Open Collections

UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Assessment of the snow-cover numerical model crocus-application to avalanches and hydrology Mingo, Laurent 1996

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

Item Metadata


831-ubc_1996-0143.pdf [ 4.87MB ]
JSON: 831-1.0050387.json
JSON-LD: 831-1.0050387-ld.json
RDF/XML (Pretty): 831-1.0050387-rdf.xml
RDF/JSON: 831-1.0050387-rdf.json
Turtle: 831-1.0050387-turtle.txt
N-Triples: 831-1.0050387-rdf-ntriples.txt
Original Record: 831-1.0050387-source.json
Full Text

Full Text

ASSESSMENT OF T H E SNOW-COVER NUMERICAL M O D E L CROCUS - APPLICATION TO AVALANCHES AND HYDROLOGY by LAURENT MINGO Maitrise de Sciences et Techniques, Universite de Provence, France, 1991 Ingenieur Dipl., Institut National Polytechnique de Grenoble, France, 1993  A THESIS S U B M I T T E D I N P A R T I A L F U L F I L L M E N T O F THE REQUIREMENTS F O R THE D E G R E E OF MASTER OF APPLIED SCIENCE in THE F A C U L T Y OF G R A D U A T E STUDIES Department of C i v i l Engineering We accept this thesis as confonriing to the required standard  T H E U N I V E R S I T Y OF BRITISH C O L U M B I A March 1996 © Laurent Mingo, 1996  In  presenting  degree freely  at  this  the  available  copying  of  department publication  in  partial  fulfilment  University  of  British  Columbia,  for  this or of  thesis  reference  thesis by  this  for  his thesis  and  study.  scholarly  or  her  for  of  Date  DE-6  (2/88)  HUcU  gain  shall  g w ^ w » w ^ _  5,  '<U  the  requirements  agree  that  agree  purposes may  representatives.  financial  The University of British Columbia Vancouver, Canada  I  I further  permission.  Department  of  be  It not  is be  that  the  for  an  Library shall  permission for  granted  by  understood allowed  advanced  the  make  extensive  head  that  without  it  of  copying my  my or  written  Abstract  Abstract  The French snow-cover numerical model CROCUS was tested with respect to avalanche forecasting issues and hydrological applications under two specific climatic conditions. Mt. Fidelity at Glacier National Park (Selkirk Mountains) and Blackcomb Mt. Resort (South coast Mountins) were chosen for the experiments. These sites are characterized by deep snow-packs (3 to 4 meter snow-pack is common) with moderate snow-pack temperature gradients in the order of 5 °C/m. Numerous time periods can also commonly experience 10 °C/m to 15 °C/m gradients as well as isothermal temperature distributions. Such snow-pack characteristics offer the possibility to assess the performances of the model under various new conditions that differ from previously published work. CROCUS proved itself being very efficient for modeling snow-depth, density and temperature profiles, which are parameters considered important for hydrological modeling. Results show that good performance of the grain simulation is only obtained for particular ranges of snow-pack temperature gradients. For values close to 5 °C/m it is sometime difficult to achieve good simulations and the model has a tendency to mistakenly emphasize facets formation. Suggestions are proposed for the remediation of this behavior. CROCUS' heat exchanges simulations at the surface of the snow-cover were processed as an attempt to track surface hoar occurrences. Encouraging results are shown.  ii  I  iii  Table of Contents  Abstract Table of Contents List of Tables List of Figures Acknowledgment  ii iv vi vii ix  Chapter 1: Introduction 1.1 1.2  1.3  Overview Issues addressed by CROCUS 1.2.1 Snow avalanches a) Avalanches as a natural hazard b) Cost c) Role of the model 1.2.2 Hydrological issues a) Basin hydrology b) Role of CROCUS 1.2.3 Additional hydrological-related issues a) Sudden mid-winter breakups in mountainous regions b) Water quality Test of the model  1 2 3 3 3 4 5 6 8 9 9 10 11  Chapter 2: CROCUS: a physically-based approach for snow-pack modeling 2.1 2.2  2.3  Purpose Description of the model 2.2.1 Physical laws incorporated into the model 2.2.2 Quantification of snow metamorphism laws 2.2.3 Discrimination of metamorphism Using the model 2.3.1 Inputs and outputs 2.3.2 Creating the input files 2.3.3 Description of the input and output files 2.3.4 Customized creation of meteo.mso 2.3.5 Visualization of the simulation  Chapter 3: Experimental set-up iv  15 16 16 22 23 24 24 25 27 30 31  3.1  3.2  3.3 3.4  The sites 3.1.1 Mt. Fidelity 3.1.2 BlackcombMt Instrumentation 3.2.1 Mt. Fidelity 3.2.2 Blackcomb Remark on new snow density Remarks on snowfall measurement  33 33 34 35 35 35 37 38  Chapter 4 : Analysis of simulation and field measurements 4.1 4.2  4.3 4.4 4.5 4.6 4.7 4.8 4.9  Avalanche forecasting: Important factors with respect to stability Snow-Depth 4.2.1 Mt. Fidelity - Winter 93/94 4.2.2 Mt. Fidelity - Winter 94/95 4.2.3 Blackcomb Mountain - Winter 94/95 Temperature profiles Density profiles Discussion on temperature and density simulations Liquid water content profiles Grain metamorphism Surface hoar Run-off  40 42 43 44 46 48 51 54 55 58 66 82  Chapter 5 : Conclusion  85  References  89  Appendixes Appendix 1 Appendix 2a Appendix 2b Appendix 2c Appendix 3 a Appendix 3b Appendix 3 c Appendix 4a Appendix 4b Appendix 4c Appendix 4d  93 94 97 100 104 107 110 114 116 123 128  V  List of Tables  Table 1: Property Damage in the USA in $US. Table 2: Key parameters and CROCUS output. Table 3: Description of the record number i for a simulation beginning at time tO. Table 4: Description of the record number i which contains the profile at the time tO+i-1. Table 5: Fulmeteo.txt format. Table 6: ICSI classification system for water content of snow. Table7: Grain type and corresponding symbol. Table 8: Summary of SHP. Table 9: Contingency table of surface hoar occurrences.  vi  List of Figures  Figure 1: Variables and simulation parameters considered by CROCUS. Figure 2: CROCUS as a core-system for avalanche and hydrological applications. Figure 3: Description of meteo.mso andprofil.mso. Figure 4: Example of graphical user interface used to visualize CROCUS output. Figure 5: Lysimeter front view. Figure 6 : Lysimeter top view. Figure 7: Snow-depth simulation - Mt. Fidelity, 1993/94. Figure 8: Snow-depth simulation - Mt. Fidelity and Blackcomb Mt., 1994/95. Figure 9: Ultrasonic gauge readings before and after wind correction. Figure 10: Temperature profiles - Mt. Fidelity, 1993/94. Figure 11: Temperature profiles - Mt. Fidelity, 1994/95. Figure 12: Temperature profiles - Blackcomb Mt., 1994/95. Figure 13: Density profiles - Mt. Fidelity, 1993/94. Figure 14a: Density profiles - Mt. Fidelity, 1994/95. Figure 14b: Density profiles - Blackcomb Mt., 1994/95. Figure 15: Liquid water content profiles - Mt. Fidelity 1993/94. Figure 16: Liquid water content profiles - Mt. Fidelity 1994/95. Figure 17: Liquid water content profiles - Blackcomb Mt. 1994/95. Figure 18: Description of grain types for dry snow with Sphericity and Dendricity.  vii  Figure 19: Grain type of failure plane for fatal slab avalanches accidents in Canada - 1972-91. Figure 20: Simulated growth and measured air temperature - Mt. Fidelity 1993/94. Figure 21: Surface hoar occurrence of January 20 and 21 1994. Figure 22: Simulated growth and air temperature - Mt. Fidelity 1994/95. Figure 23: Meteorological conditions and simulated growth - Mt. Fideliry, Dec 94/Jan 95. Figure 24: Meteorological conditions and simulated growth - Mt. Fideliry, Feb/Mar 95. Figure 25: Meteorological conditions and simulated growth - Blackcomb Mt., Nov 94/Jan 95. Figure 26: Meteorological conditions and simulated growth - Blackcomb Mt., Jan /Feb 95. Figure 27: Meteorological conditions and simulated growth - Blackcomb Mt., Mar/Apr 95. Figure 28: Snow-pack bottom water run-off.  viii  ACKNOWLEDGMENT I first want to thank my supervisor Professor Dr. David McClung for giving me the opportunity to work in the fascinatingfieldthat is avalanche research. I am very grateful to him for finding a truly exciting subject to work on and for providing me with a.great independence of work. I want also to thank Eric Brun of the "Centre d'Etude de la Neige" - France - for providing us with CROCUS and for being helpful and supportive during the project. I thank David Skjonsberg and Bruce McMahon of Glacier National Park for their help and for allowing me to access the necessary data to accomplish this project. I am particularly grateful to Jeff, Larry and Jon for the time spent to help me on the field. I am very grateful to Bill Mark and Paul "Bones" Skeleton of Blackcomb Mt. Resort for making all the necessary arrangements to facilitate my work at the site of Blackcomb Mt. and for their availability to help me out when necessary. Thanks a lot to all the Blackcomb's employees! I also want to thank Alan Dennis of the Canadian Avalanche Association for his cheeriness every time I went to Revelstoke and stopped by the Avalanche Centre. This project would not have been possible without the financial participation of the National Science and Engineering Research Council (NSERC) and the International Council for Canadian Studies (ICCS). I acknowldedge their contribution to this project. Finally, I am especially thankful to Alan Boulton, Padme Cooke, Urs Fischer, Sabry Khalfallah Pierre Longnus and Sophie Royer, who accompanied me during some of the numerousfieldtrips necessary to do this work and helped me a lot. We all had so much good time in the mountains while working and...skiing.  ix  "The mountain may well be a way of escape from the cities and men, from the turmoil and doubt, from the perplexities and uncertainties and sorrow that tread our lives. But in the truest and most profound sense it is an escape not from but to reality" James Ramsey Ullman.  Chapter 1.  Introduction  Chapter 1 Introduction  1.1 Overview  The aim of this work is to present a study on the snow-cover numerical model CROCUS tested under specific climatic conditions as found in some of the western Canada's mountain ranges. Developed by the Centre d'Etude de la Neige (CEN) in Grenoble - France, the model principally addresses avalanche forecasting and hydrological applications (Brun et Al. 1989, 1992). It is a physically-based model requiring meteorological inputs to run. In return, it provides a simulation of the physical parameters of the snow-pack as described on Figure 1 (Braun and Al. 1994). Today, what makes CROCUS a potentially top-of-the-line tool for the above mentioned applications is its uniqueness among snow models to simulate the type and size of grains present at each depth within the snow-pack along with temperature, density and liquid water content versus snow-depth. By pointing to each of the issues addressed by CROCUS it will be shown how it can bring solutions to them and why it can be an asset for operational use. Figuring out the real capabilities of the model during field testing, pointing out its strengths and weaknesses, investigating potential adjustments to make and assessing its compatibility to each considered issues are the objectives of the work presented in this thesis. While Chapter 2 will be devoted to a broader description of CROCUS, Chapter 3 will deal 1  Chapter 1. Introduction  with the experimental set-up necessary to collect the data to run the model. In Chapter 4, comparisons of field measurements and simulation will be presented and an analysis will be carried out.  PROCESSES ATUOSPHEHE  Figure 1: Variables and simulation parameters considered by CROCUS (Braun and A l , 1994).  1.2 Issues addressed by CROCUS  Most of the land mass in the Northern Hemisphere is snow-covered at some time. While people in northern or mountainous climates try to adapt to long-term snow-covers, most of the temperature zones struggle through intermittent snow events that disrupt normal life. As  2  Chapter 1. Introduction  our society advanced, we have developed some of the technology to deal with snow and have greater use of snow as a natural resource. Much of the history of snow-cover research revolves around two major themes - avalanches and water resources -. These "good and evil" aspects of the snow-cover are the main part of the mankind's highly double relationship with snow. Much of the early attention focused on snow-cover was due to these two subjects, and they still explain and justify most of the snow research done today (Colbeck, 1987).  1.2.1  Snow avalanches  a) Avalanches as a natural hazard McClung and Schaerer (1993) described how avalanches generally affect people, cause property damage, affect environment and how some of the major industries are affected by avalanches: •Transportation: avalanches cause interruption of movement on highways and railroads in mountain corridors. Large cost of snow removal and repair. Deaths, injuries, and destruction of vehicles occurs. •Construction: Avalanches destroy buildings and kill or injure residents. Engineers must make informed decision regarding the placement, design, and protection of facilities and operations in avalanches-prone mountainous terrain. •Tourism: In mountainous recreational areas, avalanches can cause deaths, injuries, bad reputations from lawsuit, restrictions to services, or selection of alternates routes.  3  Chapter 1.  Introduction  b) Cost YEARS COST  70 -75  75-80  80-85  85-90  300,000  450,000  400,000  675,000  Table 1: Property Damage in the USA in $US.  Property damage in North America from avalanches is relatively minor, but true costs are hidden. Protective defenses costs against avalanches and the feasibility studies connected with land-uses planning are far more significant: about 4 times the annual property damage costs. Insurance bill against liability for operations such as helicopter and sndwcat ski companies and ski areas are tremendously increasing. Other costs are due to lengthy closures of rail and road routes and ski facilities during periods of high danger or during avalanche control operation. A closure costs people and companies money in terms of time and business lost and it exerts a pressure on the governments and organizations responsible for avalanche forecasting and explosive control. In B.C. About 70 areas on highways have been identified as needing avalanche forecasting and/or control. In western Canada, the bill for operational control and forecasting is about 10 million $CND per year (McClung and Schaerer, 1993).  c) Role of the model The potential suitability of CROCUS to address avalanche issues is in the simulation of the snow-pack's physical parameters. Having access through simulation to internal variables  4  Chapter 1. Introduction  versus the depth of the snow-pack is highly valuable. The kind of information provided is aimed to complement the work of the avalanche forecaster in supplying snow profile information at a rate that cannot be reached by manual profiles and, virtually in every remote locations, providing the fact meteorological inputs are available for this given site. For instance, grain metamorphism is one of the key parameters to determine the presence of weak layers and evaluating the capability of the model to simulate grains type is part of the work described in this thesis. With such a tool, the forecaster can use this information along with field observations for slope stability assessment. He/she can also directly use the output of the model to run other expert systems and obtain a stability assessment to be compared with his/her own. Hence, testing each key parameters is one of the aim of the present work.  1.2.2  Hydrological issues  Why is snow important as a water resource? When it falls to the ground and accumulates, snow may be considered as water in storage. In Canada, about 36 % of the total annual precipitation is in the form of snow compared with about 5 % average for the rest of the world. The northern location of the country is a primary reason for this characteristic. In addition, western mountainous areas are subject to warmer temperature due to the ocean influences. These latter are at the origin of orographic uplifts of the mild oceanic air masses and therefore these regions get important snowfalls. During the spring, when the winter snowpack melts, it becomes a significant portion of the water available for stream flows. Snow supplies at least one third of the water used for irrigation in the world and is an important  5  Chapter 1. Introduction  contributor to hydropower reservoirs. The fact that snow acts as water storage over the winter and provides soil moisture recharge in the spring is of particular importance to agricultural productivity in some regions (Colbeck, 1987). In British-Columbia most of the territory of the province is covered by snow during the winter, the impact of snow on watershed andriversis obviously important. Let us take an example with the Fraser Basin by detailing its geography and climate (Hutchison, 1987).  a) Basin -hydrology - Geography of the Fraser basin The Fraser River drains a 230,000 km basin of high plateau and mountainous country which occupies the greater portion of the southern half of British-Columbia. The central Interior Plateau is flanked by the Coast Mountains, which border the sea to the west, and by paralleling Columbia and Rocky Mountains on the east. This plateau is roughly wedge-shaped with land up to 2000 meters above sea-level in the narrow southern section, decreasing to 1500m and less at its widest point in the region of Prince George. Between the Columbia and the Rocky Mountains lies the Rocky Mountain Trench, a great trough extending from south of the international boundary to the northern part of the Province. The Fraser River,risingon the western slopes of the Rockies, flows northwesterly through the Rocky Mountain Trench, skirts the northern tip of the Columbias Mountains and cut diagonally southward across the Interior Plateau in a deeply incised channel before turning westward past the southern end of the Coast Mountains to enter the sea at the southwest corner the Province. From the east, the  6  Chapter 1.  Introduction  Quesnel and Thompsonrivers,two of the major tributaries, drain the Columbia Mountains to join the Fraser River at central and southern point in the Interior Plateau. The Coast Mountains contribute to run-off by way of the Nechako River system in the northwest, the Chilcotin River midway in the Fraser Basin, and through the Harrison and Pitt Rivers at the southern end of the range. In the north, the Stuart River, which forms part of the Nechako River system, drains the northern portion of the Interior Plateau, while the McGregor River, flowing from the western slopes of the Rockies, supplements the Fraser River east of Prince George. In the Fraser River system, there are numerous lakes with areas greater than 7 km , 2  and of these, the 10 larger, each with an area in excess of 100 km . 2  - Climate Air masses which invade the basin of the Fraser River from various directions play an important role in the development of the climate in this interior region. During the long cold winters, moist maritime air from the northwest penetrates deeply into the Interior Plateau, bringing snow to all areas. Each year, the accumulation of winter precipitation in the form of snow is acted upon by rapidly rising spring temperatures to start the first freshets in the tributary streams that, in their turn, coalesce to form the annual spring run-off.  - General pattern of precipitation The moist maritime air which moves into the Fraser River basin is lifted by the Coast Mountains and the westward slopes receive substantial quantities of precipitation by the  7  Chapter 1.  Introduction  orographic lifting o f the ocean air mass. Once past this range, the air descends onto the Interior Plateau, temperatures rise and precipitation diminishes. A s the air moves eastward, driven onward by the prevailing winds from the ocean, it is forced to rise over the Columbia Mountains, which form the eastern boundary o f the Fraser River basin, and there precipitation are also heavy.  - Snow precipitation  Upstream o f Hope, approximately 3 5 % o f the annual average precipitation, as recorded at the valley level meteorological stations, is in the form o f snow. It appears that some 70% o f the Fraser River basin lies above 1000 m, and as a result, most of those areas are covered by snow in winter. The rising spring temperatures, and so some extent the addition o f rain, ripen the accumulated snow-pack preparatory to the annual melt which creates the spring run-off. The volume o f run-off, and to a lesser extent the magnitude o f the peak flow at downstream points on the Fraser River system, is dependent upon the water equivalent o f the accumulated snowpack.  b)  Role of C R O C U S  A s a result o f the amount and extent o f snow covered terrain, the role o f snow will have to be taken into consideration when dealing with a broad range o f inter-related water issues. Calculation o f snow-melt will have considerable economic importance for flood forecasting and especially for successful operation o f hydroelectric schemes and irrigation schemes.  8  Chapter 1. Introduction  Hydro-power production, irrigation., fisheries and environmental issues can all together greatly be quantified by snow-pack modeling. Today, models used to treat hydrological problems are still based on conceptual approaches, principally on degree-day methods. Although they require straightforward parameters to run and can be extended to wide ranges without high technological constraints, some situations cannot be simulated. For instance, relatively warm air temperatures do not necessarily mean warm snow-pack when clear skies prevail. Such situation can lead to errors on the snow-melt simulation which could be correctly reproduced with a physically-based approach which includes the radiation budget of, the snow-cover directly derived from actual radiation measurements. In simulating the snowdepth and the density versus depth, CROCUS can follow the water-equivalent of the snowpack, the snow-melt and the water storage available for further melting. The hydrologist can then use this information to feed a run-off model arid derive stream flows once a terrainfeature model is integrated to the scheme. The direct key parameters generated by CROCUS for hydrological application are snowdepth, density of the snow-pack and free liquid water content of each considered layer.  1.2.3  Additional hydrological-related issues  a) Sudden mid-winter breakups in mountainous regions Ice jam flooding is known for causing lots of damage in many parts of Canada (Watt, 1989). It can be created by sudden unexpected mid-winter breakup. To reduce flood losses during  9  Chapter 1. Introduction  these events, breakup forecasting models were developed (Hebabi and Al. 1992; Beltaos and Burrel 1992). Costerton and Doyle (1995) have presented the Similkameen river and Nicola river case studies relating ice jam flooding caused by sudden breakups. They present a forecasting procedure which considers the increase of flow as a function of meteorological drivers and limiting factors. They came to the conclusion that, ideally, snow-pack data should be included into the procedure with a particular consideration for snow-pack temperature profile and density. Knowledge of the presence of ice layers was also identified as an important factor to look at.  -Role of CROCUS With this respect, the simulation of parameters such as temperature profiles, density of the snow-pack and presence of ice layers will have to be carefully assessed to estimate the suitability of CROCUS as an potential effective tool for mid-winter breakup forecasting in mountainous regions.  b) Water quality The hydrochemistry of water appears to be subject to important variation caused by the snowmelt. On a global basis, water chemistry is affected during the spring melt. It is principally due to the impact of the pollutants contained in precipitation and accumulated on the snow-pack all over the winter period. Other major solute supply comes from terrestrial sources depending on the water routing across a catchment, according to the interaction of solute sources and  10  Chapter 1.  Introduction  run-off pathways. On a daily basis too, water chemistry fluctuates according to diurnal flow cycles as a result of the variation of radiative energy input to the snow-cover. It is also apparent that most pollutants are retained in the snow-pack during the winter period with little or no snow-melt before the spring. It was observed that 50-80% of the pollutant could be released with the first 30% of the melt water. The average concentration of pollutants is this fraction would reach 2-2.5 times the concentration in the snow-pack itself, with peak values 5 times greater than the snow-pack pollutant concentration for the very first fractions of melt (Johannessen and Henriksen, 1978; Caine, 1989).  - Consequences and role of CROCUS The sudden release of the pollutants during the first phase of the snow-melt during spring causes rapid changes in the chemical composition of streams and lakes. The impacts of these changes are largely unknown, but most likely have an effect upon the plankton and littoral communities. The effect on fish is best understood and the changes may lead to severe physiological stress and occasionally massive fish kills. In addition the spring melt occurs at a time which is critical to the hatching stage of salmonid fish species. Again, CROCUS could be an efficient tool to deal with such issues, since timing of snow-melt can be obtained from the observation of the snow-pack bottom water run-off simulation.  11  Chapter 1. Introduction  1.3 Test of the model  In its last developments in France, CROCUS has been integrated with a suite of modules as depicted in Figure 2.  Modulel Meteorological optimal Interpolation  1 CROCUS Snow-cover simulation!  1 Module 2a Snow-pack stability and avalanche assessment  Module 2b Hydrological applications  Figure 2: CROCUS as a core-system for avalanche and hydrological applications.  The first module is an interpolation model called SAFRAN. It is fed with the whole variety of available meteorological data: visual/automatic weather station network, upper air weather  12  Chapter 1. Introduction  balloon, meteorological models, past meteorological conditions. Eventually, it provides CROCUS with the necessary data set on an hourly basis and for 300m elevation increments on six aspects (N, E, W, S, SE, SW) for 23 principal ranges in the French Alps (Durand and Al. 1993). These simulated profiles can be either directly used by the user or plugged into another model for stability assessment or for run-off forecasting in a basin. On the basis of the physical parameters simulated by CROCUS, module 2a first derives the hardness of each layer using empirical relations (as opposed to physically-based). Afterwards, an expert system provides a stability assessment. Module 2a is called MEPRA (Giraud, 1991). Correspondingly, module 2b uses the water storage and melting parameters to derive run-off. Since these schemes use CROCUS as a common core-model from which most of the output quality depends upon, it is crucial to focus on this core in order to assess its performances and its suitability to the potential application presented earlier in this chapter. To do so, the model was tested on a local scale (as opposed to meso-scale) with full-instrumented sites. Simulation were systematically confronted to field data collected nearby the automatic measurement site. Two different sites were chosen: Mt. Fidelity at Glacier National Park in the Selkirk Mountains and Blackcomb Mt. in the South Coast Mountains range. Specific climatic conditions at each site are a good opportunity to observe the performances of the model for different snow-pack characteristics. An overview of the key parameters I want to look at in this study are summarized in Table 2.  13  Chapter 1. Application  Introduction Key parameter  Avalanches  Grain type  Avalanches  Surface Hoar  CROCUS  Comment  YES  /  Mass growth due to condensation is simulated and will be compared to surface hoar growth.  Avalanches  Hardness  /  Empirical  relations  exist,  they  are  not  physically-based, so not included in the model. Avalanches  Temperature profile  YES  Hydrology  Density profile  YES  Hydrology  Snow-depth  YES  Hydrology  Snow-pack run-off  YES  Breakups  Temperature profile  YES  Breakups  Density profile  YES  Water Quality Timing of run-off  YES  Table 2: Key parameters and CROCUS outputs.  14  Chapter 2: CROCUS: a physically-based approach for snow-pack modeling  Chapter 2  CROCUS: a physically-based approach for snow-pack modeling  2.1  Purpose  So far, the majority of snow-pack mathematical models have been based on the degree-day approach which only addresses snow-melt problems. This method has the great advantage of requiring only a few input parameters and hence it rmnimizes the field instrumentation necessary to gather these data. However, during the past 10 years important technology advances have increased the capabilities of weather instruments, computers and data communication protocols. As a result, physically-based models for snow-cover are available and easily operated. Unlike the degree-day method, the approach takes into consideration physical laws to represent the phenomena to be simulated. Although they require more input parameters, today technology enables physically-based models to exhibit their potential without being limited by their need in numerous parameters. CROCUS is a physically-based snow-cover model. Its aim is to simulate the physical parameters of the snow-pack when snow is present on the ground. To do so, CROCUS needs two main sets of input data. First, it requires the usual data of an initial snow profile as initial  15  Chapter 2: CROCUS: a physically-based approach for snow-pack modeling  data which can be as simple as a no-snow-on-the-ground situation when the simulation is started before the first snowfalls of the season. Thereafter, the model is fed with ongoing meteorological data used to predict the evolution of the snow-pack. Weather data are much more accessible than internal snow-pack parameters and offer more flexibility: local weather measurements can be made routinely and to a certain extent, successfully automated. They also offer the potentiality of being extended on larger geographical scales to enable coverage of large areas. At contrary, internal snow-pack parameters can only be observed on the spot, prevailing this spot is accessible. Hence, the simulation of these internal parameters obtained directly from meteorological inputs enables to expand the area under investigation and, because of their greater time-availability, allows to provide the evolution of the snow-pack close to real-time.  2.2  Description of the model  2.2.1 Physical laws incorporated into the model In this section, a description of the model is provided and a summary of the detailed description of Brun and Al. (1989) is given. Initially, CROCUS was developed to simulate energy and mass exchanges of the snow-pack at a given location as a function of the meteorological input. The approach was to simulate the energy and mass evolution of the snow-cover as a function of past and present weather condition. At this stage, the energy and mass balance consisted of taking into account: incoming and outgoing long-wave radiation,  16  Chapter 2: CROCUS: a physically-based approach for snow-pack modeling  short wave radiation, turbulent exchanges between the snow surface and the atmosphere, heat exchanges due to precipitation, heat conduction through the snow-pack, water movement through the snow-pack, snow settlement and heat transfers between snow and ground. Eventually, metamorphism algorithms for grain metamorphism were introduced into the model. They were establishedfromprevious studies on temperature gradient and wet-snow metamorphism and experiments on dry and wet snow samples. Metamorphism algorithms were necessary to improve the derivation of the settlement, and the albedo which both depend on the simulated stratigraphy, i.e. the type and size of snow grains constituting the different layers of the snow-cover. To do so, continuous parameters describing the shape of crystals were defined as function of the prevailing temperature, temperature gradient, and for wet snow, as function of wetness for the layer considered. Furthermore, to derive the mechanical properties of the layers constituting the snow-pack - one of the necessary conditions to describe the stability of the snow-pack - , it is crucial to be able to simulate the grain characteristics.  -Long-wave radiation: QI In the 5-40um range these infra-red radiative exchanges are confined to the snow surface. The energy balance at the surface simply considers the incident radiation Q>1- and the gray-body emission of the snow surface at the temperature T. The emissivity 8 of the snow, ranges from S  0.98 to 1 and is assumed to be equal to 1. If a is the Stefan constant.  17  Chapter 2: CROCUS: a physically-based approach for snow-pack modeling  Ql = 8 Q i - e a T s  s  4  Infra-red radiation can be obtained from meteorological parameters such as humidity, temperature and cloudiness. However, the use of infra-red radiometers is recommended. First because the presence of observers to record the cloudiness is not always convenient and second, because radiometers directly take into account the presence of surrounding emission sources such as trees or snow slopes. For instance, a site situated under a canopy would receive an important part of infra-red radiation from the vegetation. This would be directly measured by an infra-red radiometer and the radiative balance would be feasible.  -Short-wave radiation: Short-wave radiation is considered in the 0.3 - 2.8pm range and it encompasses visible and near infra-red wavelengths. Three subranges are introduced: (0.3 - 0.8pm), (0.8 - 1.5pm) and (1.5 - 2.8pm). For each of them albedo and absorption coefficients are defined based on the theoretical work of Warren (1982), Sergent and others (1987). _R  Solar radiation penetration into the snow-cover follows an exponential function e  w  Z  with P  strongly dependent on wavelength. A value is defined for each subrange as a function of the density and the "optical" grain size. Similarly, albedo is defined as inversely proportional to grain size. For the visible range (0.3 - 0.8pm), albedo is expressed as a decreasing function of the snow surface age. The coefficient used with the age was fitted at the Col de Porte in France by the CEN. This forested site experiences considerable vegetation fragments in the snow-cover falling off the nearby trees such as pine needles, moss. As a result, it might be  18  Chapter 2: CROCUS: a physically-based approach for snow-pack modeling  necessary to decrease the magnitude of this coefficient for a high alpine area where the albedo is likely to remain higher during longer periods like in my study. Direct measurement of the solar radiation is recommended although hourly interpolation of the incoming solar radiation as a function of the latitude, longitude, elevation and cloudiness are sometimes used. Potential solar masks such as mountains, trees can also be defined, nevertheless cloudiness is required and like for infra-red radiation, a radiometer proves to be more adapted. At this stage three coefficients have to be defined. Their role is to produce three values of solar radiation in the three defined subrangesfromthe initial value of the sensor. Ideally they should be function of the type of clouds, their thickness, their vertical distribution in the atmosphere. However, such information is not usually available and the coefficients are taken constant for each subrange. In the model the coefficients are: 0.3 -0.8um: Cl =0.51 0.8 - 1.5um: C2 = 0.34 1.5-2.8um: C3 = 0.15 Usually, the radiometers used to measure the visible component of the solar radiation will be sensible in the (0.3um - 2.8um) range. For instance, assurning 1000 W/m are measured by the 2  radiometer, Cl, C2, C3 will give out to 510 W/m for the first subrange, 340 W/m for the 2  2  second one and 150 W/m for the last one. 2  Note that part of the range encompasses near infra-red wavelengths, although the measurement is referred as visible radiation. The reason is that the physical effects of the  19  Chapter 2: CROCUS: a physically-based approach for snow-pack modeling  radiation on the snow-cover can be described similarly within this range as opposed to higher infra-red's wavelengths treated as described in the previous section.  -Turbulent exchange between the snow surface and the atmosphere: The sensible and latent turbulent flux are expressed in the model according to Deardorff (1968). Since the air above the snow cover is usually warmer than the snow surface due to infra-red loss, the boundary layer tends to be stable. Hence, the turbulent transfer coefficients are low, and for slight wind conditions, turbulent heat exchanges are small relative to heat conduction and vapor diffusion energy exchanges. Therefore in the model, two coefficients were added to the wind velocity term to perform the calculations when the wind velocity is low. Initially the wind appeared as a single order factor W. This was then replaced by a+bW with a and b requiring field adjustment for a given site. In this study, these heat exchanges were used to derive mass variations of the snow-cover to determine whether they are relevant indicator for surface hoar occurrence (Chapter 4).  -Heat exchange due to precipitation Two assumptions are made. First, snow falls at the snow-surface temperature. Second, rainfall temperature is assumed to equal to the air temperature. As a result, snowfall does not generate direct heat exchange as opposed to rainfall. This latter produces an energy proportional to the considered mass of water, the specific heat of water and the temperature difference between snow and water.  20  Chapter 2: CROCUS: a physically-based approach for snow-pack modeling  -Heat conduction through the snow-pack Temperature gradient governs the heatflowof the inner snow-pack and hence determines metamorphism. The heatfluxis proportional to it with a coefficient of proportionality A, depending on the vapor density, and on the vapor diffusion coefficient in snow. -Water movement through the snow-pack Waterflowoccurs when water saturation exceeds the irreducible water saturation (Colbeck, 1972). This latter is function of the grains size and type. However, the model is onedimensional and it does not take percolation effects into account. A model assumption is also that the water run-off is totally absorbed by the ground.  -Snow settlement Snow settlement is the result of the combined effects of grain metamorphism and the weight of the upper layers. A settling law was established by Navarre (1975) and is used in the model. - d e / e = (-CT/t]).dt  with e layer thickness, rj vertical stress and T| viscosity which is a function of both temperature and grain type.  -Heat transfer between snow and ground  21  Chapter 2: CROCUS: a physically-based approach for snow-pack modeling  Because of the inter-annual variation of ground temperature, an energy Qg, generally positive, is supplied to the bottom of the snow-pack. It depends on climatological and soil type at the specific location. This heat transfer process usually carries small energy amounts in comparison to other energy supplies. It is almost constant throughout the winter and decreases during the melting period where cold waterflowsthrough the ground. However, it is considered constant in the model with a magnitude of 50-60 cal/cm/s (units system used in 2  the model).  2.2.2 Quantification of snow metamorphism laws Snow metamorphism potentially affects all the properties of the snow-pack. In particular, mechanical properties and albedo are highly dependent on the grain type. The problem to be solved is: "If a snow layer is exposed to given conditions, what happens to this layer at later time?" To solve it the Centre d'Etude de la Neige (CEN) conducted metamorphism experiments in a cold lab on various snow samples. Their results, along with the work of previous scientists were put together into the model. To incorporate the grain type simulation into the model Brun and Al. (1992) introduced continuous parameters to describe the grain forms. This resulted in the concepts of dendricity and sphericity being added into the model as new variables. • Dendricity, quantifies how much of their initial shape the crystals still retain. • Sphericity describes the degree of spherical shape.  22  Chapter 2: CROCUS: a physically-based approach for snow-pack modeling  When dendricity reaches 0 % , almost no branches are predicted in the layer, crystals are in a state between faceted and rounded grains (Colbeck and Al. 1990). Then sphericity close to 0 % describes a faceted grain, while 100% sphericity indicates rounded grains. In addition, grain size is used to describe the evolution of facets towards depth hoar and fine rounded grains towards coarse rounded grains. During a snowfall, the snow flakes are assumed to be stellar with maximum dendricity of (100%) and a sphericity of 50%. From this stage, it is assumed the actual form will be rapidly reached through metamorphism. Actually this will not hold for graupel for example, and development and/or improvement of automated discrimination of falling snow particles could be helpful (Muramoto and Al, 1993).  2.2.3 Discrimination of metamorphism From experiments which led to the laws of metamorphism used in the model, the discrimination of the type of metamorphism is based on the magnitude of the prevailing temperature gradient within a given layer. For dry snow, when |AT/AZ| < 5 °C/m a low-gradient metamorphism scheme is used. Dendricity will decrease with time and sphericity increases. The higher the temperature the larger the decrease of dendricity with time, resulting in the loss of stellars' branches. The trend is towards the creation of typical rounded grains. When |AT/AZ| > 5 °C/m a strong-gradient metamorphism scheme is applied. Dendricity still decreases. As opposed to the precedent  23  Chapter 2: CROCUS: a physically-based approach for snow-pack modeling  case, sphericity decreases too. Grains become more angular and eventually can reach the state of faceted grains., and when more growth prevails, reach the form of depth hoar. For wet snow metamorphism, sphericity and dendricity are controlled by the water content of the layer considered.  2.3  Using the model  2.3.1 Inputs and outputs As briefly shown in chapter 1, the following meteorological data are supplied once an hour to the model: - air temperature - wind speed - relative humidity - incoming short-wave and long-wave radiation - amount of snow precipitation - density offreshsnow - amount of liquid precipitation - soil thermal flux. If there is already snow on the ground, a snow profile is taken to supply initial data. In return, CROCUS provides a simulation of the internal natural layers for the location where the measurements had been collected.  24  Chapter 2: CROCUS: a physically-based approach for snow-pack modeling  For each layer, the output parameters are: - temperature - density - grain size and type - liquid water content - history. Total snow depth and bottom water run-off are also returned. History (h) describes the status of a layer. 0, 1,2, and 3 are the four possible values for this variable. - h= 0 describes a layer being always dry - h= 1 corresponds to a layer which previously reached the state of depth-hoar and remained dry; - h= 2 corresponds to a refrozen layer, - h= 3 describes former depth-hoar previously wetted. This variable is used by the module MEPRA to determine the hardness of each layer.  2.3.2 Creating the input files Two data files are necessary as input data for the model: meteo.mso and prqfil.mso (Figure 3). Meteo.mso contains the input meteorological data. Profit.mso contains the initial snow profile obtainedfromfieldmeasurements. Once running, the model expands profil.mso with each new simulation profile it produces. Both datafileshave a text format.  25  Chapter 2: CROCUS: a physically-based approach for snow-pack modeling  METEO.MSO n+1 hours  CROCUS  PROFIL.MSO initial profile TZ  n+1  n simulation loops  Figure 3: Description of meteo.mso andprqfil.mso.  There are two ways to create meteo.mso. One is to use one program (xiniadi.bas) of the software package provided with CROCUS. In this case, weather data are supplied by a human observer twice a day from observations made at 8am and 1pm. The previously described weather parameters are recorded and entered into a computer. Infra-red radiation is computed as a function of temperature, humidity, cloudiness. Solar radiation are derived from the date and time, the latitude, the aspect, the slope inclination, and the cloudiness. Hourly values are interpolated according to the twice daily data. Even though this approach seems simple to set up, it is likely the uncertainty on the interpolation will introduce major inaccuracies in the simulated profiles. In particular, the estimation of cloud cover performed twice a day to enable the model to compute the incoming radiation (solar and infra-red) introduces an important uncertainty. This is in contradiction with my aim to assess the capability of the model by carefully looking at each variable and its associated applications, and also with considering CROCUS as a core system for further developments. These implies to feed the model with  26  Chapter 2: CROCUS: a physically-based approach for snow-pack modeling  top-quality data by preventing intermediate interpolations which can only be approximate in this particular case. Hence this method was not used in this study, however, it is described in Appendix 1 as well as the software package. The second method requires the hourly weather. In my study, they were obtained by field instrumentation. It requires more work but allows a greaterflexibilityin the use and test of the model. Moreover, once the data acquisition process is well established, one is close to real operational mode where the model would run automatically after each new data set being recorded. This method consists in building meteo.msofromthe various measurement systems installed on the field and adapt their data format to meteo.mso. To do so, software development is necessary to treat the different type of errors inevitably occurring in the data collection and to format the data files. Forprofil.mso,  an initial snow profile has to be provided to CROCUS. To do so xcaradi.bas -  one of the programs available in the software package with the model - is used. Xcaradis.bas also saves the initial attributes of the profile which are: date, time and number of hours of simulation.  2.3.3 Description of the input and output files  27  Chapter 2: CROCUS: a physically-based approach for snow-pack modeling  - Meteo.mso'.  Input data as they appeared in meteo.mso are listed in Table 3. Each line is made of 62 characters, and for a simulation during n hours, n+1 records are required.  Type of data  Units  5  Air temperature at tO+i-1  1/100 °K  27215  4  Wind velocity  1/10 m/s  30  3  Air relative humidity  %  98  Incoming short-waves [tO+i-2, tO+i-1] 10" cal/cm/s 6  2  within [0.3, 0.8 um[ 5  within [0.8, 1.5 um[  5  within [1.5, 2.8 um]  5  5840  Incoming long-waves [t0+i-2, tO+i-l] IO" caVcm/s 6  2  7150  5  Rainfall [tO+i-2, tO+i-l]  1/100 mm  100  4  Snowfall [tO+i-2, tO+i-1]  1/100 cm  250  3  Grain type offreshsnow: fixed  dendricity  990  6  Unused data  5  Soil thermal flux  IO cal/cm/s  60  2  Carriage return  -6  2  Table 3: Description of the record number i for a simulation beginning at time tO.  28  Chapter 2: CROCUS: a physically-based approach for snow-pack modeling  - Profilmso: Profil.mso  is described in Table 4. Record 1 contains the initial profile while records 2 to n+1  contain the simulated ones. The length of a record is 1581 characters.  Digits  Type of data  Units  8  Initial profile attributes: Year, month, day, time  YYMMDDHH  4  Duration of the simulation (equal to N)  hours  4  Standard air pressure at the simulation location  hpa  2  Slope of the simulated snow-cover  degrees  50*4  Layers thickness (from bottom to surface)  1/100 cm  50*5  Layers temperature  1/100 °K  50 *4  Layers density  1/10 kg/m  50*4  Layers liquid water content  1/100 % Vol.  5  Total snow depth  1/10 (-990 to 990)  50*4  -l*dendricity if dendricity > 0  3  else sphericity. 50*3  Sphericity if dendricity > 0 else grains size.  50*1  History of the layer  4  Bottom water runoff during the last hour  2  Number of numerical layers  50*6  Snowfall date of each layer (day, month, year)  2  Carriage return  1/10 for sphericity 1/100mm for size 1/10 mm DDMMYY  Table 4: Description of the record number i which contains the profile at the time t0+i-l.  29  Chapter 2: CROCUS: a physically-based approach for snow-pack modeling  Depth is taken normal to the slope. The number of numerical layers variesfrom0 to 50. If there are fewer than 50 layers, the remaining space is filled with zeros.  2.3.4 Customized creation of meteo.mso  As one can see from meteo.mso format, the file does not include the date and time corresponding to each data line. The information is carried by two other files (also with other information): simul.mso and carsim.mso. Basically, both are created when meteo.mso is created by interpolation of twice daily data (with xiniadi.bas). These are importantfilesfor the graphical interface when the user wants to visualize and store some simulated profiles after running CROCUS and when the initial attributes of the simulation are needed (date, time of the initial profile, number of hours of simulation). Nevertheless, having the date and time information appended to meteo.mso would be convenient and would ease the whole data handling. That is the reason why the so-called fulmeteo.txt was created for the present work. Digit  Description  8  date: MM/DD/YY  1  blank  4  time  1  blank  62  Meteo.mso format  Table 5: Fulmeteo.txt format.  30  Chapter 2: CROCUS: a physically-based approach for snow-pack modeling  Once set up, it is used to derive meteo.mso. Fulmeteo.txt is built with the hourly data measured in the field. Errors and missing data must be corrected. Once the initial attributes of the simulation are stored in, the program lauubc.bas produces meteo.mso corresponding to these attributes. Meteo.mso can either be extracted from the whole fulmeteo.txt or only a part of it, again with date and time cut off to match meteo.mso's format. In the meantime, simul.mso and carsim.mso are created just as though the interpolation would have been run saving the attributes for later use. Table 5 presents the format offulmeteo.txt. Once everything is ready, crocus.exe is run andprqfil.mso is expanded with the simulated profiles.  2.3.5 Visualization of the simulation  Form  Dens.  -kit HH  LWC II  -31/ b1 B1/ 1  1b5  0  m  D  lb/ 1  3oa  0  13/ 5  ]]0  0  311  0  11/ 5  .  w II  E  2b/12/ 1"t 1B/12/ R"t b/12/ RW 3/12/ Rit 1b/11/ R"t  11/ 10  0  11/ 111  U D  11/ i—i—i—I—i—i—i—i—i—r -EO -1B -1b -1if -12 -10 -a -b - i . -3 bOQ ttBO WSD ]h0 300 M 1 BO 120 bO 20 1B 1b 1W 12 10 B b \ 2  12  • TEMPERflTURE TS=268.5 T-18=-6.1 H=211.4cm • DENSITY HASS£=71.09 t 0.00 /cm2 • U0L- LUC * v o i . g  Figure 4: Example of graphical user interface used to visualize CROCUS output.  31  Chapter 2: CROCUS: a physically-based approach for snow-pack modeling  The program xresadi.bas is used to use to display the result of simulation. Figure 4 shows typical output. The menu also allows saving some profiles chosen by the user. In this case, two files are generated: resdel.mso and resull.mso. Respectively, they contain the saved profile and additional attributes. These enable re-use of a profile once a new session is initiated with xcaradi.bas. However, a profile saved in this way is linked to its attributes and is not always convenient to re-use especially if the user wishes to modify a few parameters. Unless the profile is meant to be re-used right away, it is advisable to save it in a specific file defined by the user.  32  Chapter 3: Experimental set-up  Chapter 3  Experimental set-up  3.1  The sites  3.1.1  Mt. Fidelity  The measurements necessary to run the model were conducted at Mount Fidelity in Glacier National Park during the winters 93/94 and 94/95. This instrumented site also is one of the study plots maintained by the Parks Canada's avalanche control staff in charge of the road safety of this portion of the Trans-Canada highway. Situated in the Selkirk range, part of the Columbia Mountains, the site is located at an elevation of 1910m a.s.L A transitional snow climate between maritime and continental types characterizes this area (Armstrong and Armstrong, 1987; McClung and Schaerer, 1993). As a result, the area receives a very large amount of precipitation with the snowfall rangingfrom10 to 15 meters per year creating a deep snow-pack (Schleiss, 1989). It usually remains at 2000mfromearly October to mid-July. Winter temperatures are moderately cold. Still, the influence of the Pacific can be felt with, sometimes, warmer periods near or abovefreezingfollowed by more intense cold periods when an arctic air-mass moves far enough south. However, these intense cold periods usually do not prevail too long. As a result, depth hoar is generally absent of the snow-pack characteristics of the area since temperature gradients are too weak. Nevertheless, facets are likely to form during the coldest periods in upper layers as well as surface hoar if clearing occurs.  33  Chapter 3: Experimental set-up  The study plot is facing south on a mid-alpine terrain with sparse trees. Generally, winds are calm to moderate. The entire area is closed to public access and guarantees virtually perfect conditions for snow research.  3.1.2 Blackcomb Mt. CROCUS was tested during the winter 94/95 at this site nearby the top of the Solar Coaster chairlift at Blackcomb Mountain Resort. Situated at 1860m a.s.l. on a wide shoulder, the site overlooks the valley bottom and faces north. The climate is typically a maritime snow climate with mild temperatures and successive frontal systems from the Pacific hitting the Coast Mountains during the winter months. Important snowfall and deep snow-pack are common. Usually,, frequent above-freezing condition alternate with colder periods resulting in numerous re-freezing layers caused by rain on snow events or melt-freeze. As for Mt. Fidelity, the snow-pack is usuallyfreeof depth hoar at the site. The predominance of ski runs nearly everywhere in the vicinity was a real problem. The instrumented site was fenced off and it is located by the Ski Patrol building. For the snow profiles,findinga placefreeof skiers and having aspect, slope inclination as similar as possible than at the instrumented site were two constraints to consider when looking for an optimal study plot. As a result, the snow profile sitefieldsite was chosen 150 m awayfromthe instruments upper on the shoulder where the Ski Patrol building is located. Gusty winds were often recorded at the site. Wind speed can often peak to 20m/s andfrequentlyaverage 5m/s. Hence, saltation and blowing snow are common at the site. It is possible that snow can unevenly be redistributed between the instrumented site and the test field site. Nonetheless, observing the model in these severe conditions can be valuable since snow condition in windy places are of particular importance for avalanches.  34  Chapter 3: Experimental set-up  3.2  Instrumentation  3.2.1 Mt. Fidelity Necessary data to run Crocus were automatically collected, except for the new snow density and the ground heat flux. A set of precipitation gauges allowed a satisfactory discrimination between rain and snow and an automatic infra-red snow-gauge was used to determine the height of new snow coupled with an automatic water equivalent gauge equipped with mixer and anti-freeze. The study plot was visited every morning at 7am to collect current snow and weather observations and maintain the instruments. During storms, the site was visited twice a day by Canadian Parks Service staff at 7am and 4pm, to double the amount of collected information. New snow density was measured once or twice a day every time the height of new snow was great enough to perform the measurement. Solar and infra-red radiation were measured with Eppley radiometers. For infra-red radiation measurement, over-heating of the silicon dome of the pyrgeometer (Albrecht and Cox, 1977; Foot, 1986) was corrected according to Alados-Arboedas and Al. (1988). The principal problem of using these instruments during snowfall, is that they can be buried by snow. Although in a remote weather station an automatic brushing system must have been considered, twice daily manned maintenance of the study plot solved the problem.  3.2.2 Blackcomb The site was instrumented with the following equipment: Ultrasonic snow depth sensor UDG101 (Campbell Scientific) for the total snow depth and the amount of new snow; temperature and relative humidity sensors, Met-One wind sensor, long and short wave Eppley radiometers. Rain on snow events were deducedfromwater equivalent readings of the  35  Chapter 3: Experimental set-up  Catskinner automatic weather station situated at 1550m, temperature readings and daily manual observations. Snowfall densities were derived from the wind and temperature according to Pahaut (1975) and Meister (1985). As for Mt Fidelity, help of ski patrollers at the site allowed keeping the radiometers free of snow after storms. A lysimeter was installed to measure the bottom water run-off of the snow-pack (Figure 5 and Figure 6). It was equipped with strong metallic grating with fine grid, strong enough to support the weight of snow and prevent rocks, gravel and dust to fall into the tipping bucket. The orifice of the bucket also had a screen to keep gravel off the counting system. 40 cm-high lateral fences were positioned on the grating's edges to minimize transversal flow over the collecting device. Transversal flows are the origin of numerous inaccuracy in direct melt-water measurement from the snow-pack (Kattelmann, 1984). Automatic data were collected with a CR10 datalogger from Campbell Instruments.  Lateral fence. Fine grid grating. Additicjnal colSector  Ground.  ——' ^ ^ ^ ^  1  1  .imeter Figure 5: Lys  36  j Tipping-bucket.  front view.  Chapter 3: Experimental set-up  Figure 6 : Lysimeter top view.  3.3  Remark on new snow density  Except when measured manually, this parameter remains quite difficult to be accurately determined. For remote stations, different type of snow-gauges are usually used. A basic snow-gauge measures the height of new snow while a heated or alcohol-filled snow-gauge measure the water equivalent of new snow. One might think the simple ratio of the height of new snow divided by its water equivalent gives the expected density. Theoretically this is no problem. However in practice, both apparatus and measurement technique have systematic errors. Typically +/-1 cm for a snow-gauge and +/- 1mm for a rain-gauge errors are common. The relative error is expressed: Am/m, with m: measured value and Am: direct error on the measurement. One can see the relative error depends upon the actual depth of snow or amount of water. During an hour, 5 cm of new snow is considered a major storm intensity.  37  Chapter 3: Experimental set-up  The relative error on the snow-gauge is then (Am/m) = 1/5, or 20%. reading. Assuming a snow  density of 100kg/m the amount of water would be 5mm. the relative error on the height of 3  water is (Am/m)  w a t e  r  = 1/5 or again 20%. As a result, the relative error on the density  computation will be (Ara/m)^ + (Am/m) equal to 40%. A more reasonable accuracy water  would involve using gauge readings over longer periods than an hour, like a day or more to derive the density. But in this case the 'real-time" density information is lost. Hence, relations to determine snowfall density as a function of other parameters easier to measure can be valuable. Pahaut (1975) proposes an empirical relation between new snow density, wind and temperature: d = 109 -8*T+26*V (W) with d: snow density in kg/m , T: temperature in °C and W: wind speed in m/s. Although wind 3  must be no greater than 5 m/s, this constraint had to be ignored for the site of Blackcomb where stronger wind did prevail. .Meister (1985) also presents interesting relations between those three variables, although these relations are not highly accurate, their precision is no worse than the measurements obtain with instruments. Hence, this approach to get densities was used.  3.4  Remarks on snowfall measurement  Wind is the first cause of perturbation for precipitation measurement. Larson and Al. (1974), Goodison and Al. (1981), and Yang and Al. (1993) describe methods to minimize wind effects on precipitation measurements and wind correction factors were proposed for specific rain and snow -gauges, mostly collecting gauges. At Mt. Fidelity, each gauge was wind protected by a large shelter. This type of protection and its associated correction factors are not found in the literature which describes other kinds of  38  Chapter 3: Experimental set-up  protection though. Since the study plot area is not prone to strong wind, this might not be an issue. The principal snow-gauge from which snowfall data were obtained is an infra-red beam gauge. A double beam is focused on an horizontal board on which fresh snow accumulates. By geometric triangulation the double beam can detect the surface of the snow cover and the height of the snow on the board is determined. Regularly, the snow is cleared off the board. Comparison of manual and automatic reading showed very few wind effect. The ultrasonic gauge used at Blackcomb directly measures the variations with the distance sensor - top of the snow-cover. Since it does not collect precipitation within an accumulation chamber, the wind does not affect the measurement with this respect. However, blowing snow does affect the readings by creating randomly distributed surfaces hit by the ultra-sonic wave which produce erratic signals. Unfortunately this indirect wind effect is not quantifiable at present.  39  Chapter 4: Analysis of simulation andfieldmeasurements  Chapter 4  Analysis of simulation and field measurements  4.1  Avalanche forecasting: Important factors with respect to stability  The nature of factors to interpret snow stability and used for avalanche forecasting can be grouped in three classes (McClung and Schaerer, 1993). In class-in are found the meteorological factors, while class-U regroups the snow-pack factors and class-I the stability factors. Meteorological factors are the most uncertain to directly assess the stability of the > snow-pack while direct stability tests can give a good idea of the stability at a given location. In class-U, information is equivalent to what one gets from a full snow-profile. Stability is not directly tested but is estimatedfromthe knowledge of the physical parameters measured within the snow-pack. Class-I and II factors require local testing. A computerized system for operational avalanche forecasting using meteorological input, ultimately requires assessing whether class-I factors can be achievedfromthe knowledge of class-UI factors. Passing to stability evaluationfromsnow-pack parameters can be obtained through expert systems (Giraud, 1991; McClung, 1993) regrouping rules of decision used by experienced avalanche forecasters. In the meantime, snow-pack parameters, if not directly measured, can be simulated using physically-based snow-cover models like CROCUS. Using  40  Chapter 4: Analysis of simulation and field measurements  such a model, first requires that class-II factors are correctly simulated to provide relevant information for the stability evaluation. Among the snow-pack parameters, some of them are primary important. Hardness, is often thefirstparameter forecasters look at for extracting slab structure of the snow-pack and for locating weak layers. Unfortunately, hardness governing laws are still quite difficult to model and a physically-based approach is not available yet. Presently, hardness is expected to be a function of the other parameters such as grain type and size, state of the layer: previously wetted or not, density, liquid water content. For instance, wind packing results infinegrains and a high density giving out a high hardness magnitude. At contrary, a layer with sufficient free-water content yields to low hardness. A study on some of these relations was presented by Brun and Rey (1987) and the expert system MEPRA (Giraud, 1991) uses different relations (not available at the time of this study) to derive hardness. Another important parameter is the type of grains found within each snow layer. Three types of grains are particularly important for the forecaster: • depth hoar, • faceted grains, • surface hoar. Jamieson and Johnston (1992) showed that most fatal slab avalanches accidents in Canada involved failure planes composed of these three type of grains. Layers with these grains are prone to exhibit critical properties like low shear strength or fracture propagation. Therefore, it is crucial to verify if their presence is reproduced by the model.  41  Chapter 4: Analysis of simulation and field measurements  Temperature profiles are also significant because they control the type and magnitude of the crystal metamorphism occurring within the snow-pack and the simulation of this parameter must be accurately reproduced. Time evolution over several days is important and it gives an idea on the type of metamorphism that may occur. Liquid-water content is also an important factors to consider, but since most of profiles in my study were obtained in dry snow-packs, comparison is somewhat limited. On a lesser extent, density is also a significant parameter but is not considered as of primary importance to define the slab structure.  4.2  Snow-Depth  Snow precipitation, settling and melting are considered when snow-depth is computed. Energy inputs at the surface and the bottom of the snow pack along with present temperature of each layer are used to compute an updated temperature profile. First, snow precipitation, if any, is added to the snow-pack. Then, according to the updated temperature profile, grain forms are deduced and they are used with the vertical stress to derive layer settlement. When the computed energy exchanges show occurrence of melting, the equivalent loss of snow is taken into account, thefree-watercontent is calculated and afinalfigurefor snow-depth is given.  42  Chapter 4: Analysis of simulation and field measurements  4.2.1 Mt. Fidelity - Winter 93/94 Mt. Fidelity - Winter 93/94  400  -i  ^  5  ^  ^  i  I M  ol  oi  ^  ^ ^ ^  ok  ol  2  ol  Mt. Fidelity - Winter 94/94  5? £P 8\ .51 8  8  S  8  8  8  S  5  J  ^ 5 ^ ^ ^ 5 c ^ 2 K  <^  «* ^ 111IIIII4 J 1 1 ! 1 1 ! ! ! * * * 4 * 4 ?  Figure 7: Snow-depth simulation - Mt. Fidelity, 1993/94.  43  ol  J  "  Chapter 4: Analysis of simulation and field measurements  The model was initialized on December 20 1993. New snow density passed to the model was obtained from the daily field measurements carried out by Parks Canada's Avalanche staff, when not available, from manual-gauge readings. 'True" snow-depth was measured with a stake at the study plot. Figure 7 compares simulation and measured values of snow-depth. Although all the features of the observation curves are well simulated, there is a well-marked gap between both curves originating during an intense snowfall period between January 3 and January 18 1994. Very few interruptions in precipitation characterize this period during which 250 cm of accumulated new snow was measured. No disfunctionment of the snow-gauge was observed, no melting was simulated and wind remained calm during this period preventing snow-drift. Hence, the settlement scheme might be at the origin of this gap. Nevertheless, accuracy is in the satisfactory range of 10%. The model was reinitialized on January 29 1994 with a new snow profile. Simulation was run until mid-May and shows excellent performance during accumulation, settlement and melting periods as presented on Figure 7. The few slight mismatches are due to occasional measurement errors caused by the snow-gauge.  44  Chapter 4: Analysis of simulation and field measurements  350 -,  Mt. Fidelity - Winter 94/95  300 250 H S  Init on Dec 12 94  200  J  I 150 a  Vi  100  50 0  Blackcomb - Winter 94/95  350 -, 300 H  Figure 8: Snow-depth simulation - Mt. Fidelity and Blackcomb Mt., 1994/95.  45  Chapter 4: Analysis of simulation and field measurements  4.2.2 Mt. Fidelity - Winter 94/95 CROCUS was initialized on December 13 1994. Figure 8 presents predicted and measured snow-depth for the entire year. Manual new snow density recordings were used as snowfall density data . No re-initialization was applied during the 6 month-simulation period. Excellent agreement between both curves is once again demonstrated. Snow-depth curves present similar slopes during the melting period demonstrating a satisfactory simulated melt rate.  4.2.3 Blackcomb Mountain - Winter 94/95 Comparison is shown on Figure 8. The particularity of this site was that accurate snowfall measurements were difficult to achieve. Although the location of the snow-depth gauge was not a wind-deposition area,fluctuationsdue to drifting caused sudden decreases in the snowdepth curve. This was the case early December when strong winds caused a 40 cm erosion of the snow-pack at the snow-gauge site. This type of situation is not yet accounted for in the model and can cause major differences between real and simulated snow-depths. Moreover, blowing snow particles are believed to act as reflective surfaces for the ultra-sonic waves emitted by the snow-depth sensor. Wind-blown snow particles are suspended in the air and the ultra-sonic wave are reflected before reaching the top of the snow-cover. This leads to an overestimation of the snow-depth and therefore of new snow, if any. Although a trend in the snow-depth curve can be extracted, direct hourly readings are impossible. As a result, twice daily readings were only taken into consideration after correcting these erratic data. Hourly snowfall was derived by dividing up twice daily sums into 12 parts, providing that the temperature was below freezing. 46  Chapter 4: Analysis of simulation and field measurements  Even though the untrue snowfall events could be spotted , the simulation cannot recreate sudden decreases due to wind. The snow-pit site turned out to be more wind-protected than the ultrasonic gauge location. As a result, during strong wind periods snow-cover was eroded more at the ultrasonic gauge than at the pit site. To overcome this problem, afirststep was to use weather data and ultrasonic snow-depth curve to highlight the major depth variations. Such events where observed few times and a correction was applied to compensate these losses of snow. Figure 9 shows the curves before and after correction along with the depth obtained during snow-pits. Notice that the terrain where the pits where made is covered by rocks leading to an inaccuracy of +/- 20 cm on the snow-depth. Afirstinitialization took place on November 28 1994, however strong wind prevailed early in December and caused unacceptable differences between snow-gauge reading and snow-depth at the pit site. Hence, the pit site was moved to a better location which was used for the rest of the season and a new initialization was set on December 25 1994. Altogether, the simulation is satisfactory and one can notice how well the melting period is reproduced in comparing the slopes of both curves. They similarity indicates effective simulation of melting rates.  47  Chapter 4: Analysis of simulation and field measurements  Blackcomb - Ultrasonic gauge reading  Figure 9: Ultrasonic gauge readings before and after wind correction. 4.3  Temperature profiles  From present temperature profile, and radiation, air temperature, wind, humidity, and soil heat flux values averaged over the last hour, heat exchanges at surface and bottom are calculated by the model. Then the temperature of each layer is determined using afinitedifference scheme (Brun and Al., 1992).  48  Chapter 4: Analysis of simulation and field measurements  - Mt. Fidelity - Winter 9 3 / 9 4 Appendix 2a (examples on Figure 10) contains the temperature profiles comparison and exhibits outstanding performances of the model. Note that CROCUS was re-initialized on January 29 1994 following the settlement problem discussed in 4.1.1. 13 Feb 1994  Init on 29 Jan  03 Mar 1994  Init on 29 Jan  Figure 10: Temperature profiles - Mt Fidelity, 1993/94  49  Chapter 4: Analysis of simulation and field measurements  - Mt. Fidelity - Winter 94/95 Here again in Appendix 2b, simulation is quite satisfactory. Temperatures and gradients are well reproduced by the model. Figure 11 shows provides two examples. 08 Feb 1995  -14  -12  -10  Init on 12 Dec  -8  -6  -4  25 Feb 1995  -2  0  -14  -12  -10  Init on 12 Dec  -8  -6  -4  -2  0  Figure 11: Temperature profiles - Mt. Fidelity, 1994/95.  - Blackcomb - Winter 94/95 One more time, very good agreement is found between simulation andfieldmeasurements (Appendix 2c and Figure 12). Cold snow-pack as well as warm snow-pack are correctly simulated. Few mismatches can be found on freshly fallen snow. Since air temperature is used to set the fresh snow temperature when it reaches the surface of the snow-cover, it takes few simulation steps for the simulated temperature to evolve according to surface heat exchanges as described in section 2.2.1. This can partially explain the slight mismatches. 50  Chapter 4: Analysis of simulation and field measurements  4.4  Density profiles  After calculation of the temperature profiles, the model makes the necessary phase changes if any. Settlement is then taken into account by decreasing the thickness of each layer and new density is derived.  - Mt. Fidelity - Winter 9 3 / 9 4 Each set of curves depict a very good similarity (Appendix 3a Figures 13, 14a, 14b). The density drops occurring in the simulation curves, (for instance at 150 cm on the profile of January 2, at 225 cm for March 3 and March 20) are due to buried thin layers of surface hoar.  51  Chapter 4: Analysis of simulation and field measurements  These surface hoar layers were previously entered into the model when observed on the field. For such thin layers, density is usually not measured, that explains why no corresponding sharp drops are found in the experimental density curves. The low surface density returned by the model on the profile of April 28 1994 is due to the presence of thin layer of fresh snow with low density in comparison to the snow-pack. The density of this thin layer was not measured on the field. 13 Feb 1994 I  1  i  450  1  i  1  Init on 29 Jan i  350  1  i  1  i  250  1  03 Mar 1994 i  1  150  I  3  5  0  Init on 29 Jan  I— —i— —i— —i— 1  50  1  450  1  350  250  r~i  r  150  3  5  0  50  Figure 13: Density profiles - Mt. Fidelity, 1993/94.  - Mt. Fideliry - Winter 94/95 The good results of the winter 93/94 are confirmed for this site where the density simulation remains satisfactory (Appendix 3b).  52  - Blackcomb - Winter 94/95  For this site, fresh snow density was obtained from Pahaut's equation (1975). Profiles are shown in Appendix 3 c. Although the trend is quite acceptable, the results are not as good as at Mt. Fidelity. Prevailing wind magnitudes often overcame the suggested domain of validity of Pahaut's equation (see section 3.3) and can explain these results.  53  Chapter 4: Analysis of simulation and field measurements  16 Feb 1994  I  1  I  450  1  I  Init on 25 Dec  I ' I  1  350  250  1  I  1  I  150  1  I  3  5  0  II  50  16 Mar 1995 1  I  1  450  I  1  I  350  Init on 25 Dec 1  I  1  250  I  1  I  1  II  350  150  50  Figure 14b: Density profiles - Blackcomb Mt., 1994/95.  4.5  Discussion on temperature and density simulations  The good performances of the model to simulate the temperature profile shows that heat exchanges are correctly modeled. Temperature gradients being successfully reproduced, a necessary condition with regards to grain metamorphism simulation is fulfilled. Density curves demonstrate satisfactory simulation especially at the Mt. Fidelity site where little wind usually prevails. For Blackcomb's density profiles, accuracy is not as good as on Mt. Fidelity. Frequent gusty winds conditions at the sites are thought to be at the origin of mismatches. Density was derivedfromall wind values and temperature during snowfall with Pahaut's equation although the equation is restricted to winds not exceeding 5 m/s. According  54  Chapter 4: Analysis of simulation and field measurements  to Meister (1985) an upper limit of 130 kg/m was chosen to be used for the site of 3  Blackcomb. This lack of manual density data can be a source of error, although operational use of the model on remote sites will probably not benefitfrombetter new snow density data. Furthermore, the snow is most likely redistributed after the storm when windy periods prevail. As a result, the actual density might have increased due to wind packing leading to erratic simulations. However, these drifts seem to occur after a month of simulation without reinitialization. Re-initialization on December 25 1994 at Blackcomb, allowed to provide very good results, especially until February 16. In future, possible way to deal with snow and wind related phenomenon is being proposed by Guyomarc'h (1995).  4.6  Liquid water content profiles  The following set of profiles show a comparison between the liquid water content (or free water content) as simulated by the model and as observed in the snow-pack at the observation sites. The x-axis shows the % offreewater by volume versus snow-depth on the y-axis. Although there are only few profiles with a significant amount offreewater within the snowpack to allow a good comparison, these results can give a rough idea of the capabilities of the model to predictfreewater content. Water content were estimated according to the ICSI classification system for water content of snow (Colbeck and Al., 1990; McClung and Schaerer, 1993). This classification is detailed in Table 6.  55  Chapter 4: Analysis of simulation and field measurements  Term  Remarks  LWC (% by volume)  Dry  T < 0 °C, snow grains have little tendency to adhere t  0%  each other when pressed together, as making a snowball. Moist  T = 0 °C, water is not visible at lOx magnification.  < 3%  When lightly crushed, the snow has a distinct tendency to stick together. Wet  T = 0 °C, water can be spotted at lOx magnification  3 - 8%  by its meniscus between adjacent snow grains. Very Wet  T = 0 °C, water can be pressed out by moderately  8 - 15%  squeezing the snow in hands. Slush  T = 0 °C, the snow isfloodedwith water.  > 15%  Table 6: Summary of the ICSI classification system for water content of snow. 28 Apr 1994  Init on 29 Jan 350 300 250 200 150 100 50 0  10  8  6  4  2  0  Figure 15: Liquid water content profiles - Mt. Fidelity 1993/94.  56  Chapter 4: Analysis of simulation and field measurements 23 Mar 1995  Init on 12 Dec  4 May 1995  Init on 12 Dec  Figure 16: Liquid water content profiles - Mt. Fidelity 1994/95.  57  Chapter 4: Analysis of simulation and field measurements  Figure 15 and 16 show the liquid water content (LWC) simulation for Mt. Fidelity for both winters 1993/94 and 1994/95. Results show excellent agreement, except for a peak value in the profile of 4 May 1995 which was not reproduced by the simulation. On figure 17 is shown the simulated and estimated LWC profiles of Blackcomb Mt. Although the number of comparisons for the LWC profiles is low, the overall performance of the model is good. However, biases can be noticed. One has to keep in mind that CROCUS is a one-dimensional model. Hence, percolation effects are not taken into account. Another assumptions, like the total absorption of the water run-off into the ground, certainly does not hold all the time. All of these can contributes to some mismatches, especially for the profile of 22 June 1995 at Blackcomb Mt. .  4.7  G r a i n metamorphism  Once a new temperature profile has been calculated, new sphericity and new dendricity are derived according to temperature, temperature gradient and liquid water content if any. Density is added to these variables to obtain grain size. To easily compare with the observations, the results are expressed according to the International Classification for Snow and Ice (Colbeck and Al. 1990). Grain types were grouped according to specific ranges of sphericity, dendricity and size. Liquid water content and history of each layer - indicating whether a layer was previously frozen - were also used to classify each grain type.  58  Chapter 4: Analysis of simulation and field measurements  Classification  Data code  Newly fallen snow Decomposing and fragmented particles Rounded grains Rounded grains developing facets Faceted grains developing rounding Solid facets crystals Cup shaped crystals Feathery crystals Ice layer Melt-freeze crystals Refrozen form (once wetted) Wet form (<lmm) Wet coarse rounded grain (>lmm)  PP DF RG mxRG mxFC FC DH SH IM mf @symbol w symbol WG  Table 7: Grain type and corresponding symbol. Figure 18 describes the main dry snow types with respect to sphericity and dendricity. In Table 7 each type and its corresponding symbol is presented. International Classification was followed as much as possible according to the last recommendation of the Canadian Avalanche Association ( CAA, 1995). However, one had to use specific characters (@symbol, w_symbol) to describe some of the snow types returned by Crocus. For instance, fine rouded grain becoming wet will be described as w_RG (w followed by the rouded grain symbol). A refrozen form, express a type of crystal that conserves part of its shapes after being wet and refrozen. For instance, refrozen facets are coded: @FC. Notice this does not necessarily correspond to the real behavior of the grains, but read out of the results provided by the model is necessary and to interpret them.  59  Chapter 4: Analysis of simulation and field measurements  PP  •  FC  5  25  Q rriixFC  50  •  75  •  • FC/RG  •  RG/FC  v  95  DTHXRG  SPHERICITY  Figure 18: Description of grain types for dry snow with Sphericity and Dendricity. - Mt. Fidelity - Winter 93/94  Profiles are compared in Appendix 4a with respect to grain forms. Many profiles are fairly well simulated, but others are not. An important mismatch occurs in the January 2 94' profile. The model returns a mostly faceted snow-pack between 65 cm up to 130 cm depth while observation shows rounded grain for most of the snow-pack, except for the top 40 cm composed of new (PP) and partlyfragmentedparticles (DF). After new initialization on January 29, the simulated profiles show generally much better agreement. On February 13, facets observed between 240 cm and 180 cm are very well reproduced by the model. Below, intermediate types between rounded and faceted grains are  60  Chapter 4: Analysis of simulation and field measurements  found and simulation remains fairly satisfactory. On March 3, March 20 and April 23 1994 the grains are reasonably well described. The refrozen crusts at 320 cm and 310 cm are also well reproduced in the simulation of March 20. However, by looking more carefully at the profile of February 13, we can observe that in the sequence of intermediate stages where crystals are found, the simulation produces a grain type with lower sphericity than expected (i.e. mxRG instead of R G or FC/RG instead of RG/FC). This is deduced by relating the ICSFs symbolism (International Commission on Snow and Ice) to its location on the snow type triangle of Figure 18. This trend is also observed on March 3 and March 20 and was generally less important when the model had been reinitialized after each snow-pit. Even though this trend is not too much prominent for the above mentioned profiles, it characterizes a bias in the metamorphism scheme which can lead, in specific cases, to poor simulation. When following the daily evolution of the different simulated temperature profiles (not shown here), the temperature gradients between 20 December 1993 and 2 January 1994 are close to 5 °C/m, sometimes slightly greater in magnitude like 5.5 °C/m, 6 °C/m, sometimes lower, depending on which layer is considered. Generally, the problem seems to originate in layers which are submitted to a gradient of temperature close to the threshold value used in the model. When the magnitude is greater like 7, 10 °C/m, faceting is well simulated. When simulation fails to reproduce the snow-pack stratigraphy, grain size is very well reproduced. Results remain fairly consistent for other profiles. Considerable difference in the size occurring on April 28 is caused by the presence of conglomerates formed by melt-freeze  61  Chapter 4: Analysis of simulation and field measurements  cycles. Hence, the size measured in the field represents the conglomerate size rather than the individual grains. Notice that the air temperatures described in the following sections are mean hourly temperatures.  - Mt. Fidelity - Winter 94/95 - Initialization on December 12: The first profile obtained on January ( Appendix 4b) corresponds to the last day of a 10-day period with clear skies and air temperatures around -10 °C. As a result, the measured profile shows some faceting. It is confirmed by the simulation which returns grain with facets. Again, the sphericity is overestimated: manual profiles present more rounded grains more than those returned by the model. Since the period of clear and cold weather lasted until the arrival of the next weather system (Figures 23, 24), simulated grains turned into facets, showing again the same bias: too much faceting. Thereafter, until the second test profile of January 23, overcast conditions and temperatures around -5 °C prevailed and facet formation stopped. The field profile shows rounded grains throughout most the snow-pack. The model was not able to simulate this profile well although a virtually perfect snow-pack temperature simulation was achieved. Again, it was noticed that the simulated temperature gradients were close to 5 °C/m during the overcast period - the model's threshold value - preventing CROCUS to initiate rounded formation. Without re-  62  Chapter 4: Analysis of simulation and field measurements  initialization, the bias can be carried until the end o f the season. This can be seen on depths from 100 cm to ground in every profile after January 9. For M a r c h 23 profile, the lower part o f the snow-pack remains biased towards facets, while the upper part, above 210 cm, is well simulated: rounded forms are well reproduced as well as fragmented particles and refrozen layers. -Initialization on January 23: Here the model is reset with a snow-pack constituted o f rounded grains (Appendix 4c). Temperature stays close to -5 °C until February 11 where a colder air mass moves onto the area for one week. The comparison o f February 8's simulation with this new initialization on January 23 presents much better agreements with field measurements than when the model was initialized on December 12. The bottom o f the snow-pack is well simulated with rounded grains, the upper part is also well reproduced. Nevertheless few errors are found. The thin faceted layer returned at 160 c m is actually due to the surface hoar form manually keyed into the model with dendricity and sphericity equal to zero and a size o f 2 or 3 mm. When the initialization was performed, the description o f buried surface hoar also matched the sphericity and dendricity ranges o f faceted crystals. Since the actual version o f C R O C U S does not explicitly simulate surface hoar, this confusion was expected. F r o m February 11 to February 25 (Figure 24), the above mentioned cold air mass stalled over the area and was followed on February 18 by warmer air with occasionally temperature above freezing, and mainly overcast skies, providing good conditions to warm the snow surface up  63  Chapter 4: Analysis of simulation and field measurements  to the melting point and creating one or several refrozen layers. This warmer weather prevailed until February 26. The simulation of February 25 shows excellent match for the whole snow-pack. Grains at the bottom remained rounded as observed on the field. Between 90 cm and 190 cm, faceting is well simulated, although the trend for too much faceting is present. Above 200 cm, rounded grains and fragmented particles are well reproduced. At 250 cm, a refrozen layer is correctly simulated. Similar encouraging results are observed on March 23 and May 4.  - Blackcomb - Winter 94/95  Initialization was done on December 25 1994 (Appendix 4d). During thefirstmonth of simulation, temperatures remained in the [0; -5] range with drops up to -10 °C late December and above freezing conditions during the dayfromJanuary 1 to 4 (Figure 25 to 27). Clear skies prevailed during thefirst12 days of the run. The upper part of the snow-pack was most likely cold, with an important gradient within the upper 50 cm. After this cold period, milder temperatures and cloudy conditions prevailed leading to a snow-pack mainly consisting of rounded-grains as observed in the field. The simulation of January 20 agreed these observations. The profile of February 16 features an ice layer at 240 cm. Some facets were observed underneath the layer. The simulation shows the presence of refrozen crystals nearby 240 cm with some faceting occurring too. Otherwise, rounded-grains are predominant both in the field  64  Chapter 4: Analysis of simulation and field measurements  and in the simulation. Between 200 cm and 150 cm, it is interesting to notice the model underestimates sphericity, since a slight faceting is simulated. On March 2, rounded grains are present at the bottom of the snow-pack and subsequently to warm cycles in February, the upper part features few ice layers, some of them quite thin, they are separated by rounded forms resulting of snowfall events between two warmer periods. The model returns reasonably well this complex succession of layers. Refrozen layers are found between 200 cm and 230 cm and 250 cm and 270 cm. Again the tendency to return lower sphericities than actually observed on the field is evident. For subsequent next profiles, same trends are observed. The simulated refrozen grains allow prediction of the presence of icy layers within the natural snow-pack and shows good agreement with the grains observed on the field. Slightly early wetting of the snow-pack is simulated. It is caused by predicted snow temperatures remaining slightly negative on May 14. However simulated wet snow-pack occurred 3 days later than actually observed on the field. For grain size, the simulation performs well for dry snow, however wet grains tend to be smaller than on the field. As stated before, individual grain observation can be mistaken by the presence of conglomerates. Nevertheless, it seems that coarse round grains take longer time to develop in the simulation than in the field.  65  Chapter 4: Analysis of simulation and field measurements  - Conclusion on grain metamorphism The model was found quite efficient to simulate: - the formation of rounded grains when the magnitude of the gradient is clearly lower than 5 °C/m, -the formation of faceted grains when the magnitude of the gradient is clearly greater than 5 °C/m, -simulate the occurrence of refrozen layers, -simulate the size of grain in dry conditions. At contrary, it failed to correctly simulate: - the persistence of rounded grains with a gradient slightly greater than 5 °C/m, mistakenly simulating facets. When real temperature gradients are much lower or much greater than the threshold of 5 °C/m, simulation should be mostly satisfactory. However in climates where gradients are near the threshold value, poor simulation is sometimes obtained. This seems to indicate that a modification of the grain metamorphism scheme would be necessary in order to fix this problem. A greater value, like 7 °C/m or 8 °C/m, might be more adapted although the threshold can depend on other parameters such as density, vapor mobility in a given layer that could be a function of temperature, the inter-grain space, relating then to the density (Colbeck, 1982, 1986; Gubler 1985; Perla, 1985). However in the model, density is taken into account only in the grain growth process of the grain metamorphism scheme.  66  Chapter 4: Analysis of simulation and field measurements  4.8  Surface hoar  In Canada, an important proportion of fatal slab avalanches accidents involved failure planes composed of surface hoar Figure 19 shows a brief summary of the work of Jamieson and Johnston on the subject (1992). The figure is based on 50 accident reports that specified the failure plane (34 accidents with amateur decision makers and 16 accidents with professional decision makers on the type of failure plane). Amateur decision maker  Professional decision maker  Surface  Surface  Figure 19 : Grain type of failure plane for fatal slab avalanches accidents in Canada - 1972-91.  One can see the importance of Hence, a tool capable of predicting surface hoar occurrences would be of a high interest. In the version of the model under test, no specific scheme is available to simulate the growth of surface hoar. Literature is still sparse on the subject and the phenomenon remains quite complex to model. Nevertheless, an attempt was made to observe the capability of CROCUS to simulate the heat exchanges at the surface of the snowpack and deduce from them the likely occurrence of surface hoar. C R O C U S simulates the mass and energy flux occurring between the atmosphere, the soil and the snow-pack. By  67  Chapter 4: Analysis of simulation and field measurements  looking at the latent heat exchanges at the surface, it is possible to retrace the type of physical reaction (condensation or evaporation) occurring at a given time. When cold air is associated with calm conditions, low cloudiness and fairly high relative humidity, conditions are favorable for surface hoar occurrence (Lang and Al., 1984; Breyfogle, 1986). In a simplified manner and with such weather conditions, the simulated condensation can be interpreted as ice growth at the surface of the snow-cover and if this growth is significant, it could be related to surface hoar.  - Mt. Fidelity - Winter 93/94  M  2E-3  Figure 20: Simulated growth and measured air temperature - Mt. Fidelity 1993/94. 68  Chapter 4: Analysis of simulation and field measurements  Figure 20 shows the simulated growth with the mean hourly air temperature measured 1.5 m above snow surface. The condensation curve exhibits several peaks. Some of them can be considered as major peaks - say, with a magnitude greater than 1 to 1.5mg/cm/h. They 2  simulate periods of important condensation and might be related to surface hoar growth under certain conditions. For instance, the so-called major peaks found after March 1 correspond to air temperatures above zero. With such weather conditions, condensation can be considered as being in the form of water droplets, not in the form of hoar. As a result, the major peaks associated with above freezing temperature are not associated to surface hoar growth. On the field, surface hoar was observed on January 20 and 21 1994 and as well on January 29, and on February 1, 3 and 5 1994. The condensation curve (or growth simulation curve) shows major peaks indicating significant condensation matching these dates. Moreover, this is associated with below freezing temperatures. Hence, these major peaks can be associated with surface hoar growth yielding to a successful prediction. Figure 21 shows the simulated ice growth curve with the prevailing meteorological conditions for part of January 1994 and can give a better idea of the simulation performance for this specific case. The major peak on the growth curve is found in the night of January 19 to 20. At the study plot, surface hoar was observed on the morning of January 20 confirming the result of the model.  69  Chapter 4: Analysis of simulation and field measurements  2E-3 —i  VAPOR to ICE GROWTH  •a 1E-3 — \  a M OE+0  ICE to VAPOR RH  Figure 21: Surface hoar occurrence of January 20 and 21 1994. Although the number of occurrences is quite low over the winter 93/94, growth curves allowed to identify the periods where surface hoar had been observed on the field.  - Mt. Fidelity - Winter 94/95  70  Chapter 4: Analysis of simulation and field measurements  For the winter 94/95, surface hoar layers were only recorded by the Parks Services when they became significant. It is likely that some occurrences are missing. As a result, a complete comparison cannot be done although a trend can be observed. Figure 22 shows the growth curve for the winter 94/95 with the mean hourly temperature measured 1.5 m above snow surface. Major peaks are more difficult to extract than for the winter 93/94.  3E-3  -i  ^ __ 1  Figure 22: Simulated growth and air temperature - Mt. Fidelity 1994/95.  71  Chapter 4: Analysis of simulation and field measurements  Figures 23 and 24 show in greater details the evolution of the growth curve with the meteorological data. All data are hourly averaged. The bottom series of graphs show the incoming solar radiation curve with its typical day/night fluctuations, the incoming infra-red radiation curve (in clear) and the air temperature (in black). Above it, onefindsthe growth simulation curve. Horizontal semi-brackets are positioned above major peaks and they are numerated allowing definition of time periods where surface hoar growth is likely. These major peaks were determined qualitatively by comparison to the whole growth curve trend. They represent what one can consider as potential hoar occurrences if the growth curves were the only information available. Lying above the growth curve snow precipitation is plotted with relative humidity. The upper graphs shows the wind speed as measured at the site. On thefield,significant surface hoar layers were found recently buried on January 17, January 26, March 8. On January 23, March 17 and February 4/5, formation was observed. In these figures, one may associate observation and simulation: January 17's buried crystals can be related to the time periods 3, and March 8 to the time period 6. On January 23, observed surface hoar is likely the one found buried on the 26. However, no significant peak on the simulation curve was observed. It is likely due to low relative humidity during the periodfromJanuary 20 to January 24 suggesting that no formation was expected. Formation on February 4-5 could be described by the condensation curve with a peak on February 5-6. March 17's hoar formation can also be described by the simulation peak on March 17/18.  72  Chapter 4: Analysis of simulation and field measurements Mt Fidelity 4 Dec 94 to 27 Jan 95 5  « E  4  -|  _  Figure 23: Meteorological conditions and simulated growth curve  73  Chapter 4: Analysis of simulation and field measurements  Mt Fidelity 28 Jan 95 to 22 Mar 95  Figure 24: Meteorological conditions and simulated growth curve.  74  Chapter 4: Analysis of simulation and field measurements  - Blackcomb - Winter 94/95 Figures 25, 26, 27 are of the same type as Figures 23 and 24: weather data along with the simulated growth are described. Unlike Mt. Fidelity's figures for 93/94, numerous peaks can be spotted and a straightforward deduction of surface hoar occurrence from only the growth curve is impossible. However, if these peaks are related to the prevailing weather conditions, it is demonstrated below that surface hoar occurrence can be spotted and match fairly well field observations. First of all, time periods corresponding to major peaks have to be found in the growth curves. On Figures 25 to 27, sixteen time periods likely to have experienced water condensation on the snow-pack surface are recognized. They are numbered on the curves. Afterwards, for each time period, weather data are carefully analyzed (although qualitatively analyzed as opposed to quantitatively) and a decision is made by accepting or rejecting this time period as being a surface hoar period (SHP). To do so, a qualifying time period has to feature no more than light wind, high relative humidity, clear skies (spotted by high (at a given date) solar radiation values during daylight) and low infra-red radiation during night and/or days, and below freezing temperature at the surface of the snow-pack. Ideally, air temperature should be measured few centimeters above the snow surface. Indeed, standard measurement for air temperature were used, with the sensor situated at about 2 m from the surface. Greater font size is then used to show a SHP on the graphs.  75  Chapter 4: Analysis of simulation and field measurements  It is important to notice that snow precipitation were only defined on a 12-hr basis due to a lack of accuracy of the ultra-sonic gauge. As a result, for small precipitation, snowfall events showed on the graph are not quite reliable for discriminating clear and cloudy skies.  - Selected time periods: Time period 1: Rejected. It occurs following a slight sky clearing: a break in the precipitation is shown, short wave radiation (SW) slightly increase and infra-red (IR) fade. However, these conditions prevailed for a short period with probably some light overcast suggested by a solar radiation peak fairly weak. Hence, this time period is rejected as being a SHP. Time period 2: Accepted. It stretches over few days. However only thefirstpart presents clear skies according to the SW and IR. Humidity is about 60% and the wind calm, this period is accepted as a SHP for January 6. Time period 3: Rejected because of cloud cover: IR high, SW low. Time period 4: Rejected. SW too low, not characterizing clear skies. Time period 5: Rejected. High winds, cloud cover. Time period 6: Rejected. Although skies were clearing up in the night of February 7, this was most likely the result of a more humid air mass pushed by another dry air mass accompanied of strong winds. As a result, the period was rejected.  76  Chapter 4: Analysis of simulation and field measurements  Figure 25: Meteorological conditions and simulated growth curve  77  Chapter 4: Analysis of simulation and field measurements  Blackcomb Mountain 16 Jan 95 to 7 Mar 95  Figure 26: Meteorological conditions and simulated growth curve.  78  Chapter 4: Analysis of simulation and field measurements  Figure 27: Meteorological conditions and simulated growth curve  79  Chapter 4: Analysis of simulation and field measurements  Time period 7: Accepted. Four major peaks are found during this period. The first three peaks are rejected because of either warm temperature, low SW or strong winds. The fourth one matches a nearly no-wind period during the coldest temperature of this time period. Although the surrounding SW peaks are not quite high, denoting some cloud cover, the drop on the IR curve suggests a clearing could have occurred during the night. Because of this, and the trend of the whole period to exhibit condensation, February 22 is accepted as a SHP. Time period 8: Accepted. The second part of the period exhibits clearing skies and low wind, still cold temperature. It is accepted as a SHP. Time period 9: Rejected. Too much wind in the first part, and too high IR at night in the second part make this period to be rejected. Time period 10: Rejected. First part is rejected because of the wind. Unlikely, the second part corresponding to March 16 - 17 is accepted since the wind faded down. Time period 11: Rejected. Wind speed is just on the limit calm/strong and IR are not quite low. The period is rejected. Time period 12: Accepted. Low wind and in the first part of the period, high humidity suggest to accept this period as a SHP. Clear skies and cold temperature confirm this for March 26 - 27. Time period 13: Rejected. Low wind, cold temperature and clear skies don't match together. Time period 14: Rejected. SW too low. Time period 15: Rejected. Not clear enough. Time period 16: Accepted: Clear skies, high humidity and low wind.  80  Chapter 4: Analysis of simulation and field measurements  Predicted dates  Observed dates  Observed size mm  Jan 6/7  Jan 6, 7  2  Feb 22/23  Feb 22  2  Feb 26  Feb 25, 26, 27, 28  1/2, 1/2; .31.5, 31.5  Missing  Mar 6  1/2 with PP  Mar 16/17  Mar 16  5  Missing  Mar 23  .3 with PP  Mar 25/26  Mar 25, 27, 28, 29  5,-, 3, 3/5, 3/5  April 15  April 15, 16  1/2, 1.5  Table 8: Summary of SHP. The sixteen time periods were analyzed and the SHP had been chosen as described above. The time periods are summarized in Table 8 and a contingency table is shown in Table 9. It shows how the selection of the accepted SHP based on the simulated growth curves and on the weather conditions relate to the observed occurrences of surface hoar.  Simulation\Observation  SHP  no SHP  SHP  6  0  no SHP  2  -  Table 9: Contingency table of surface hoar occurrences.  81  Chapter 4: Analysis of simulation and field measurements  One has to remember that surface hoar growth is a complex phenomenon that can be interrupted only by slight changes in the meteorological condition. It also depends on the location, and the overall result for this site seems to be promising. Although these results are encouraging, it is demonstrated that the growth curve alone did not make possible the discrimination of SHP. It was necessary to carefully analyze the weather data to make a final decision. Condensation on snow surface can occur on various forms and surface hoar being one of them, growth curve and direct weather data analysis seems to be essential to figure out when a SHP occurs.  4.9  Run-off  Unfortunately, the collecting device installed on the site of Blackcomb Mt. (Chapter 3, Figure 5 and 6) did not operate properly. The orifice of the tipping-bucket was found obstructed despite the two screens installed. It seems the sudden initial run-off carried gravel onto the second screen and displaced it. This caused gravel to strongly interfere with melt-water flow by limiting theflowinto the counting system and eventually overflowing the collecting bowl of the instrument. Eventually total obstruction occurred took place. Nevertheless, one can observe on the bottom water run-off curves on Figure 28, that the first run-off peak measured by the gauge (supposedly not obstructed yet) matches thefirstsimulation peak. A 3-day delay is observed after 5 months of simulation without re-initialization. This 3-day lag is due to the  82  Chapter 4: Analysis of simulation and field measurements  simulation's slight delay to reproduce a 0 °C snow-pack. This can be considered a quite satisfactory result after 5 months of simulation. Another simple way to assess the snow-melt simulation is to look at the snow-depth curves. For both locations, Blackcomb and Mt. Fidelity, melting is well reproduced, simulated slopes of snow-depth curves during melting periods are similar to measured data and confirm the capabilities of the model to time and quantify snow-melt run-off and melting rates.  6 -i  Tipping Buckett Simulation  2 H  l H  1  I 1 1 1  1 1  1  1 1  I  1 1  I 1 1 1  1 1  1 1 1 1  1 1  1 1 11  1 1  I 1 1 1  1p  P1 1  1  a, a, a a a p. a a a a a > i a a i ' a •' « i ' a j 3 3 3 3 3 3 3 5 <  S 3 j3 "3 "3 3  Figure 28: Simulation and measurement of the snow-cover bottom water run-off.  83  Chapter 5: Conclusion  Chapter 5  Conclusion  The aim of this research project was to test the numerical snow-cover model CROCUS. This model, designed by the Centre d'Etude de la Neige - France - is a physically-based numerical model providing the user with simulated physical parameters relating to the inner snow-pack. Temperature profile, density profile, liquid water content profile, type and size of grains in each snow layer, snow-depth, bottom water run-off are returned by the model. To run, CROCUS requires meteorological data on an hourly basis: air temperature, wind speed, relative humidity, amount and type of precipitation, density of new snow, incoming solar and infra-red radiation. CROCUS proved to be efficient to simulate the snow-pack characteristics when tested by the CEN under the specific climatic condition of the test site of the Col de Porte in the Massif de la Chartreuse in the French Alps (Brun and Al. 1989, 1992). The importance of the work presented here stretches on the necessity to learn about the capabilities of CROCUS while performing under new climatic conditions such the ones prevailing in the Coast Mountains of southwestern British-Columbia as well as in the Selkirk Range of the Columbia Mountains in eastern British-Columbia. To do so, twofieldsites were chosen and the required instrumentation was installed on the field allowing continuous collecting of meteorological data necessary to run the model. Thefirstsite under test was  84  Chapter 5: Conclusion  situated at Mt. Fidelity in Glacier National Park where an intermediate climate between continental and maritime usually prevails. Blackcomb Mt. was the second site where the model was tested. A marked maritime snow climate normally characterizes the area. Hydrological forecasting, flood forecasting, and more particularly avalanche forecasting were in mind when testing the different parameters of CROCUS. The model performed extremely well for simulating snow-depth, snow-pack's temperature and density profiles on both testing sites and showed a great potential of the model for dealing with hydrological issues. In particular, the accuracy of the snow-depth scheme associated with density profile could provide extremely valuable information for water management, reservoir control for hydro-power production and river level control for fisheries. When one associates the temperature profile simulation to density and snow-depth, one can get highly valuable information on the potential of the snow-cover to release water. Flood control could also greatly take advantage of the excellent performances of the model to simulate the snow-pack temperature. Quite interesting results were discovered with respect to the metamorphism simulation. One knows that the model has the capability to simulate the type of grains that can be found within the snow-pack. This is of a primary importance when one wants to estimate the suitability of the model for avalanche forecasting and/or snow stability assessment. The grain metamorphism scheme is mainly based on the simulation of the temperature profile. The good behavior of this latest is a strong point here. However, climatic conditions influences the performance of the model in its present version. Simulation performed well when temperature  85  Chapter 5: Conclusion  gradient within the snow-pack were situated clearly off the threshold of 5 °C/m. In the model, this threshold is a frontier between in one side a strong gradient metamorphism scheme where facets form (gradient stronger than 5 °C/m), and in the other side a weak gradient metamorphism scheme during which rounded grains form (gradient weaker than 5 °C/m). When the prevailing meteorological condition led to gradient slightly greater than the threshold, the model creates faceted grains, despite the fact that rounded grains had been observed in the field. It appeared the incidence could be quite critical in the mountain climate of our first test site - Mt. Fidelity -. This site has the particularity to experience usual weather conditions leading to temperature profile lying quite close to the 5 °C/m mark. As a result, simulation could strongly derive out of tracks. On the other hand, when gradients were clearly situated away from the 5 °C/m mark, simulations were fine. After checking the different snow profiles obtained by the CEN at the Col de Porte in France (Brun and Al. 1992), one can notice that the gradients experienced at this site were most of the time well marked far away the 5 °C/m mark: 15 to 20°C/m were current, and once the melting periods started, almost isothermal snow-packs were found. Under such conditions, the sensible zone around 5 °C/m was unexplored. The site of Blackcomb allowed to test the grain simulation for temperature gradients mostly ranging between isothermal and 5 °C/m. Simulations were then satisfactory. , As a result, on can suggest to bring some modification on the threshold value used into CROCUS. According to the presentedfieldobservations, setting the threshold to 7 or 8°C/m could improve the simulation. These values would also be closer to the current estimation (10 to 20 °C/m) for the so-called 'critical gradient" (Colbeck, 1982). One can also suggest that  86  Chapter 5: Conclusion  the temperature could be incorporated into the metamorphism scheme in such a way that the threshold value depends on it (Colbeck, 1986). Surface hoar is a quite important crystal type found in most failure plane of fatal slab avalanche in Canada. It was important to explore the capabilities of the model to predict or at least, help to predict the formation of surface hoar. Technically, CROCUS does not simulate surface hoar growth. However heat exchanges at the surface of the snow-pack are simulated. From the knowledge of these heat exchanges, one can determine whether any condensation occur onto the surface of the snow-cover, and possibly one may be able to track surface hoar occurrence. Ideally, more specific instrumentation systems would have been necessary to perform such a task. However, the standard weather data collected at the site, along with manned observation and heat exchange simulation allowed to get an estimation of the possibility of simulating surface hoar growth. Quite encouraging results were obtained, although in most of the cases, meteorological data were necessary to determine whether or not a potential condensation occurrence could be related to surface hoar. Overall, CROCUS appeared to be an efficient tool for snow-pack modeling. As described earlier in this Chapter, potential application are numerous and varied. The suitability of the model for avalanche forecasting was shown. However one has to keep in mind that this suitability does not mean that CROCUS is an ultimate tool for avalanche forecasting . Hardness is not simulated by the model. The main reason is that, today, there are no physically-based relationship between the physical parameters of the snow-pack and the hardness. Hardness can only be estimatedfromthese physical characteristics, mainly based on  87  Chapter 5: Conclusion  previous statistical observations. CROCUS being physically based, hardness has to be included in 'ttownsteam" models such MEPRA (Giraud, 1991). As a result it would be highly valuable to know how well the hardness estimation schemes perform to assess the whole system. At last, CROCUS can tremendously help forecasters. The capability to feed the model with weather data at a large scale - scale of a mountain range for instance - is definitely a strong asset. Valuable information about the snow-pack's condition on various aspects, elevation ranges can be obtained. This refers to the SAFRAN - CROCUS - MEPRA chain, used in many ranges in the French Alps. Such system could be applied in Canada on specified areas like mountain zones crossed by transportation systems. In British-Columbia quite numerous critical areas wOuld qualify for such a system where there is enough available meteorological data. Ski resorts could also greatly beneficiate of the capabilities of the model. The idea would be to help forecasters to make decisions in a better and more efficient way, not to replace them, field experience remaining unique and not replaceable.  88  References  References  Alados - Arboledas, L., J. Vidas, and J.I. Jimenez. 1988. Effect of solar radiation on the performance of pyrgeometers with silicon domes. Journal of Atmospheric and Oceanic Technology, Vol. 5, pp. 666 - 670. Albrecht, B. and S. Cox. 1977. Procedures for improving pyrgeometer performance. Journal of Applied Meteorology, 16, pp. 188 - 197. Armstrong R. L. and B. R. Armstrong. 1987. Snow and avalanche climates of the western United States: a comparison of maritime, intermountain and continental conditions. IAHS Publication No. 162, pp. 281 -294. Beltaos, S. and B.C. Burrel. 1992. Ice breakup and jamming in the Restigouche River, New Brunswick. Proceeding of IAHR Ice Symposium, Banff, Alberta, pp. 437 - 449.  Braun, L.N., E. Brun, Y. Durand, E. Martin, P. Tourasse. 1995. Simulation of discharge using different methods of meteorological data distribution, basin discretization and snow modelin Nordic Hydrology, No 25, pp. 129 - 144. Breyfogle, S.R. 1986. Growth characteristics of hoarfrost with respect to avalanche occurrence. Proceedings of ISSW, Lake Tahoe, California. Brun, E., E. Martin, V. Simon, C. Gendre, C , Coleou. 1989. An energy and mass model of snowcover suitable for operational avalanche forecasting. Journal of Glaciology, Vol. 35(121). pp. 333 -342. Brun, E., P. David, M. Sudul and G. Brunot. 1992. A numerical model to simulate snow-cover stratigraphy for operational avalanche forecasting. Journal of Glaciology, Vol. 38(128). pp. 13 22. Brun, E. and L. Rey. 1987. Field study on snow mechanical properties with special regard to liquid water content. Avalanche Formation and Effects. IAHS publication No. 162. pp. 183 - 193. Canadian Avalanche Association. 1995. Observation guidelines and recording standards for weather, snow-pack and avalanches. Caine, N. .1989. Diurnal variation in the inorganic solute content of water draining from an alpine snow-pack. CATENA. Vol. 16, pp. 153 - 162.  89  References  Colbeck, S.C. .1972. A theory of water percolation in snow. Journal of Glaciology, 11(63), pp. 369 -385. Colbeck, S.C. .1982. Growth offaceted crystals in a snow-cover.CKKEL Rep. 82-29.  Colbeck, S.C. .1986. Classification of seasonal snow-cover crystals. Water Resources Research. Vol. 22, No. 9, pp. 59S - 70S. Colbeck, S.C. 1987. History of snow-cover research. Journal of Glaciology, Special Issue.  Colbeck, S.C, E. Akitaya, R. Armstrong., H. Gubler., J. Lafeuille, K. Lied, D. McClung, E.  Morris. 1990. The International Classification for Seasonal Snow on the Ground. Internati  Commission on Snow and Ice of the International Association of Scientific Hydrology & International Glaciological Society.  Costerton, R.W. and P.F. Doyle. 1995. Forecasting sudden mid-winter breakups in mountaino  regions. Proceedings of C.S.H.S. Mountain Hydrology Symposium, Vancouver, B.C., pp. 105 111.  Deardorff J.W. . 1968. Dependence of air-sea transfer coefficients on bulk stability. Journa  Geophysical Research. 73(8), pp. 2549 - 2557.  Durand, Y., E. Brun, L. Merindol, G. Guyomarc'h, B. Lesaffre and E. Martin. 1993. A  meteorological estimation of relevant parameters for snow models. Annals of Glaciology 18  65-71.  Foot, J.S. .1986. A new pyrgeometer. Journal of Atmospheric and Oceanic Technology. Vol. 3, pp. 363 - 370.  Giraud, G. .1991. MEPRA: Modele Expert d'aide a la Prevision du Risque d'Avalanches.  Proceedings of the Symposium of Chamonix on Snow and Ice. ANENA. Pp. 248 - 254.  Goodison, B. E., H.L. Ferguson, and G.A. McKay. 1981. Measurement and data analysis. Handbook of snow, Ed. D.M. Gray - D.H. Male.  Gubler, H. . 1985. Model for dry snow metamorphism by interparticle vapor flux. Journal  Geophysical Research. No. 90, pp. 8081 - 8092.  Guyomarc'h, G. .1995. Estimation du risque d'avalanches. PROTEON: PRevision de VOccurence de Transport Eolien de Neige. Neige et Avalanches. ANENA. No. 70 - Juin 95, pp. 16-21.  90  References  Hebabi, S., N. El-Jabi and S. Sarraf. 1992. Analyse hydrometeorologique des debacles de glace de la riviere Nashwaack (Nouveau-Brunswick). Canadian Journal of Civil Engineering, 19(2) pp. 349 - 354.  Hutchison, B. The Fraser. Series: The Great Rivers in Canada. Irwin, Toronto 1982.  Jamieson, B. and C. Johnston. 1992. Snow-pack characteristics associated with avalanche accidents. Canadian Geotechnical Journal. No. 29, pp. 862 - 866. Johannessen, M. and A. Henriksen. 1978. Chemistry of snow meltwater: changes in concentration during melting. Water Resources Research. Vol. 14, No. 4, pp. 615 - 619.  Kattelman, R.C. .1984. Snowmelt lysimeters: design and use.Proceedings of the 52nd Sno Western Conference, Sun Valley, Idaho, pp. 68 - 79.  Lang, R.L., B.R. Leo and R.L. Brown. 1984. Observation on the growth process and strength characteristics of surface hoar. Proceedings of ISSW, Aspen, Colorado. Larson, L.W. and E.L. Peck. 1974. Accuracy of precipitation measurement for hydrological modeling. Water Resources Research. Vol. 10, No. 4, pp. 857 - 863.  Meister, R. 1985. Density of new snow and its dependence on air temperature and w Workshop on the Correction of Precipitation Measurements 1-3 April 1985. Zurich, Switzerland.  McClung, D. M. and P.A. Schaerer. 1993. The avalanche handbook. Seattle, WA, The Mountaineers. Muramoto, K. I., T. Harimaya, T. Endoh. 1993. A computer database for falling snow-flakes. Journal of Glaciology, 18, pp. 11 - 16.  Navarre, J.P. .1975. Modele unidimensionel devolution de la neige deposee. Modele perc neige. Meteorologie, 4(3), pp. 103 - 120.  Pahaut, E. .1975. Les cristaux de neige et leurs metamorphoses. Monographic de la Meteorolog Nationale No. 96. EERM/Centre d'Etude de la Neige, St.-Martin d'Heres, France.  Perla R., and C.S.L. Ommanney. 1985. Snow in strong or weak temperature gradients. Part I experiments and qualitative observations. Cold Regions Science and Technology, 11, pp. 23 - 35  Sergent, C, P. Chevrand, J. Lafeuille and D. Marbouty. 1987. Caracterisation optique de differents types de neige. Extinction de la lumiere dans la neige. Journal de Physique (Pari Colloq. Cl, pp. 361 - 367.  91  References  Schleiss, V.G. 1989. Rogers Pass, Snow Avalanche Atlas. Glacier National Park, B.C., Canada. Environment Canada, Canadian Parks Service - Revelstoke B.C. Warren, S.G. .1982. Optical properties of snow. Revue of Geophysics - Space Physics. 20(1), pp. 67 - 89. Watt, E. .1989. Hydrology offloods in Canada. National Research Council, Ottawa, Ont. Yang, D., J.R. Metcalfe, B. E. Goodison, and E. Mekis. 1993. True snowfall. 50th Eastern Snow Conference & 61st Western Snow Conference, Quebec City, Canada.  92  Appendix 1: Creation of meteo.mso  Software package: - crocus.exe - modgeon.bas: Characterization of the geography of the site. Elevation, orientation of the site are keyed in. Solar masks are defined if necessary. - xcaradi.bas: Date of the initial profile is entered as well as an initial profile. - xiniadi.bas: Manual input of the weather data. - xresiadi.bas: Plotting of simulated profile. Meteo.mso: 1) Define the geography of the site with modgeon.bas. Posgeo.mso is returned. 2) Run xcaradi.bas to define the time of beginning of the simulation and to enter the initial profile manually. Carsim.mso, projil.mso are created. 3) Run xiniadi.bas to key in the daily weather data. Simul.mso and meteo.mso are created. CROCUS Simulation: 4) Crocus.exe can then be run to create the simulated profiles. Projil.mso is expanded. 5) Xresadi.bas is used to visualize each simulated profile.  93  Appendix 2a: Temperature profiles Mt. Fidelity - Winter 1993/94  X-Axis: Temperature: °C  Y-Axis: Snow-Depth: cm  94  95  96  Appendix 2b: Temperature profiles Mt. Fidelity - Winter 1994/95  X-Axis: Temperature: °C  Y-Axis: Snow-Depth: cm  97  99  Appendix 2c: Temperature profiles Blackcomb Mt. - Winter 1994/95  X-Axis: Temperature: °C  Y-Axis: Snow-Depth: cm  100  101  02 Mar 1995  I  1  I  Fnit on 25 Dec  '  I  1  I  1  I  I  1  16 Mar 1995  350  1  Measured  1  t  I  1  Init on 25 Dec  I  1  I  1  I  1  350  1  300  300  250  250  200  200  150  H 150  100  H 100  Crocus 50  50  J  -16  I  I  I  -14  I  L  -12  -10  1  1  1  I  -8  28 Mar 1995 1  I  I  -6  I  -4  I  I 0  -2  0  1  1  1  I^JL  \  -  -10  350  1  -  _  -12  -8  11 A p r 1995  Init on 25 Dec 1  -14  ^  .  \ \  -  \-  I  -6  -4  -2  0  Init on 25 Dec  I  1  -i  I  1  1  1  1  350  r  300  300  250  250  200  H 200  150  H 150  100  / H 100 50  50  i • 14  -12  -10  -8  -6  -4  , i -2  A& 0  I  0  -14  -12  i  I  i  -10  Temperature profiles Blackcomb - Winter 1994/95  102  I -8  i  I -6  i  I -4  i  I -2  J-^J  0  o  14 May 1995 "i 1 1  Init on 25 Dec 1 II 1 I 1 I  1  i i i i_ I i I . I • -12  -10  I  Init on 25 Dec 1  300  I  - f 250  250  200  200  -# 150  150  100  100  50  50  Crocus  •14  I  1  Measured  -A—  J  22 Jun 1995  300  r  -8  -6  -4  I -2  . •14  0  -12  -10  -8  Temperature profiles Blackcomb - Winter 1994/95  103  -6  i i i i_ -4  -2  0  Appendix 3a: Density profiles Mt. Fidelity - Winter 1993/94  X-Axis: Density : kg/m  3  Y-Axis: Snow-Depth: cm  104  02 Jan 1994  450  350  Init on 20 Dec  250  150  29 Jan 1994  50  450  Init on 20 Dec  350  Density profiles Mt. Fidelity - Winter 1993/94  250  150  50  20 Mar 1994  450  350  Init on 29 Jan  250  150  28 A p r 1994  50  450  Init on 29 Jan  350  Density profiles Mt. Fidelity - Winter 1993/94  106  250  150  50  Appendix 3b: Density profiles Mt. Fidelity - Winter 1994/95  X-Axis: Density : kg/m  3  Y-Axis: Snow-Depth: cm  107  109  Appendix 3c: Density profiles Blackcomb Mt. - Winter 1994/95  X-Axis: Density : kg/m  3  Y-Axis: Snow-Depth: cm  110  Ill  14 May 1995  450  350  Init on 25 Dec  250  150  22 Jun 1995  50  550  450  Init on 25 Dec  350  Density profiles Blackcomb - Winter 1994/95  113  250  150  50  Appendix 4a: Grain metamorphism Mt. Fidelity - Winter 1993/94  114  Init on 20 dec 93 Proffltton2JMM PP  1/1  PP  19  Init onl) Fob pronto on) Mir 94  Init on 29 Jan profit** on 11 Feb 94  OTP OFK  U  Df  -SH-  mstf.  m-\  re  i  FC  u  "Ft—  u  miFC UJ  FOBG M 'FORG™ UH RGIFC  3" >  FCJRG  Ul  3«  RGK  u  RQFC  UV1  FC1RG  1  'ROFC  U l  R&fC  l  RGfC u u  uflC -FC-  miRG -FCIRG-J-m  RG/FC FUKS  RG/FC  u  lnJton29Jan profHet of 28 Apr94  Init on 3 Mar profiles on 20 Mar 94 m1H-  turn- " m-  PPIDF  1  PPIDf  U  RG  Ul  " " ^  U  u  m WG  uu  RG  Ul  Mw -  RG  Ul  ma-  RG  Ul  3" 3"  WG  u u u u  SG  !1l-  n  •*%  7U -  m-  m  u  RG .  u u u 1  JRG/FC  lntton12Jan94 profileiof23Jan9S  m  IT U u  • OF-  M-  r«  1  -PPIDW- J R G K f CT glxRG -WG- M  -SH—  n  OF  ou  WG  DFffC  |-M w  ui  DfSG «RGCF>-ffl  » 111 u  »WG»  m-|  PHDF "OFCT-l  raAG  IB  WG -*G-  in m in-  WG  o u4H  U  RG  u  imRG  U  FC  3*  2"  m » in m H  OB  in  1 ~FC~  M K  U  FC  NH  M  n  h«  n M -  »-  t  mFC  1  FMG  1  oFC  1  PMG  H C X  u RG  Ml  U  U  Appendix 4a: Grain metamorphism - Mt. Fidelity Winter 1993/94  -115  BAG  X 11  »ORG»L I  Appendix 4b: Grain metamorphism Mt. Fidelity - Winter 1994/95 Init 12 Dec  116  Mt Fidelity  S n o w profiles of 09 J a n 95 - Init on 12 Dec 200  200 190 —]  PP SH-  1/2 2/4 2  RG  1  -_pp  180  PP/DF 190  DF/FC  170  FC/DF RG  RG/FC  1  ==RG/FC==  2c  RG  1  150 140  0.3  =mxFC= mxFC  0.4  FC  0.5/1  160  .  180 170 160 150 140  0.4  mxFC 130  130 120  RG  \— 120 - 0.5/1  0.4  FC/RG  0.8  mxFC  110 1  W  O  ffi!  RG/FC  100  RG/FC  X  1  0  => o  0.5/1  0.8  FC  1  mxFC  f— 90 80  0.8  RG/FC  mxFC 70  1 0.8  FC/RG  60  f - 60  FC/RG \— 50  50  40 —  RG/FC  mxFC  h- 40 r— 30  30 —\  FC/RG =RG/FC==  20 10 -\  4c  •h" 20 0.8  @RG  0.8  =wRG~ =@RG"  RG/FC  0 —  1  I  100^^:  1  80 H 70  Q  =IM=  0.8  Appendix 4b - Plot I: Grain metamorphism, Mt Fidelity 94/95.  117  r - 10  CO O)  •» X  Mt Fidelity  Snow profiles of 23 Jan 95 - Init on 12 Dec  220  -SH-  2/3  210  DF  1/1.5  200  220  PP/DF  210  =DF/PP=^ RG/DF  — 200  DF/FC  1/1.5  — 190  190  DF/RG 180 —\  RG  180  0.5/1  ==RG/DF= \— 170  170 0.3  160 —\ 150 —i  RG  .5/1  0.3  0.4 0.4  140  mxRG  \— 160  RG ==mxRG= RG  u  a $ UJ O  120  RG  0.4  0.5  mxRG  > c  90 —  o 120 Q > Z) o  tn °  z  E _„„ < (A 110 _l M_  £ 2 no 0Q£ O Ol 100 '55  140 130  130  E  150  :  0.8  RG  FC  0.5  100 CO O) h- 90  FC 80  80 70  0.8  FC  60  60  RG  FC/RG  50  mxFC 30  RG FC/RG  20 10  50 40  40 30  70  RG  DRG  0.8  1/1.5  0.8  0 —i.  == RG== W  Appendix 4b - Plot 2: Grain metamorphism, Mt Fidelity 94/95. 118  i— 20 10  Mt Fidelity  Snow profiles of 8 Feb 95 - Init on 12 Dec  PP/DF -@RG/mf~ _..SH—DF/RG  1/1.5  DF/RG  1/1.5  DF/RG  1/1.5  ~RG~"  0.5/1  RG  1/1.5  _SH-~•  1/2 4.5  0.9  1/1.5  DF/PP @mxRGDF/FC  DF/RG  6/8  RG  0.4  RG  0.8  FC  0.8  mxFC  1  ""FC"'  0.8  mxFC  1/1.5  RG 1/1.5  RG/mf  1/2  FC/RG RG  0.5/1  mxFC 2/3  FC/RG RG  0.5/1  0.8  @RG  Appendix 4b - Plot 3: Grain metamorphism, Mt Fidelity 94/95.  119  Mt Fidelity  S n o w profiles of 25 Feb 95 - Init 12 Dec 290  PP  0.5/1  DF  05/1.5  DF  1/1.5  DF =@RG==  280 PP "PP/DF  1/2  1  RG  0.5  DF/RG  0.5/1  0.5  DF/FC @mxRGDF/FC  270 260 250 240 230  DF/RG RG/DF  220  0.5/1  RG  0.5/1  RG  0.5/1  TCTRG  1/1.5  RG/FC  0.5/1  0.3 0.9 0.3 0.4 0.4  ==RG== ©RG/FC-@RG— FC/RG =RG/FC=  0.4  mxRG  190  0.4  RG/FC  180  210 200  170  170  E  E o  Q J Ul o  > Ui  160  RG/FC  0.3  RG  c 150 (A  <^  Ui o 1 4 0 m sz O a "55 1 3 0  RG/FC  X  RG/FC  0.4 0.4  mxRG =RG/FC=  140 130  i '5^5  110 100  0.5/1  90  FC  80 70  RG  0.8  0.5/1  60  mxFC RG  FC/RG  1/1.5  50 40  mxFC RG  1/1.5 "FC/RG"  RG  0.8  1/1.5  @RG  30 20 10 0  Appendix 4b - Plot 4: Grain metamorphism, Mt Fidelity 94/95.  120  C  X  0.8  RG/FC  O  H  120  1  N  150  0.5/1 0.4  FC/RG  160  Mt Fidelity :  S n o w profiles of 23 Mar 95 - Init on Dec 12  ==pp=:=  0.5/1  PP/FP  1  TP" ~ p~  1 1 0.5/1  0.3  0.5  0.3  F  ::RG:: RG  "RG"  170 Q Ul  >  E u 160  0.5/1.5 1/4 0.5/1  RG "RG/FC" ... SH—  0.5 0.5/1.5 4/8  RG  0.5/1.5  280  RG  0.5 0.4  RG @mxRGmxRG  0.3  RG  0.9 0.3 0.4  -@FC-@RG-RG/FC  0.4  0.5  0.5  DF/PP DF/RG =@RG==( RG/DF  RG/DF  0.5 0.5  RG  290  RG/FC  0.5  0.4  RG  OB ght  "55 130 z  240 230 220 210 200 190 180  160 _  o c 150  Ul to o 140  250  170  i  (0  270 260  8:111 ==RG== RG/FC @RG RG  =PP/DF=f  150 ^ E < (A -I *140 2 ° 130  RG/FC  0.5  120 110 100  0.8  1 RG  0.5  0.8  mxFC  IIIoZ mxFC  90 80 70 60 50  FC/RG  RG  0.5/1  40  mxFC  30  1  FC/RG  20  0.8  @RG  10 0  Appendix 4b - Plot 5: Grain metamorphism, Mt Fidelity 94/95. 121  E °  CO O)  '5  Mt Fidelity =WG/PP=  Snow profiles of 4 May 95 - Init on Dec 12  ==WG==  0.5/1 0.6/1 2  WG  2/2.5  WG  2/2.5 1/1.5 0.5/1  RG  0.5  0.5 1.1  RG w RG ""WG""  0.9  w RG  0.6  w RG  0.3  W  05 1  1  —@RG—  1.5  RG ==RG==  0.5/1  -FC/IM--  1.5  w RG w RG/FC  1 0.5/1  0.5  -wRG—  w_RG  wRG/FC  0.4  w RG —  0.8  mxFC  1  "FC""  0.8  FC/RG  1/1.5  -\ No data  mxFC  0.8  @RG  Appendix 4b - Plot 6: Grain metamorphism, M t Fidelity 94/95  122  Appendix 4c: Grain metamorphism Mt. Fidelity - Winter 1994/95 Init 23 Jan  123  Mt Fidelity  Snow profiles of 8 Feb 95 - Init on 23 J a n 250  PP/DF -@RG/mf~ —SH— DF/RG  1/1.s  DF/RG  1/1.5  DF/RG -------  1/1.5  h— 240  1/2  230  4.5  1/1.5  0.9  DF/PP L — @mxRGDF/FC r— 220 210  DF/RG  200  0.5/1  190  RG  1/1.5  0.3  -SH-  6/8  0.8  180  RG  170 2  RG  mxRG —FC— I— 160  0.8  mxRG  0.8  RG/FC  h- 150  1/1.5  140  UJ o  r—  RG  130 I-J  1/1.5  120 110  0.5  RG/mf  100  RG  90  1/2  80 70 — I 60 50  RG  RG  0.5/1  — 40 — 30  2/3  20  RG  |  0.5/1  1.2  RG  — I 10 0  Appendix 4c - Plot 1: Grain metamorphism, Mt Fidelity 94/95.  124  2 _  c  2f M-  ®  Mt Fidelity  Snow profiles of 25 Feb 95 - Init on 23 Jan 290  PP  0.5/1  DF  05/1.5  DF  1/1.5  DF =@RG=:  1/2 1  RG  0.5  DF/RG  0.5/1  RG/DF  0.5/1  RG RG FC/RG  0.5/1  1/1.6  RG/FC  0.5/1  280  PP PF7DF 0.5  260  DF/FC @mxRGDF/FC  250 240  DF/RG DF/FC  230 220  DF/RG  0.5/1  RG/FC RG/FC  270  210  0.3 0.9  ==RG== -@RG/FC-  0.4 0.4  ==RG/FC=mxRG  0.4  RG/FC  180  0.3  RG  170  0.8 2 0.8  FC ...FC— mxFC  200 190  160  H  ° S 150 < tn 140 |  0.5/1 0.8  FC  E o  130  O  '5 X  FC/RG  RG/FC  0.5  FC/RG  120  0.5  RG/FC  110  mxRG  100  0.6  0.5/1  90  RG  80  0.5  RG  70  0.5/1  60  RG  1/1.5  RG  50 40  RG  1/1.5  30 20  RG  1.2  RG  1.3  ==WG=  1/1.5  10  Appendix 4c - Plot 2: Grain metamorphism, Mt Fidelity 94/95.  125  0  Mt Fidelity  S n o w profiles of 23 Mar 95 - Init on 23 J a n ==PP/DF==  ==pp= r  0.5/1  PP/FP  1  :  "TP ~FP  HRS::::::  RG  ~-||~==RG== RG/FC @RG RG  0.3  1 1 0.5/1  280 ™R6/DF~ RG RG  0.3 0.5  0.5 0.5  m  0.4  0.5  0.5  0.5/1.5  0.4  1/4  0.4 0.4  RG  0.5  0.3 0.9 0.3 0.5  RG TfG7Tc"~ —SH—  0.5/1.5  RG  0.5M.5  RG gmxRGmxRG —RG"~ "mxRCT"' RG  260  240 230 220 210 200 190  0.5  180  4/8  RG  0.3  170 E 160 _ ° ° %  FC -FC—  0.8 2  0.5  mxFC  0.8  RG/FC  270  250 RG/DF  0.5/1  RG/FC  290  DF/PP  0.5  52  140  2 °.  130  '5>  120 110 100 RG  0.5  90 80 70  RG  0.5  60 50 RG  40 30 20  RG  0.5/1  1.2  RG  10  1.3  —W G -  0  Appendix 4c - Plot 3: Grain metamorphism, Mt Fidelity  126  94/95.  c  160  Mt Fidelity  Snow profiles of 4 May 95 - Init on 23 Jan  =WG/PP= "TOT" ==WG==  0.5/1 0.5/1 2  WG  2/2.5  WG ==w„RG==  2/2.5 1/1.5 0.5/1  RG  0.5  -Mr  h  w_RG "wHRCT  1  1 1.5  i  —@RG—  0.6  w RG  0.5  ==RG== --FC/IM-  0.5/1 15  w_RG W'FTGTFC"  1 0.5/1  w_RG  —wRG— 0.5  w RG  0.8 2  w RG -vVG---  0.8  w RG  0.5  w RG  0.5  RG  1  WWSIFU"  wRG/FC  0.5 1.1  05  =WG|w_FC=  RG  0.3  1  1/1.5  No data  RG  Appendix 4c - Plot  1.3  RG  1.3  WG  4: Grain metamorphism, Mt  127  Fidelity  94/95.  Appendix 4d: Grain metamorphism Blackcomb M t - Winter 1994/95  128  Blackcomb Mt.  Snow profiles of 20 Jan 95 - Init on 25 Dec  240  240  —W_PP—  —DF/PP--  230  DF  1.5  DF/PP  1.5  230  DF/PP  220  220 —I-  210  210  DF  1.5  190  RG/DF  0.5  180  DF/RG  0.3  170  =RG/DF= RG  0.5 0.5  RG  0.5  200  200  DF/RG  190  —RG—  160  0.3  RG  0.4  mxRG  180 170 160 150  150  RG  140  a  RG  130  RG  tn o m £ O O1110  x  140 0.4  E *  0.5  RG  E o 130 Q *  0.5  I*  120 _ | „_ 3 O  0.5  110  RG  0.5  RG  0.5  0.3  100 90  80  RG  70  — I 80  0.5  0.5  RG 70  60 60  so —\ @FC/RG  0.7  1/1.5  RG 50  40  1.2  RG/FC  1.2  FC/RG — 30  30 —| 20  DFC/RG  1/1.5  40  — 20  10  1.5  @mxFC  0  1.5 1.5  ==WG== -w mxFC- L-  Appendix 4d - Plot 1: Grain metamorphism, Blackcomb Mt.  129  'S  x  RG  100 90  tn cn  94/95.  10 0  Blackcomb Mt. 260  Snow profiles of 16 Feb 95 - Init on 25 Dec 260  ..pp..  260  DF 240 0.9 0.3 0.5 0.6 0.4 0.7  230 220 210  RG  0.5  ==pp== \— PP/DF ==DF/PP== FC @RG/FC h==mxFC== ==FC== @FC/RG FC/RG -@FC-  RG  0.3  0.5  RG/FC  230 220 210  190 180  180 170  240  200  200 190  250  RG  170  0.5  160  0.4  mxRG  160 150  160 (J  Q £ 140 Ul o  RG  0,5  140  > c  0.4  £ ^2 130  CO o ffi £ Oo> 0)  RG  130  E o  uj o  z> o  120 tn o)  1 2 0  '5>  110  110 100  0.3  RG  90  90 80  RG  80  0.5/1  70  70 0.5  RG  0.7  RG  1.2  RG/FC  1.2  FC/RG  1.5  @mxFC  1.6  ==WG==  60  60  50  50 40  RG  30 20 10  100  RG  1/2  0  Appendix 4d - Plot 2: Grain metamorphism, Blackcomb Mt. 94/95  130  40 30 20 10 0  Blackcomb Mt.  Snow profiles of 2 Mar 95- -Init on 25 Dec  ==FC==  1/1.5  0.8  —DF/PP—i— 280 DF/FC -@RG/FC-k ==FC/DF== @mxFC r~  FC/DF  1  0.6  ; ; @ T C 7 R G ; U SO  DF/RG  0.5  0.4  FC/RG |— 240  --DF/RGRG/DF —IM DF/RG  0.3/0.5 0.3  0.4 0.4 0.9  RG/DF  0.5  —RG/FC— mxFC h ==@FC== @FC/RG 220 ==mxRG=4- @ F C - f— 210 @FC/RG -©mxRG-F 200 mxRG —@FC-  ==IM== -DF/RG-RG  1.5 0.5  RG  0.5  RG  0.5/1  0.3  0.9 0.3 0.7 0.8 0.5 0.4 0.7  1 1.5  2  7  0  2 6 0  2  2 3 0  190 180 170  0.4  RG  -  160  E  160  ° *o  140 130  RG  120  RG  110  1/1.2  0.3  RG  100 90 80 70  RG  1.5/1.8  RG  1/1.5  RG  1.5  @FC/RG  0.5  RG  0.7  RG  60 50 40  1.2  RG/FC  1.2  FC/RG  1.5  w mxFC  30 20 10  1.5/2  0  Appendix 4d - Plot 3: Grain metamorphism, Blackcomb Mt. 94/95.  131  1" o  3 *  CO O)  •» X  Blackcomb Mt  Snow profiles of 16 Mar 95 - Init on 25 Dec 310  I  ...pp...  —SH PP DF  1.5 1.5  DF  1.5  =@RG/FC=  1  RG/DF  0.5  @RG ~@RG/IM~ ==@RG== ==RG== —IM RG RG ==@RG== —IM—  2 2 1  RG  DF/PP 0.3  1.5  (— 300  290 DF/FC @mxRGHF" 280 DF/RG 270  0.4 0.3 0.4 0.8 0.6 0.4 0.4 0.9 0.3 0.5 0.8  0.5 0.5 0.5 1  0.4 0.4  =RG/DF=f FC/RG --JBRG-=RG/FC= @mxFC @FC/RG#  260 250 240 230  mxRG 220 RG/FC @FC/RG ==RG== ^ 210 ==FC/RG==k @mxFC \— 2 0 0 RG -@RG/@FCp- 190 - 180  0.5/1  E  - 170 Q  —IM— RG mxRG/@RG  0.4  RG  1  - 160  - 150 3 O - 140  1.5  - 130  RG  RG  1  - 120  0.5/1  0.3  RG  -  110  -  100  - 90 - 80  RG  1 0.5  RG  - 70 - 60  mxFC  1/1.5  0.7  RG  - 50 - 40  @FC/RG  1.5/2  1.2  RG/FC  - 30  1.2  FC/RG  - 20  1.5  WG  - 10 - 0  Appendix 4d - Plot 4: Grain metamorphism, Blackcomb Mt. 94/95. 132  o $  Ui cn  '55 x  Blackcomb  Snow profiles of 28 Mar 95 - Init on 25 Dec 350  350 340  —SH—PP/DF  3/3.5 2  330  RG/DF  1/1.5  320  RG  1  310  DF  2  300  RG  0.5  290  340 330 320  0.4  --DF/PP--DF/FC—  310  ~w_FC—  300  DF/FC  290  "DF7RG"  280  mxRG @mxRG-  270  280  -@RG/IMRG/DF  1/1.5 1/1.5  270  RG  0.5  0.3  @RG/FC  2  0.3  RG/FC RG" @RG @RG/IM  0.5 0.5  0.4  RG  250  0.3 0.4 0.8 0.6  "^RG-  240  0.4  RG  260 250 240 230 220 210 C 200  o  Q > 190 Ul O  5RG  1.5 1.5 1.5  RG RG  1.2  RG  0.5  TffxFC"' RG/@RG  1.5  0.9 0.3 0.8 0.5 0.4 0.7 0.4  260  @mxFC §)FC/RG  230  :  220 L  SFC/RG ==RG== 5FC/RG  O O) 160  0.4  RG  130 120  RG  110 100  RG 0.3  RG  90 80  RG  90 80  1/1.2  70  70 0.5  60  RG  60 50  50 40 30  150 140  RG  110 100  O  190 Q > "J O  0.7 DFC/RG  < I  160 (0 O)  130 120  c  —i <*170 3 O  1  X 150 140 —  200  180  Ml  tn o 170  210  RG  40 30  2/2.5  20  1.2  FC/RG  10  1.5  WG  20 10 0  0 Appendix 4d - Plot 5: Grain metamorphism, Blackcomb Mt. 94/95.  133  ^  S n o w profiles of 11 A p r 95 - Init o n 25 Dec  Blackcomb Mt.  320  PP  310  PP =DF/PP=  1/1.5  300  DF/FC | _ 290 PP/DF - RG==@RG== KG ==IM== | M  RG  0.5/1 0.5/1 0.5  0.4  ==FC==  0.8  @RG  0.6 0.3  @RG @RG-~  270 f— 260  0.5  0.4  =IM== RG IM@RG IM RG @RG/IM  280  0.3 0.5  0.4 0.8  1.5/2  0.6  0.5  . 1  0.4  RG __IMRG  0.9 0.8 0.5 0.4 0.7  RG  250 240  RG  0>RG— 230 =RG== ' gmxFC h- 220 =@RG/FC210  RG  h- 200  gFC/RG 190 ^FC/RG E -@RG—f— 180 RG , _ u ~@mxFC-(— 170 UJ i  o <c 160 _J "  —|M— RG/mxRG  150 £ 0.4  0.5  RG  140  mxFC/@RG  1  130  mxFC/@RG  1  120 110  ftmxRG  1/1.5  100 0.3  RG  90 80  @RG  70  @RG  0.5/1  0.5  60  RG  50  @RG  40 0.7  RG  1.2  FC/RG  1.5  WG  30 20  5FC/RG  Appendix  1.5  10 •*— 0  4d - Plot 6: Grain metamorphism, Blackcomb Mt. 94/95. 134  O)  '3 X  Blackcomb Mt. w_RG/FC  290 280 270 260  —— — -  260 240 230 220  ——— _ -  210 200 190 180  E o  u  > ocIt) a. UJ  1.5/2  WG  1  ==@RG==  1  w_RG  0.5  —IM—  0.5  w_RG  0.8  wJRG  0.8  290 280 270 0.9  _—_  1.5  WG  1.5 1 1  RG  0.9  W  0.5  w RG  0.8  w_RG  0.6  0.8  0.4 0.9 0.3 0.8 0.5  1  250  ==wRG= w RG  230 220 210 200 190  @FC/RG f— 1 8 0 ==RG== =@FC/RG> 170 -»<®RG—  E u  160 150  —  160 ==@RG==  0.8  0.4  RG  '3  120  140  1  120  110  110  100  100  90  WG  1  90 0.3  80 70 60 50  WG  1  WG  1.5  WG  1.5  RG  60  RG  60 40  40 0.7  30 20  80 70  0.5  mf  RG  30 20  1.6/2  10 0  1.2  FC/RG  10  1.5  WG"""  0  Appendix 4d - Plot 7: Grain metamorphism, Blackcomb Mt. 94/95.  135  3 O 10  130  WG  ° i  1 5 0 < </> —I t—  CO o CO JZ 1 4 0 O) 130 X  O  260  240  1  "URG"  WG  w_RG  " WG  1T7T  —- @WG R G —- w _ R G — —m —  170  Snow profiles of 14 May 95 - Init on 25 Dec  a>  '3 X  Blackcomb Mt. 140  Snow profiles of 22 Jun 95 - Init on 25 Dec  —i  I— 140  130 - f  WG  1.5  130  120 —\  WG  1.5  120  110  WG  1.5  r— 110  h - 100  100 —\ WG  1.5 90  90  g  80  80  O  0  Ul o  * " 70 (0 ° O cn '5 1 60  0.9  WG  70  w RG  60  1.5  50  50  40  40 WG 30  30 —f WG  1.5 — 20  20 —\  10  g  — 10 WG  Appendix  4d - Plot 8: Grain metamorphism, 136  1.3  WG  1.6  —WG-  Blackcomb Mt.  -  94/95.  s=  3 *  =) o ± £ to O) "35 1  


Citation Scheme:


Citations by CSL (citeproc-js)

Usage Statistics



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"
                            async >
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:


Related Items