A 0 PEAK 1 HAY 11 0.66 10. 0.0 S 2 HAY 12 181. 0.78 10. 2.2 S 3 HAY 13 100. 0.65 9. 19.9 s 4 HAY 14 0.0 0. 0.0 5 HAY 15 4.2 4.9 12. -3. 338. 1.5 0.01 0. 0.0 6 HAY 16 4.8 5.3 19. 0. 267. 2. 1 0.35 4. 8.5 T 7 HAY 17 -2. 4 4. 1 12. -6. 152. 0.66 10. 8.8 S 8 HAY 18 0. 1 4.0 12. -10. 0.74 1. 3 0.06 1. 0.0 9 HAY 19 16. -6. 291. 0.72 1.4 0. 10 2. 0.0 10 HAY 20 1.8 5.1 7. -4. 244. 0.70 1.7 0.35 5. 0.0 11 HAY 21 2.3 5.1 11. -4. 289. 0.28 7. 0.0 153. 2.4 12 HAY 22 1.9 5.5 5. -1. 149. 0.67 10. 0.4 T 193. 13 BAY 23 1.7 5.4 8. -1. 204. 1.8 0.73 10. 0.3 S 152. 1« BAY 24 0.7 5.5 8. -1. 153. 0.73 10. 0.8 S 155. 15 HAY 25 -1.2 4. 3 4. -4. 227. 0.65 10. 3.9 s 131. 16 HAY 26 1.6 6.0 8. -3. 138. 0.78 10. 15.9 T 135. 17 HAY 27 1.4 5.1 6. 1. 290. 20.4 B 554. 7.1 18 HAY 28 -2. 3 3.6 4. -5. 293. 317. 19 HAY 29 -2.3 4.2 2. -4. 135. 211. 20 HAY 30 -1.8 3.7 6. -7. 167. 21 HAY 31 -0. 2 4. 5 6. -5. 117. 6.2 Z 141. 22 JUNE 1 -0.5 4.6 8. -2. 268. 1.4 0.61 9. 0.0 S 123. 23 JUNE 2 -0. 9 4.1 6. -6. 331. 0.74 0.41 6. 0.0 107. 24 JUNE 3 -1.6 4.4 6. -6. 228. 0.70 1.8 0.50 6. 5.3 S 124. 25 JUNE 4 0.4 5.3 11. -4. 146. 0. 85 0.65 9. 16.0 s 131. 26 JUNE 5 2.4 4. 4 12. -6. 365. 38. 0.75 0.24 3. 0.0 141. 2.5 27 JUNE 6 3.8 4.4 12. -1. 303. 316. 41. 0.70 0.32 5. 0.0 178. 2.6 28 JUNE 7 4. 8 5.0 14. 0. 359. 335. 87. 0.69 1.4 0. 16 3. 0.2 R H 19. 284. 5.9 29 JUNE 8 5.4 13. 2. 311. 315. 0.68 1.3 0.35 6. 0.4 B H 26. 549. 9.8 30 JUNE 9 2. 1 5.8 11. 2. 164. 0.67 0. 80 10. 4.0 R 566. 31 JUNE 10 1. 4 4. 9 7. 0. 289. 0.67 1.5 0.63 9. 2.4 T 418. 6.2 32 JUNE 11 -0.2 5.0 5. -1. 216. 0.75 10. 11.0 S 473. 31 .TUNS 12 -r . H 4 . 0 r > . -U. 29^. 0 . 7U 1. 1 0. SO 7. 9.6 S 121 . BOB 195 CN cn m m m ts r» ( N <N ^ O* CNCNCr.m*-morxr-mo m tf m c* * o* **)« rs ^ ^  a*. H tf tft**rMvovoj»inr-in CDr>*\OV©vOCOCn^vO»-rnOC©rn<NtftfinfNCOC*® tfcornsor^tfC7«cr>ocDo^Lncnvocntfinfncorn& oc^C4v0oo9mr^ci\0tfrntf^rnvonocir4or*ao^voomc*^tf cnrnaor^r^^inotff^r^^ror^cNc^cD^r^ cNrnc^r^o^o^c*cocDr^ \Otftfr^c7»*—«—eop»voo^cNcNr^ *- »- ^ *• «» ^  ^  *- «• ^» ^> <^  *- r» ^r-^^v- ^. ^ 4 cor^ou^r^c^rnojtfcNtff^a^invoincotf^t^un^oe^ v B a n g s n s a i f l s i v s n s j v a a » u » a : » » ui H ca « ui a cu c d c a m f f i c a a cu H as m a i m m o s a a m o a c a E ^ o o i n o o o r ^ o o ^ ^ v o o o o o i n o o o r ^ r ^ o o o t f r n o o O v o o o o o o o w ^ o o o o o o r ^ f n ^ s o o i n ^ - o r - o o t f o o a* o <*n «— o o o cn o o t N ^ s o o o o o o o ^ - o f n n o o t n e o o o o r - o o e o o o t N r M o o o o o o v m o i o ^ o e D o r ^ o ^ ^ r o o u » o o ^ o ^ l D y ^ * f l O f f > ( I ) ^ f i ^ ^ m ^ < ^ o > ^ w ^ ^ • o o o > o ^ ^ ^ ^ f f l * o c ^ ^ * - » • ^ o o o ^ t f o ^ o c D o ^ , ' 0 » o o> 3-m i n ^ h i n o t v o o ^ t f ^ i f l i f t f f o N O f N o i f l r i i o N h t f l M J i w i n < o«oeo9< o 9 « N i n r n « tf tf m o vo • P 4 r h u i o n * ^ t M * a * n u n o ^ n i n \ o u i t * v i o r » o r * v o ^ » a u i o ( O o o ^ « p » r ^ ^ u • • • • • • • • • • • • • • • • • • • • • • • • • • • • • o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o a r» M O * { N O 0 D « f r* t>J f f' O r- r-tNniso «ntNn*ooN**«N*cno/ w o» n f in * O * - ^ * " ^ M v » * " O C > l ^ ^ » - O O «- ^ ^  CD m vo co ca r- vovovovovovovovovovovovo^ vovovotosovovovovovointninu^ ininu^  , - ) • • • . • • . . • • • • • • • • • ^ O O O O O O Q O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O # • • • • • • • • • • • • • • • • • n r> « r» ~ — o o o o o o o m CN in r- uj m co c* * m oo *-H • • • • < m v* r> p»-f r - fsj M»r*»o»nooDP,ohnin<»n»o»oinN vo in r* rvi r>voa^ r*rfcoi»o»inf>iinir>\o<,noiOvo(Nfnvo»o tf m «*> c* c*CNrvifnrvirn^^<srs<N^c<mr^^rstMrn<No* riminfon a- CT> intnmocnfnocncovotfCPcncn ( N » - fs©cntftfcnco<N(,nin<NvocDr»-m CN » - * - ^ - CN » - » - « - ^ - < N T ~ » - » - C M r - e n ^ H > c n r > c o r ' i t f v o » c n » " v o o o c o © i > m c N » - C N » - r N * - r M r n f N CN CN rn CN CN ^  CN I I I f i l l I I I I rtfrnvor>votnvor>r»mtf •<tfr^cc»-ininr^csrncocDino^^»nc^ovor*c*^^tfCD S ^ «- *- »- »- «- *- ^- v *• ^ «- v «- t- «- w- t- «- r» i - «- ^ r- *-vocN^ rN^ in^ cN»i3CNunrncNvainc©a>cncnrn^ c^  o cu . . , . vooc*cDoc*inoj\oQ*rs»-^ u^ cf»vnr^ rn»^  co H^cnrntfr^vorntfinojcsoocnu^r^votfCNrs^ o m tf tn vo r* CD 0> o «- CN rn tf tn vO r- GO cn o MM *~ ^ *~ «~ CN CN CN CN CN CN CN CN CN CN rn PQ UJ M M MM PQ HM w W HM U MM UM » UM pg m PM 3B as Z 3G a x M » a as an as a as S s s » o a O D a a s D S a a n r , ^ n n ^ tf m vo r - CO cn O r-CN m tf m VO co cn o » -m m en rn rn tf 9 9 9 9 9 tf tf tf vn m 'CNCNCNCNCNCNCNCNCNCNrnm a a o u a o a o u 3 D O a s o «! « "1 ts « «: •« 4 a in o r- CO en o m CO 00 00 CO CO CO OA o o c o 3 DATE T VP MAX BIN K K (ACT) Cj* ALB SIMC CD C PPT a A Q PEAK BUS % 93 AUG 11 8.8 8.6 14. 6. 17 5. 0.20 0.46 8. 1.1 R 294. 4.4 4 94 AUG 12 8.3 7.5 14. 4. 237. 0. 20 2.4 0. 46 7. 0.0 202. 4. 95 ADG 13 5.5 7.8 9. 4. 112. 0.20 1.4 0.80 10. 7.1 B 223. 3. 1 3 96 ADG 14 5.3 6.8 12. 3. 190. 0.20 0.0 B 142. 3. 97 AUG 15 6. 2 6.9 12. 1. 206. 0.20 0.0 B 110. 2. 98 A 06 16 3.9 7.5 7. 4. 40. 0.20 0.88 10. 7.1 B 139. 2.4 2 99 AUG 17 3.5 6.9 7. 1. 82. 0.20 0.69 10. 0.4 B 121. 2 100 AUG 18 4. 9 6.6 11. 0. 269. 0.20 0.0 93. 2 101 AUG 19 2.9 6.6 5. 3. 77. 0. 20 14.5 R 190. 2.8 2 102 AUG 20 3. 3 6.4 8. 1. 220. 0.20 3.6 B 147. 2.5 2 103 ADG 21 3. 9 7. 0. 155. 0.20 0.0 108. 1 104 AUG 22 3.5 6.7 7. 0. 74. 0. 20 5.5 B 1*1.. 3.1 1 105 AUG 23 8. 3. 108. 0.20 0.66 9. 2.4 B 108. 1.6 1 106 AUG 24 5.7 6.8 10. 3. 198. 0. 20 1.3 0.42 5. 1.3 B 102. 1.5 1 107 AUG 25 2. 7 6.2 7. 0. 109. 0.20 0.61 9. 2.3 1 92. 1.3 1 108 AUG 26 1.9 6.0 5. 1. 131. 0.20 1.6 0.68 8. 0.0 T H 83. 1 109 AUG 27 3.3 6.9 6. 1. 52. 0.20 10.0 B 126. 3.7 1 110 AUG 28 4. 8 7.3 7. 2. 52. 0.20 0.0 112. 1 111 AUG 29 8.5 6.8 16. 2. 202. 0. 20 0. 26 7. 0.0 79. 0 112 AUG 30 9. 5 6. 1 16. 4. 244. 0.20 2.0 0.03 1. 0.0 H 59. 113 AUG 31 9.4 6.7 18. 3. 251. 248. 115. 0.20 1.7 0.02 0. 0.0 a 48. 114 SEPT 1 8. 1 7.4 15. 3. 205. 0.20 0. 30 4. 0.0 B 41. 115 S EFT 2 5.6 7.9 10. 4. 119. 0.20 0.0 38. 116 SEPT 3 5.8 8.3 8. 5. 49. 0.20 1.9 B 48. 117 SEPT 4 6. 1 8.1 7. 6. 56. 0.20 11.3 B 118 SEPT 5 3.2 6.8 7. 2. 76. 0.20 13.5 B 119 SEPT 6 0.5 5.7 5. -2. 111. 0.20 0.60 8. 3.6 S 120 SEPT 7 0.9 5.0 8. -4. 199. 0.20 0.0 84. 121 SEPT 8 4.0 5.6 13. -2. 23 5. 0.20 0.0 B 71. 122 SEPT 9 8.5 6.8 18. 2. 231. 0.20 0.0 62. 123 SEPT 10 8.6 5.9 16. 4. 207. 0.20 0.0 53. 124 SEPT 11 7.0 6.8 13. 2. 161. 0. 20 1. 1 0.32 10. 0.0 a 46. 125 SEPT 12 4.9 3. 131; 0.20 2.4 0.74 9. 0.8 B 48. 126 SEPT 13 4.6 6.6 83. 0. 20 1.5 B 45. 127 SEPT 14 5.2 7.5 137. 0.20 3.0 B 64. 128 SEPT 15 7.4 6.9 221. 0.20 0.4 B 38. 129 SEPT 16 9.2 7.8 204. 0.20 0.0 32. i 130 SEPT 17 108. 0.20 0.0 30. 131 SEPT 18 194. 0.20 0.0 27. 132 SEPT 19 201. 0.20 0.0 26. 133 SEPT 20 187. 0.20 0.0 21. 134 SEPT 21 191. 0.20 0.0 19. 135 SEPT 22 0.20 0.4 B 18. 136 SEPT 23 0. 20 0.0 17. 137 SEPT 24 0. 20 0.0 16. 138 SEPT 25 0.20 0.0 15. 139 SEPT 26 165. 0.20 0.0 13. 140 SEPT 27 180. 0.20 0.0 13. 141 SEPT 28 124. 0. 20 0.0 12. 142 SEPT 29 145. 0.20 0.0 11. 143 SEPT 30 167. 0.20 0.0 11. 144 OCT 1 119. 0. 20 0.0 10. 145 CCT 2 124. 0.20 1.9 B 18. 146 OCT 3 0. 20 0.0 B 13. 147 OCT 4 104. 0.20 0.0 R 12. 148 OCT 5 120. 0.20 3.0 B 19. 149 OCT 6 0.0 12. 150 OCT 7 0.0 11. 151 OCT 8 2 .0 R 13. TEMPERATURE <->c SOLflR RADIATION A A A A A A A A ^ 5?-I CL. PRECIPITATION h O . -1 I 1—u 64 65 66 67 68 69 7fl' 7l' 72 73 74 75 76 77 7s' 79 Bo' Bl" B2 63 B4 BS 86 87 B8 B9 SO* 3)' 92 33 94 95 96 97 9fl' 99100] Jl]02103]04105]06107]OBI09] 1011 l i 12113] 141 15316: AUG AUG SEPT I JULY 15 15 1 So i i 1 1 — i — i — i i i i ~i 1 1 — i — i — i i i i ~i 1 1 — i — i — i i i 20} £ ?IOr to 0.0132 h (f>*5.3 cw) •'<j,« 0.0061 K (h<5.3 cm) 3.0 S 5 % tolerance liwiT* O Salt dilution jaugin^ h Total retention <j«ujir>j I I l i i I i i I I I l I I i I I l J I i i i ' ' i 0.1 0-2 OS I 2 5 10 Discharge, (J, (litr«/sec) 2 0 50 100 APPENDIX 4 Stage - discharge relation, APPISDIX 5 Data used for radiation nodellirq. (Refer to DATE T Q* L Cn June 6 3.8 303. 41. -50. 0.32 June 7 4.8 359. 87. -25. 0. 16 June 15 3.9 152. 30. -22. 0.75 June 16 4.8 252. 76. -10. 0. 54 June 17 7.0 375. 69. -58. 0.00 June 18 6.9 254. 72. -17. 0.37 June 27 5.9 361. 93. -48. 0.05 June 29 6.7 181. 50. -20. 0.39 June 30 4.3 247. 71. -25. 0.50 July 2 2.6 227. 65. -25. 0.50 July 3 3.7 148. 52. -7. 0.72 July 7 4.8 94. 43. 4. 0. 80 July 11 4. 4 248. 87. -17. 0. 47 July 18 6.7 313. 93. -44. 0. 10 July 19 7.9 27 9. 90. -36. 0.28 July 20 6.0 164. 55. -19. 0.74 July 22 4.7 152. 58. -10. 0. 59 July 23 7.8 261. 89. -29. 0. 52 July 25 9.0 330. 114. -37. 0.C3 Correlations, leans, and standard deviations T K i Q* L* Cn c T 1. H 0.40 1. 0* 0.60 0. 69 1. i * -0.37 -0. 82 -0. 37 1. cn -0.53 -0. 92 -0.68 0.81 1. c -0.48 -0. 89 -0.65 0.78 0.95 1. Mean Standard < deviation T 5.56 1. 70 Kl 247. 4 81.8 Q* 70.3 21.9 1 * -26. 1 16. 1 Cn 0.412 0.256 C 0. 616 0.350 6.2, and eqs. 6.6) c ALBEDO Q* 0* (fro* Ki) (froa 0.5 C.70 56. 60. 0. 3 0.69 67. 72. 1.0 C.66 41. 43. 0.7 0.66 59. 66. 0.0 0.66 80. 80. 0.7 0.65 62. 61. 0. 1 0.61 97. 97. 0.7 0.61 55. 43. 0.9 0.61 70. 74. 0.7 0.60 68. 69. 0.9 0.60 49. 49. 1.0 0.59 38. 33. 0.7 0.58 78. 81. 0. 1 0.56 101. 96. 0.7 0.55 95. 93. 1.0 0.55 61. 65. 1.0 C.55 57. 51. 0.7 0.55 90. 97. 0.0 0.54 113. 107. Notes: 1. K i , Q*, and L* are in H/n*; T is in °C 2. Estimated net radiation, Q* , is calculated froa the regression equations 6.6a and b. 3. A correlation coefficient of |r|<0.46 is not siqnificantly different froa zero at the 5X level. to o o APPENDIX 6 Energy and water balance suaaary. (Refer to section 6.4) >AIE T Q* K» L*e OH QE 2a 4. 8 87. 111. -44. 67. 7. -3. 29 5.4 99. -36. 63. 7. 0. 35 3.0 29. 0. 29. 4. 0. 36 3.9 30. 52. -11. 41. 5 . 2. 37 4. 8 76. 86. -27. 59. 13. 0. 38 7.0 69. 127. -47. 81. 8. -2. 39 6. 9 72. 89. -27. 62. 7. 1. 40 3.5 75. -22. 53. 6. 0. 41 4.2 104. -36. 69. 3. -1. 42 5.6 123. -43. 80. 6. -1. 43 2.9 83. -27. 56. C -3. 44 2 . 2 79. -23. 57. 3.' -1. 45 -0. 1 68. -16. 52. 0. -2. 46 -0. 1 133. -43. 90. 0. -5. 47 3.5 102. -29. 73. 1 . 0. 48 5.S 93. 141. -44. 96. 8. -1. 49 7.5 113. -33. 80. 12. -1. SO 6.7 50. 70. -15. 55. 9. 2. 51 4.3 71. 96. -26. 70. 6. 0. 52 2. 1 78. -18. 59. 3 . 0. 53 2.6 65. 91. -23. 68. 3. -2. 54 3.7 52. 59. -10. 49. €. 0. 55 4.4 89. -22. 67. 9. -1. 56 6.2 138. -42. 96. 7. -1. 57 7.0 83. -19. 63. 10. 4. 58 4.8 43. 39. -1. 37. 3 . 2. 59 4.6 94. -23. 71. 10. 2. 60 3.3 83. -19. 64. c -1. 61 3.7 145. -42. 103. 5.' -2. 62 4.4 87. 104. -26. 78. 4. - 1. 63 4.7 104. -26. 78. 6. 0. 64 3.6 69. -12. 57. 3 . 1. 65 6. 1 128. -34. 94. 6. 0. 66 8. 2 149. -42. 107. 1 1 . 0. 67 9.5 151. -42. 110. 11. 0. 68 7.4 150. -41. 109. 1 1 . 0. 69 6.7 5 3 . 138. -37. 101. 11. 0. 70 7.9 9 0 . 126. -31. 94. 10. 3. 71 6 . C 5 5 . 74. - 1 3 . 61. 8 . 3. 72 4 . 0 5 5 . - 6 . 49. c # 2. 73 4 . 7 5 8 . 6 8 . - 1 1 . 58. 6 . 2. 74 7. 8 8 9 . 118. -28. 89. 14. 4. 75 6.7 151. - 4 0 . 111. 16. 3 . 76 9 . 0 114. 152. - 3 9 . 112 . 1 2 . 0. 77 5 . 7 8 6 . - 1 6 . 7 0 . 9 . ~-1. 78 7. 0 148. - 3 8 . 110. 1 2 . - 2 . 79 7. C 4 4 . - 1 . 4 2 . 6 . 2. 80 4 . 9 3 6 . 1. 3 7 . 6. 4 . 81 6. 6 7 8 . -1 3. 64. 9 . 4. 82 7 . 7 102. - 2 2 . 8 0 . 9 . 2. 83 7 . 9 5 6 . - 6 . 5 0 . 1 3 . 4. »H*°E QM((0 8 P E (calc) (obs) 4. 71. 67. 0.2 0.1 7. 70. 92. 0.4 0.0 4. 33. 28. 3.0 0.0 8. 49. 60. 1.5 -0.1 13. 72. 71. 93. 26.2 0.0 0.0 6. 87. 89. 101. 28.5 0.0 0.1 8. 70. 60. 97. 27.2 0.0 0.0 6. 59. 46. 42. 11.7 9.7 0.0 2. 71. 46. 0.0 0.0 5. 85. 78. 0. 0 0.0 2. 58. 50. 2.4 0. 1 1. 58. 7. 1.1 0.1 -2. 50. 14. 6.6 0.1 -5. 85. 25. 0.0 0.2 0. 73. 67. 51. 14.5 0.0 0.0 6. 103. 89. 76. 21.5 0.0 0.1 11. 91. 92. 115. 32.3 0. 0 0.0 10. 66. 89. 116. 32.7 0.5 -0. 1 5. 76. 64. 67. 18.9 0.0 0.0 2. 61. 50. 42. 11.8 1.0 0.0 1. 69. 39. 50. 14. 1 0.0 0.1 6. 55. 60. 77. 21.6 3.2 0.0 8. 75. 89. 78. 22.0 3.7 0.0 7. 102. 110. 102. 28.6 0.0 0.0 14. 77. 107. 132. 37.0 0.0 -0.1 5. 42. 67. 5.0 -0. 1 12. 83. 114. 10.4 -0.1 4. 68. 82. 67. 18.8 0.3 0.0 2. 106. 85. 88. 24.8 0.0 0.1 3. 81. 78. 74. 21.0 0.0 0.0 6. 84. 64. 77. 21.7 0.0 0.0 4. 61. 67. 55. 15.6 1.6 0.0 6. 99. 92. 100. 28.1 0.0 0.0 10. 117. 124. 122. 34.4 0.0 0.0 10. 120. 124. 131. 36.8 0.0 0.0 11. 120. 117. 117. 32.9 0.0 0.0 1 1. 112. 110. 99. 27.5 0.0 0.0 13. 108. 128. 0.0 -0. 1 11. 73. 53. 12.9 -0. 1 7. 57. 71. 2. 1 -0. 1 8. 66. 107. 0.0 -0.1 18. 108. 171. 175. 47.2 0.0 -0. 1 19. 129. 142. 132. 35.0 0.0 -0.1 11. 124. 121. 115. 30.0 0.0 0.0 9. 78. 64. 57. 14. 8 0.0 0.0 10. 120. 107. 98. 24.8 0.0 0. 1 8. 50. 96. 8.7 -0. 1 10. 48. 117. 3.3 -0. 1 13. 77. 78. 2.6 -0.1 12. 92. 9 9 . 0.0 -0. 1 17. 67. 128. 2.0 -0. 1 NOTES: 1. Onlts: T i s i n °C; B, P. and E are i n aa/day; a l l others are in «/•*... 2. B i s streaa runoff i n ••/day. calculated assuainq 10* qreater e f f e c t i v e watershed area. 3. 0M(|O I s calculated assuainq 8J . l i q u i d water content, and usinq area of p a r t i a l snow cover is the late season. 4 . Evaporation i s calculated at aet. s i t e , f o r snow only. i i I I | M O 

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            data-media="{[{embed.selectedMedia}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
https://iiif.library.ubc.ca/presentation/dsp.831.1-0094465/manifest

Comment

Related Items