STUDIES OF BLOWING SNOW AND ITS IMPACT ON THE ATMOSPHERIC SURFACE LAYER
SERGIY A. SAVELYEV
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1+1 Canada Abstract
In January - May of 2004 as a part of the Canadian Arctic Shelf Exchange Study experiment, an on-ice camp and a meteorological measurement site were established on first-year landfast ice. Standard meteorological and turbulent flux measuring in strumentation was complimented with a set of sensors dedicated to the detection of airborne particles and measurements of various parameters of snow transport.
Snow cover probing and manual observations at the ship meteorological station and on the ice were performed on schedule according to the activities plan. Pho toelectric particle detectors, designed and fabricated at York University, Toronto, were installed at various heights above the snow surface and provided continuous information on snow particle flux during this period.
Drifting or blowing of snow in the course of the experiment was detected for
40% of the time. The criteria for blowing snow event was to last at least one hour and be separated from the previous event by greater than one hour. These criteria resulted in identification of 32 events. We propose a method of prediction of the
iv threshold wind speed that has to be attained for blowing to begin. The method is different for three types of snow surface forming processes: solid precipitation, hoarfrost deposition and wind hardening.
The aerodynamic roughness length Zom for snow covered seasonal ice was derived from pairs of wind speed and temperature profiles measured during the experiment.
Its median value is 0.001 m with variations that span two orders of magnitude.
This value is valid for flow with friction velocity u* greater than 0.35 m s"1 and less than 0.7 m s_1 (maximum encountered). No dependency of roughness length on suspended snow particle density in the reported range of u* was revealed. The
Maximum Likelihood approach is at the base of our profile fitting procedure. The effect of random measurement errors on the result of fitting is examined.
The quantitative assessment of the particle load in the multicomponent flow requires proper instruments to measure mass or volume fraction of individual con stituents. Three generations of photo-electronic counters have been developed. The first two variants only counted particles without sizing them. The third variant has an ability to measure the time-of-flight of the particle through the sensor field of view. This time can be converted into estimates of the particle size if certain assumptions are made. Calibration procedures are developed that allow for accu rate estimation of the minimum detected particle diameters depending on both the particle position in the sampling volume and its speed.
v Acknowledgements
My first and foremost gratitude goes to Professor Peter Taylor. It is with his guidance and help that this work came to a conclusion. In so many ways he influenced my way through the graduate studies that emphasizing just the scientific supervision does not do full justice to his role. I consider him my mentor and role model.
I am grateful to my supervisors, John Miller and Jack McConnell for challenging me to be better, for encouraging me or warning when I tried to do things beyond my abilities.
Professor John Pomeroy jump-started our work with particle counters. Many thanks to personnel of Electronics and Machine Shops of the Faculty of Science and
Engineering of the York University. Jim Hodges and Harvey Emberley patiently translated our vague ideas into precise electronics design. The microcontroller ex pert Ivan Nesterenko made the third generation of counters possible.
One can not wish for better chance to upgrade knowledge and professional
vi experience than the opportunity I've been given in the overwintering expedition on the board of the CCGS "Amundsen". Funding for this work was provided by the
Canadian Foundation for Climate and Atmospheric Sciences (CFCAS). Space on the Amundsen during CASES was made available through ArcticNet. I thank the entire crew and the group of researchers that made this experiment unforgettable.
Names of my closest colleagues Mark Gordon of York University and Professor
Tim Papakyriakou of University of Manitoba have to be mentioned in particular.
Professor John Hanesiak was not on the ship in person but contributed in many ways from his office at University of Manitoba. The scientific collaboration with him resulted in several published papers.
Professor Cheryll McKenna-Neuman provided us with the opportunity and as sistance to investigate the performance of particle counters in wind tunnel of Trent
University, Peterborough.
There were several dream winters in Churchill Northern Studies Center, Churchill,
Manitoba. This is where one of my excuses for doing thesis for so long is grounded.
With personnel and surroundings like those in CNSC you just want to do it again.
Here should go a complete list of people that made those expeditions so special. I can't help but mention Qiang Huang and Roger Voloshin although anybody from that list is well worth mentioning.
My colleagues from "Zephyr North", Burlington, deserve special thanks. I
vii learned a lot from collaboration with Paul Stalker and Jim Salmon. It is Dr. Jim
Salmon who persuaded me to listen to my supervisor Professor Taylor and return to York University to complete my thesis.
As usual, my family and friends stand by me, support me on the bumpy road of my career no matter what.
vin Table of Contents
Abstract iv
Acknowledgements vi
Table of Contents ix
List of Tables xiii
List of Figures xv
1 Introduction 1
1.1 Snow in a geophysical context 2
1.1.1 Blowing Snow 5
1.1.2 Threshold velocity 8
1.1.3 Snow particle size distribution in blowing snow events .... 11
1.2 Gauges to measure snow transport 15
1.3 Objectives of the study 19
ix 2 On-ice stage of the Canadian Arctic Shelf Exchange Study exper
iment in January - May of 2004 (CASES04) 22
2.1 Introduction 22
2.2 Meteorological towers absolute and relative locations 25
2.3 Instrumentation details 26
2.3.1 Wind measuring devices 33
2.3.2 Temperature/Relative Humidity sensors 35
2.3.3 Snow Depth Ranger 36
2.3.4 Visibility Sensors 37
2.3.5 FlowCapt anemo-driftometer 40
2.3.6 ZEBRA Field Mill 40
2.3.7 Digital Imaging 43
2.3.8 Particle Counters 44
2.3.9 Snow Depth, Density and Salinity 47
2.3.10 Snow Traps 49
3 Snow and its transport in CASES04 51
3.1 Introduction 51
3.2 Snow density 54
3.2.1 Density of surface snow moved by wind 56
x 3.2.2 Surface snow density 59
3.2.3 Density distribution within snow pack 64
3.2.4 Pockets of faceted crystals within snow pack 66
3.3 Salinity of the snow cover 69
3.4 Statistics of the blowing snow events 71
3.5 Threshold wind speed observations and prediction 74
4 Aerodynamic roughness length of a snow covered ice surface based
on CASES04 data 80
4.1 Introduction 80
4.2 Site location and profile measuring instrumentation in CASES04 . . 83
4.3 Monin-Obukhov Similarity Theory (MOST) form of mean wind speed
and temperature profiles 85
4.4 Maximum Likelihood approach to fitting curves to observations . . 89
4.5 Fitting data to MOST profiles 93
4.6 Application of the fitting method to artificial profiles 102
4.7 Momentum roughness in CASES04 108
4.8 Influence of snow drift on momentum roughness 115
5 Light beam interruption counter 121
5.1 Basics of individual particles light shadowing detection 122
xi 5.2 Parameters suitable for detection 126
5.3 Limitations of beam interruption detection 129
5.4 Electronics design of the York University particle counter 132
5.5 Physical realization of counters 134
5.6 Calibration of photoelectric counters 135
5.6.1 Spinning wire calibration 140
5.6.2 Calibration for specific purpose 155
5.7 Modifications to the original counter design 157
5.8 Counter with ability to measure particle time-of-flight 160
5.9 Possible development of York University counters 165
6 Summary and Discussion 168
Bibliography 184
xn List of Tables
2.1 Geographical locations of the CCGS "Amundsen" and meteorologi
cal towers of York University during ice-camp phase of CASES 2004
experiment 27
2.2 Distances based on GPS locations 28
2.3 Instruments installed at York University meteorological Tower 1. 30
2.4 Instruments installed at York University meteorological Tower 2. . 31
3.1 Measurements of overnight hoarfrost growth made on several occa
sions during CASES04 63
3.2 Dependance of the number of blowing snow events on the accepted
duration of clear amidst blowing and blowing amidst clear periods. 73
3.3 Two consecutive records from data file of observations, the first one
is taken in no drift conditions while the second one is for the start
of the blowing snow event 75
xiii 4.1 Summary statistics of fitted parameters resulting from application
of several profile fitting techniques to a set of wind speed and air
temperature profiles under stable atmospheric stratification, L = 50
m. Profiles were generated by adding random, normally distributed
errors to MOST curves. "Seed" column indicates parameters of orig
inal MOST curve 119
4.2 Summary statistics of fitted parameters resulting from application of
several profile fitting techniques to a set of wind speed and air tem
perature profiles under unstable atmospheric stratification, L = - 50
m. Profiles were generated by adding random, normally distributed
errors to MOST curves. "Seed" column indicates parameters of orig
inal MOST curve 120
5.1 Characteristic sizes of some physical objects in 2 - 70 //m range . . 141
5.2 Diameters of "equivalent" spheres (microns) that cast the shade of
the same geometrical area as thin wires. Two sensors of different
diameter are considered 143
5.3 Minimum detected wire diameter (calculated) at various positions in
the sampling volume. Results of the two-part test for Unit 8 149 List of Figures
2.1 The red star denotes the location of the on-ice stage project site
of CASES04. The underlying map is an excerpt from the NWT
Explorers Map created by The Atlas of Canada, Natural Resources
Canada 23
2.2 Sketch of sampling/activities sites in close proximity to the CCGS
"Amundsen" 24
2.3 10 m meteorological tower (Tower 1). Sonic Ranger SR50 to record
snow depth is mounted on the horizontal boom. Visibility Sensor at
1.5 m post is at the left of the picture 29
2.4 Wind measuring sensors 34
2.5 Part of wind speed time series on April 05, 2004. Cup Anemometers
at 1.0 m (purple line) and 2.0 m (blue line) do not function for some
time due to hoarfrost 35
2.6 Temperature and humidity measuring sensors in radiation shields . 36
xv 2.7 Part of temperature time series registered by thermocouples on Febru
ary 20, 2004. Measurements are affected by data logger enclosure
opening around 18:15 UTC 37
2.8 Record of dunes passing under the SR50 on April 08, 2004. It took
about an hour for an approximately 2mx3mx0.02m dune to pass.
10 m wind speed was 7 - 8 m s_1, wind direction was approximately
100 degrees true 38
2.9 Ultrasonic Distance Ranger 39
2.10 Visibility sensor at 3.3 m post 39
2.11 FlowCapt at the bottom of Tower 2, Particle Counter post (left) and
Electric Field Meter (far right) 41
2.12 Time series of measurements by the Visibility Sensors (top panel)
and the FlowCapt anemo-driftometer (lower panel). Particle counts
per second at 0.08 m height are also shown 42
2.13 Electric Field Meter and Video Camera 43
2.14 Particle Counters and mobile snow trap in drifting snow 45
2.15 Particle Counters of Tower 2 relative position above snow cover dur
ing the experiment 46
2.16 66.0 cm3 volume snow sampler 47
2.17 Snow traps 50
xvi 3.1 Time series of particle flux at 0.5 m height (top panel) and average
snow depth in the cone of the SR50 sound beam (bottom panel). . 53
3.2 Histogram of snow depth measured on April 25 - 27 in the vicinity
of the meteorological site 54
3.3 Histogram of snow density sampled from moving or deposited surface
snow during blowing events. 39 samples from CASES04 constitutes
data for the graph at the top panel. 47 samples behind the histogram
at the bottom panel were taken in Churchill, Manitoba or in Toronto,
Ontario 58
3.4 Histogram of top 2 cm of immobile surface snow density (161 sam
ples, top panel) and time history of 105 cases of density sampling
made in the second half of on-ice stage of the project (bottom panel).
Snowflake symbol denotes samples of precipitated snow, triangle
symbol denotes samples of surface hoarfrost, open circle symbols
stands for regular snow surface sampling 60
3.5 Surface hoar crystals (hoarfrost). Photos by S. Savelyev 61
3.6 Snow density profiles taken in the vicinity of met towers. Dashed
lines indicate the surface of two distinct layers. Different symbols
are used for each of 14 profiles 65
xvii 7 Time history of the near-surface faceted crystals density probing.
The background is the surface layer density shown on Figure 3.4.
Solid line represents linear regression fit, coefficient of determination
R2 = 0.3 68
8 Salinity of the snow pack measured in the vicinity of met towers.
Dashed lines indicate the surface of two distinct layers. Different
symbols are used for each of 13 profiles. Salinity scale is broken
between 1.1 and 1.2 to allow for more detailed representation of the
surface layer. Note the non-zero salinity at the top of the snow pack. 70
9 Dependance of the threshold wind speed on the maximum wind speed
of the previous blowing snow event. Filled circles stand for the regu
lar observations of blowing/drifting; open circles denote cases when
snowfall or ice fog were present when blowing begun which made it
difficult to accurately determine the threshold velocity. Snow flake
and diamond symbols are used for cases when snowfall or ice fog
/ hoarfrost, respectively were registered within an interval of calm
weather preceding the blowing snow event. The solid line is a linear
fit to 16 observations denoted by filled circles (R2 = 0.60, p-value <
0.0005) 77
xvm 1 Wind chart of 10 m level wind based on 10 min averaged observations
during the on-ice stage (January 15 - May 7, 2004) of CASES04. Size
of the directional bins is 11.25 degrees 84
2 MOST profiles for different atmospheric stability situations. Left :
Wind Speed. Right : Potential Temperature. Each curve is cal
culated with different value of Obukhov length L. Friction veloc
ity u* or temperature scale 9* are fixed, as well as momentum and
temperature roughness lengths, Zom and zot- Dashed lines represent
(U*/K) \a{z/zQm) and (9*/K)\n(z/zot), respectively 100
3 Scatter plot and box-whisker plot of momentum roughness and fric
tion velocity derived by application of the two-profile method to a
set of wind speed and temperature profiles. Left : Stable stratifi
cation. Right : Unstable stratification. Profiles were generated by
adding random, normally distributed errors to MOST curves. Stan
dard deviation of errors are 0.1 m s"1 for wind speed and 0.05° for
temperature. Cross and circle symbol shows coordinates of the orig
inal MOST curve. Bin size is 0.05 m s_1 107
xix 4 Momentum roughness via friction velocity derived by application
of two-profile method to a set of 10 minute averaged wind speed
and temperature profiles measured during overwintering in Cana
7 dian Arctic (CASES04 project). Results with z0m < 1.0 x 10~ m
were discarded. Left : All measurements when wind speed and tem
perature profile were available were processed. Right : Only pairs of
wind speed / air temperature profiles with wind speed exceeding 2
m s_1 were processed 110
5 Momentum roughness via friction velocity derived from 1 hour aver
aged wind speed and temperature profiles measured during overwin
tering in Canadian Arctic (CASES04 project). Results with zom <
10E-07 m were discarded. Left : Result of the two-profile method.
Right : Result of wind speed profile fitting with a constraint imposed
by measured A9 113
6 Aerodynamic roughness length derived by the profile method as a
function of snow particle number density. Number density is cal
culated from 10 minute averaged particle flux measured at 0.5 m
nominal height above the snow surface and wind speed interpolated
to that level 118
xx 5.1 Sketch of a particle moving through a light beam and corresponding
voltage monitored at the sensor 123
5.2 Particle moving through the light beam. Top : Succession of particle
positions along the trajectory. Middle : Time variation of the voltage
at the sensor. Each graph ends at the time instant corresponding to
the position at the top panel. Bottom: Time change of the lit area
due to shadow cast by particles of different diameters on the sensor
surface. Particles move with 15 m s_1 velocity. Sampling area is of
300 lira, diameter. Time instants are shown for the 100 yum diameter
particle (blue line on the graph) 127
5.3 Circuit schematic of the particle counter used in CASES04 133
5.4 Physical dimensions of particle counters (in millimeters). Counters
are shown in operational position, mounted on vertical post. The
insert shows a nozzle with an aperture that limits photo sensor's field
of view. The diameter of the aperture on devices used in CASES04
was 150 /xm 134
5.5 Calibration arrangement of several units at the same height above
the ice. Churchill, Manitoba. Winter 2005/06 137
5.6 Time series of particle counts from three detectors installed at 50 cm
above the ice. 2005/01/29, Churchill, Manitoba 138
xxi 5.7 Scatterplots of data from different units against each other 139
5.8 Sketch of wire inserted into the center of sensor's field of view. At this
position the area shaded by wire (outlined by red line) is maximized. 143
5.9 Calibration assembly consisting of the wheel with thin wires, DC
motor with tachometer, micrometer as a translation device (front of
the picture), pulse generator (on the right) 147
5.10 Drop in sensor voltage produced by wires of different diameters put
into the light beam at different distances from the sensor. Similar
symbols denote results of the experiment with different wires at the
same position in the sampling volume. Solid lines are polynomial fits
to respective experiments 148
5.11 Counters readings of beam intersection by wires of different diam
eters for various speeds of crossing. Unit 7 - circle symbols, Unit
16 - diamond symbols. There are three groups of identical diameter
(10.16 /mi, 12.7 /im, 25.4 //m) wires in each group placed on the
wheel. Solid lines are maximum possible counts if all wires in groups
with wire diameters indicated next to the line are detected 154
xxn 5.12 Relationship between Meteorological Optical Range measured by vis
ibility sensor at 1.5 m height and number density calculated from par
ticle counter data at 2.0 m height. Measurements are made during
CASES04. Power fit (solid line) is for the number densities greater
than 0.01 cm-3. Coefficient of correlation R2 = 0.93 156
5.13 Circuit schematic of the second generation particle counter. Photo-
diode detector is used in photoconductive mode to gain speed of
operation 160
5.14 Signal processing flow chart. Each pulse is measured in terms of
pulses of known duration generated by processing circuitry. Signal
pulse duration is assigned to one of 32 bins based on its length. The
counter of the respective bin is augmented. This sequence is carried
out for 30 seconds. The accumulated counts in all 32 bins are output
at the end of a 30 second interval in one of two available serial port
protocols 163
5.15 Circuit schematic of the time-of-flight measuring device 164
xxm 1 Introduction
This work is concerned with particle-laden air flow in the surface layer of the Atmo spheric Boundary Layer (ABL). The flow considered is in a turbulent state similar to a boundary layer type flow studied in Fluid Mechanics. The Atmospheric Bound ary Layer is sometimes designated as a non-canonical boundary layer in a sense that it differs in many aspects from the classical Fluid Mechanics counterpart. The ABL is defined by the extent of variations of physical parameters of air caused by the diurnal cycle of momentum transfer and heating and cooling of the Earth's surface, while "classical" boundary layer in turbulent flow in pipes or in channels is defined by velocity or momentum thickness. The latter is the extent of the layer near the boundary where the bulk of momentum changes take place, from zero velocity at the boundary to about 99% of the free stream value. The surface layer comprises approximately one tenth of the ABL.
Compared to the situation of a simple flow when only one fluid is present the flow of a multicomponent fluid may involve interactions between components, phase
1 changes and self-interaction of the components. Another prominent feature of such fluids is an existence (and motion!) of singular surfaces that separate components.
A continuum approach or continuum model is chosen to conceptually describe the situation of multicomponent flow. Field equations of the model may include the jump conditions on singular surfaces. The balance of mass, momentum and energy contain terms that describe exchange through the interfaces. Constitutive or mate rial equations that describe how stress and heat are transported within the material are much more complicated compared to a one component fluid. The continuum model equations are derived from postulates of conservations of mass, momentum, energy and entropy. The system of equations is not closed so that additional equa tions are sought based on material properties of constituents. Although there are rules as to how to derive the material relationships, the actual form of relationships for a multicomponent fluids are not well established or understood. The same is true for the boundary conditions. To a large degree this work is devoted to exper iments that are intended to provide insights on the properties of flow that involve airborne snow particles.
1.1 Snow in a geophysical context
Depending on the situation the meaning of the term snow varies. One can distin guish precipitated snow, snow lying on the ground or snow cover and blowing snow.
2 Precipitating snow has a variety of crystal forms depending on the conditions in which the ice crystals grow. The density of snow flakes is that of the ice, usually taken to be 917 kg m-3. This is the so called true density - the ratio of the mass of the ice to the volume of the ice. Snow flakes precipitate as individual crystals or as a conglomeration of crystals. It could be disks, needle-like forms, prisms or various dendritic or branched forms.
Snow on the surface is an aggregation of ice crystals. Liquid water is usually present as well, and its amount characterizes snow wetness (dryness). Ice crystals form a certain texture (skeleton, matrix) with air filling spaces between crystals.
The density of snow cover is the density of the mixture - the ratio of the mass of all constituents in a material body (air, water, ice, other inclusions) to the volume of the body. The magnitude of the density of snow cover is roughly half of the ice density. Due to moisture and temperature gradients within the ice matrix, bonds can form between individual crystals. Sound heard sometimes when walking on the snow originates from breaking bonds and the crystals themselves. The process of bonds forming or disappearing, crystals growing and reshaping and changes in the ice matrix is referred to as snow metamorphism. The snow grain is understood as the smallest distinguishable constituent of the snow pack. It could be one or many ice crystals. Grains can be connected into clusters or into conglomerations commonly called chains. There exist several classifications of snow grains based on
3 their appearance and size. The widely accepted classification is that of Colbeck
(1997). A densification of the snow pack is an increase of snow cover density due to compaction of snow under the force of gravity. It is customary to model metamor- phic changes of density as an additive term to the gravitational compaction. So the term densification can be applied to the density variations due to metamorphism as well.
Snow particles in blowing snow are separated particles. Although it is common to observe the precipitated snow flakes carried by wind in the blowing snow event snow flakes are quickly broken into smaller parts. The source of airborne particles other than precipitation comes from grains of snow pack extracted from the ice matrix and picked up by the wind. The density of the airborne particles is the true ice density. In order to quantify the amount of suspended particles their number per unit volume (number density) is frequently used. If the particle size distribution or mean particle size is known, their volume fraction in the air can be deduced from the number density and the true ice density. The average diameter of blowing snow particles as reported by Schmidt (1981) is in 100 - 300 /an range. Particles are considered to have a spherical shape and move with velocity of the mean flow.
The later assumption that the averaged horizontal component of particle speed coincides with the average wind speed at the same level was tested by Schmidt
(1982b). The real shape of the particles in drifting/blowing snow is not spherical,
4 they are rounded fragments of precipitation snow flakes or snow cover grains of irregular shape. Schmidt (1981) suggested approximating fragments by spheres of their equivalent diameter, the equivalent diameter being a diameter of a sphere that results in the same cross sectional area as the area of the original particle.
The latter is computed as the product of particle's two biggest planar dimensions.
1.1.1 Blowing Snow
Particle-laden geophysical flows involve several interacting processes each with a specific set of scales that allows different approaches to model individual processes.
Initially, at low speeds, the flow is particle-free. With increase of fluid velocity granular material is extracted from the underlying bed and set into motion. The terminology for the various flow regimes are based on different kinematic regimes or the specific kind of particle trajectory. Rolling of material along the bed is referred to as raptation or creep, while hopping motions of particles that bounce along the surface is called saltation. Completely airborne particles that are maintained in the air by turbulent diffusion offsetting gravity are said to be in suspension. This picture originates from the studies of aeolian transport and is first attributed to
Bagnold (1941). Recently some researchers (Jenkins and Hanes, 1998; Pasini and
Jenkins, 2005) have argued that there is a transition process between the saltation and suspension phases. At some point the increase in the energy of the fluid flow,
5 the concentration of saltating particles increases to such an extent that collisions between them are frequent. At this stage the momentum from the rising particles is transferred to particles already airborne. It is argued that this particle pressure keeps a significant amount of material in the air forming the so called particle sheet. The suspension commences from this stage if fluid velocity continue to rise. It was suggested that particle spin (White and Schulz, 1977) and electrostatic charge (Schmidt et al., 1999) could play a role in increasing the saltation height and consequently in the onset of turbulent suspension.
The depth of the saltation layer is of order 0.1 m depending mostly on the wind speed and snow surface conditions. It seems that there are no geographical differences in the vertical extent of the saltation while the extent of the blowing snow layer is considered to be a few meters or few tens of meters in the northern hemisphere and up to several hundred meters in the Antarctic (see Schmidt, 1982b, and references therein).
It was observed at the early stages of the sand saltation research that in many cases the fluid drag alone is not sufficient to explain the amount of particles ex tracted from the bed. In wind tunnel experiments it took much stronger winds to initiate the saltation compared to cases when seeding of particles was intro duced. The mechanism of extracting particles from the bed by bombardment by loose material is now incorporated in many models of particle-laden flows. It is
6 considered that an airborne particle at the end of its trajectory collides with the surface particles and the impact causes dislodging of surface material which in turn is entrained into the flow. The phenomenon can be observed while walking upon the snow surface on a day with light wind when the wind by itself is not strong enough to cause drifting. On the other hand snow particles dislodged by pedestri ans initiate the drift that afterwards can maintain itself for a significant amount of time. The source of airborne particles can be precipitated snow, snow trapped on tree branches or other vegetation. In some cases hoarfrost can form on the snow surface and it is easily broken by even light winds. The threshold velocity needed to initiate snow drift when no loose particles are available is called (after Bagnold) the fluid threshold while the impact threshold velocity term is used to describe situations when loose material is in abundance.
From a meteorological observer point of view, the definition of blowing snow event is centred around the reduction of visibility at the observer's eye level by a given amount due to obstruction caused by airborne snow particles. The snow particles in blowing snow event can originate from falling snow or be extracted by wind from the snow cover. The Meteorological Service of Canada has put a threshold visibility for blowing snow at 9.7 km although a blowing snow warning will be issued only if visibility is predicted to drop below 1 km. However we note that ice particles in ice fog can cause a low visibility but this does not constitute blowing
7 snow. There are several meteorological terms related to the severity of blowing snow, the most recognizable are blizzard and drift. For blowing snow to be called a blizzard the wind speed and temperature should be above and below, respectively some predefined values for a certain amount of time. So the blizzard is an event with persistent strong wind at significantly low temperature (sometimes windchill is used as a scale instead of air temperature). The exact values of wind speed, temperature and time duration are country specific. In Canada the conditions must last in excess of 4 hours with wind speed more than 50 km hr-1, with visibility caused by blowing snow less than 1 km and wind chill lower than - 25° C. Low intensity blowing snow is said to be drifting. In this case particle movement above the surface is visible as coherent streaks of airborne snow immediately above the surface but the visibility at eye level remains high. The snow particles move predominantly in saltation mode.
1.1.2 Threshold velocity
The transition from particle-free to particle-laden flow occurs when the fluid velocity reaches some threshold value. Obviously this value is important from the point of view of the prediction of the start of the blowing snow event. In addition it is considered that the threshold velocity for the particular event determines how much snow will be in suspension in later stages of the event because it is closely
8 related to the surface conditions (Schmidt, 1980). This does not exactly agree with the fact that the onset of blowing depends strongly on loose particles availability.
The same snow cover conditions and history may not result in the same threshold velocity if for example, snow precipitation is stored in trees and would provide the necessary impact when wind speed increases compared to the absence of such a source.
Snow surface grains can rapidly develop high cohesive strength by growing bonds between grains. The process is usually referred to as sintering. Unlike dry sand for which the threshold velocity mostly depends on particle mass or diameter the sintered snow exhibits little dependency of threshold velocity on snow density or typical size of snow grains. Instead the strength of bonds dominates the threshold for onset of drifting. There are also cohesive forces associated with liquid water in the snow matrix. Their relative importance increases with the temperature.
Theories developed for granular material such as sand have limited validity in the case of snow.
The threshold velocity is understood either as the maximum value of wind speed
(or friction velocity) for which no particle motion is detected or the minimum wind speed when particles just start to move (Schmidt, 1982a). Although it is relatively easy to define the threshold velocity or threshold friction velocity as related to the state of flow when no particle is entrained into the fluid the actual definition
9 requires determination of the procedure and often the height above the bed where the measurement of particle load takes place. The definition of the indicator will also influence the actual value assigned to the threshold conditions. The comparison of the threshold values obtained in field experiments and in the wind tunnel requires extra care. For example, the onset of saltation in the wind tunnel experiment of
Nishimura and Hunt (2000) was monitored to the accuracy of one diameter shift of particles comprising the bed. Not only is such accuracy hardly achievable in the field but also the values of the threshold velocities are not directly comparable with those from field experiments. Particle movement in the wind tunnel will not stop after initiation because the wind speed will often increase by the design of the test. On the other hand there is no guarantee that wind will not subside in the field even after blowing initially began. The blowing/no blowing conditions are often determined by visual observations supplemented by analysis of measured meteorological variables an example of which can be seen in Li and Pomeroy (1997) or Mahesh et al. (2003). Li and Pomeroy (1997) suggested a formula that relates threshold wind speed at 10 m height (Ut(10)) and air temperature at 2 m (Ta) based on analysis of meteorological observations in the Canadian prairie provinces. It is
2 Ut(10) = 9.43 + 0.18 Ta + 0.0033 T a (1.1)
where Ta is in °C and numerical constants have proper dimensions to ensure that resulting wind speed is in m s_1. 10 If sensors that measure the number of air-borne particles or some of their param eters are employed in the experiment the onset of particle movement is detected based on sensor measurements. It could be an instantaneous value that signals the onset depending on probe sensitivity or some kind of analysis based on a set of observations made during drifting/blowing. An example of the latter is a for mula suggested by Schmidt (1981) that relates the threshold velocity and moving particles' mean diameter determined at 25 mm above snow surface. An implicit assumption in such cases is about the lasting influence of the threshold velocity on transport of particles during the whole duration of the event.
We would like to emphasize the fact that the formula of Li and Pomeroy (1997) is the only one suggested that can be used for prognosis. All other approaches are diagnostic ones.
1.1.3 Snow particle size distribution in blowing snow events
Within the snow cover the size of ice particles is not easy to define. Individual ice crystals are connected by bonds and form chains of particles. Particle size estimated by snow stratigraphy surveyors are based on ice skeletons manually broken into individual grains. This procedure is, to a significant extent, subjective. On the other hand airborne particles are separated naturally. The particle size distribution is of significant interest to researchers because it allows us to quantify the mass of
11 particles entrained into the fluid, calculate mass transport and estimate forces of interaction between the fluid and particles.
Budd et al. (1966) first suggested that particles size distribution can be fit into a Gamma probability distribution function (PDF) based on the analysis of results obtained in the Antarctic. Their data were the first and for some period of time the only measurements of the particle sizes in blowing snow. The form of the two parameter Gamma distribution Ga{x; a, /?) is expressed as Ga(x;a'^) = f^)^exp("i)' (a>o-/3>°)' (L2) where x stands for the particle size and is a positive number, T is the Gamma function. The shape parameter a was estimated to vary from 12 to 16.1. /3 is often called the scale parameter and sometimes the spread parameter. We prefer the latter notation as being less ambiguous. Later experiments reported by Schmidt
(1982b) and Dover (1993) found estimates of a lying between 5.1 and 15, and between 0.6 and 1.9, respectively. In Gordon and Taylor (2009b) snow particle size measurements were taken by a novel method employing a digital video camera. The variation of the shape parameter is reported to be from 1.25 to 3 with an average value of 1.9. In the recent project in the Canadian Eastern Arctic, Gordon et al.
(2010) estimated the shape parameter to be in the range from 4.4 to 6.4. Smith
(1995) argued that a should equal to 2 in order to satisfy restrictions imposed by the sublimation process. The value of a = 2 is often accepted in numerical models 12 of blowing snow. The log-normal distribution was also tried as an alternative to the gamma distribution and was usually rejected with a reference to the decision made in Budd et al. (1966). Nevertheless some researchers have used the log- normal distribution as an approximation to the measured particle size distribution
(c/. Gubler, 1981).
The particle size distribution and the value of the shape parameter were observed to vary with height, in most cases it is considered that these parameters decrease with the distance from the surface. The product of shape parameter a and scale parameter (3 of the Gamma PDF equals the mean value of x - the mean particle size in our case, while (a — l)/5 equals the mode of the distribution, i. e. the most frequently encountered particle size (within some small interval) if a > 1. Usually a and /3 are found as a result of fitting of the Gamma PDF to empirically observed sizes. The mean particle size then is just an alternative form of the output of the fitting procedure.
The proposed relationships between mean particle radius f and the height are due to Pomeroy (1988) (as a result of analysis of data reported in Schmidt, 1982b)
f = 4.6 x lO-V0-258 (1.3) and due to Dover (1993)
f = 7.5 x 10"5 - 3.78 x 10"6z (1.4)
13 where radius and distance from the snow surface z are in meters.
The mean particle radius measured in experiments was reported to be from 43 to 83 /^m (Budd et al., 1966) and from 50 to 110 /xm (Dover, 1993) at the same location in the Antarctic. Also in the Antarctic Nishimura and Nemoto (2005) observed mean radius from 36 to 110 //m (their Figure 9, p. 1655). Observations of
Schmidt (1982b) in mid latitudes of the northern hemisphere resulted in f varying from 43 to 90 jum. Gordon and Taylor (2009b) found the mean radius to vary from
52 to 86 fiva. in the experiment in Canadian subarctic (near Churchill, Manitoba) while in the Canadian Eastern Arctic Gordon et al. (2010) estimated f to fall within
35 - 74 /im interval. The estimate of f based on visibility measurements in CASES04 produced the cross section area averaged particle radius to be near 50 /xm (Huang et al., 2008).
The lower bound on the blowing snow particle size is usually imposed by the measuring device. The minimum radius detected by the counter described in Brown and Pomeroy (1989) is 22.5 fira while the digital camera assembly used in Gordon and Taylor (2009b) or the device used by Nishimura and Nemoto (2005) could not detect particles smaller than 25 jim. in radius. The upper bound is also limited by the measuring device but it is less critical than the minimum detected size in composing the overall picture because of the positive skewness of the observed size distributions and the fact that there are very few suspended particles with radius
14 greater than 1 mm.
1.2 Gauges to measure snow transport
An assessment of the amount of snow entrained into the air flow is required to investigate how flow properties are altered by the snow component in the fluid.
It includes measurements of instantaneous concentration of the airborne particles at different heights above the surface and the rate of the snow transport. Gauges that trap snow from the flow were traditionally used for this purpose. Two major varieties of snow traps are mesh-type or bag traps that allow air to pass through the fine mesh but intercept particles and devices that use the effect of sudden flow speed reduction by means of fluid flow volume expansion. It is believed that flow obstruction by these devices is too big to get accurate measurements. The snow trap efficiency or the ratio of the mass of intercepted particles to the total amount of airborne particles in the sampled volume is a topic of discussion. Another drawback of snow traps is the necessity to continuously attend gauges during the measurement cycle which poses a certain amount of hazard for the researcher exposed to high wind at low temperature.
A number of alternative approaches were undertaken with the aim of achieving a higher degree of automation and improve the accuracy of measurements. Two broad categories of sensors can be outlined based on the physical parameter to
15 be monitored. The momentum of the moving particles is used in acoustic and in piezoelectric sensors. The light attenuation by airborne particles is an effect used in photoelectric devices. The latter can be considered as an integral over the sampling volume or at the individual particle level.
A counter reported in Tug (1988) translates the impact of each particle on the piezo crystal into an electrical pulse whose magnitude is proportional to the parti cle's momentum. Pulses are counted into 4096 bins, drift flux is computed as an integral over all bins. Wind tunnel calibration with particles of known size and mass is needed. In a device called a FlowCapt (Chritin et al., 1999) the sound pressure caused by particles hitting the teflon tube is measured by an array of mi crophones situated inside the tube and is translated into the mass flux and wind speed estimates. The attenuation or diffraction of electromagnetic waves by differ ent materials is behind a variety of instruments used in geophysics. An example is a visibility sensor used in CASES04 (see Chapter 2) which measures an integral re sponse of the volume of fluid with suspended particles to the illumination by light.
Optical Particle Counters (OPC) such as used in aerosol studies (e.g. Heintzenberg and Rummukainen, 1993) analyze particle distributions in a sample of air extracted from the flow. This could be considered as an instantaneous distribution. Another type of particle counter detects and registers particles at a point one by one. The distribution is then calculated based on measurements made during the certain time
16 interval.
Sommerfeld and Bussinger (1965) describe a counter that senses illumination at the two branches of a photoresistor bridge. A particle crossing the light beam casts a shadow on one of the photo-resistors. The consequent change of resistance is compared to that of the resistor in the unobstructed path. Two light beams are required and one of them should be unobstructed by particles at all times. The latter requirement was hard to achieve during blowing snow. The utility of the device was limited to moderate blowing only.
Following the work of Hollung et al. (1966) started at the University of Wash ington, Schmidt and Sommerfeld (1969) and Schmidt (1977) developed a particle counter that had the ability to measure particle size and mass flux. The voltage drop caused by a particle crossing the light beam was monitored and a pulse issued if the drop was larger than some threshold value. There were two sensors situated behind vertical slits in the sensor cover. Two pulses were created when a particle crossed each portion of the light beam. The time between pulses was measured and the particle velocity was calculated based on the time and known distance between the slits. Care was taken to place the counter in such a manner that particles cross each beam in a sequence. The device of Schmidt (1984) was a second generation counter that improved significantly on the first design. Several researchers repro duced the counter of Schmidt design while making changes and improvements. In
17 some instances improvement was only due to new electronic components that be came available as in the project reported in Wendler (1989). And in other cases the device was developed to such an extent that the design can be considered in its own right. The example of this latter case is a particle counter design reported in
Sato et al. (1993).
The same idea of monitoring the voltage drop due to particle shadowing of the sensor otherwise fully illuminated by light was used in a device developed in
Switzerland (Gubler, 1981). There was only one sensor in this design and pulse height is proportional to the area of the shadow (particle cross-sectional size). A particle of a certain size was assigned to one of five classes. The device outputs mass flux.
The blowing snow particle detector of Brown and Pomeroy (1989) was developed with the aim to eliminate some shortcomings of the Schmidt counter. It employed advanced electronic components and it was simplified to only count the number of particles passing through the field of view of the sensor. No attempt was made to discriminate sizes. When a prototype of this counter became available to the York
University research team, electronic components had since become outdated and no longer in production. An attempt was made to reproduce the Brown-Pomeroy counter with new components and at the same time make changes to the electronic design to take a full advantage of the functionality of new components. The York
18 University counter will be a topic of one of the following chapters.
1.3 Objectives of the study
Blowing snow is an example of particle-laden flow in the Atmospheric Boundary
Layer. In the northern hemisphere the phenomenon is believed to be confined to the surface layer while in Antarctica deeper layers are possible. Multicomponent flow can be modeled in the framework of a continuum approach similar to the situation of a simple flow. The continuum model requires material constraints to be incorporated in order to close the system of equations on which the model is based. Initial and boundary conditions should also be formulated to have a well posed problem.
Field experiments are a very useful tool to gain understanding of the nature of the material constraints, boundary conditions and temporal and spatial scales of the phenomenon. The objective of the thesis is to analyse the results of an Arctic-field experiment conducted both in simple flow and multicomponent flow conditions, to quantify flow properties in both situations and discover changes in flow properties, boundary conditions and scales of the phenomena.
The development of a device that allows for quantification of the particle load, volume and/or mass fraction of the solid component of the fluid is another goal of this thesis. This task includes analysis of the potential and limitations of pho-
19 toelectric approach to the sensing of particles in the air, the design and physical implementation of various models of the sensor, and the development of calibration procedures.
The transition from simple to multicomponent air flow above snow-covered sur face commences when drag imposed by wind causes entrainment of snow grains from the underlying bed into the flow. The process depends both on flow prop erties and on the properties of the snow cover. Careful observations of the snow properties are required to relate them to the onset of blowing snow. If most im portant or frequently occurring snow surface forming processes are identified then it would allow us to narrow the list of possible predictors for the onset of drifting snow. To discriminate states of the flow a criterion of particle entrainment needs to be decided upon. We use a method based on the direct measurement of particles number densities as provided by our photoelectric particle counters.
Savelyev et al. (2006) investigated the relationship between measured sensible and latent heat fluxes and measured particle number densities. Gordon et al. (2009) presented some particle size information from our study while Huang et al. (2008) investigated the impact of blowing snow on visibility. In this work we will analyse the turbulence scales derived from observations of mean flow properties at various heights above the snow surface and inspect if the influence of blowing snow can be identified. The aerodynamic roughness length of the snow-covered ice and its
20 dependence on particle load will be examined.
We investigate whether our York University particle counters can be developed into sensors with the ability to measure particle sizes. Particle size-distribution and its variations with flow properties allows for complex analysis of the multicomponent flows.
21 2 On-ice stage of the Canadian Arctic Shelf
Exchange Study experiment in January - May of
2004 (CASES04)
2.1 Introduction
To assess the impact of variability in climatic and physical forcing of the snow and ice cover on the ice-related biological component of the Arctic ecosystem re searchers from York University, Toronto, Canada took part in the Canadian Arctic
Shelf Exchange Study (CASES) experiment. Funding for their involvement was provided by the Canadian Foundation for Climate and Atmospheric Sciences as a part of the support of research on blowing snow. The overall research programme was funded by the Natural Sciences and Engineering Research Council of Canada
(NSERC) while the Canada Foundation for Innovation (CFI) provided funds for the refurbishing of the Canadian Coast Guard Ship "Amundsen".
The author was responsible for planning, preparation, installation and mainte-
22 Figure 2.1: The red star denotes the location of the on-ice stage project site of
CASES04. The underlying map is an excerpt from the NWT Explorers Map created by The Atlas of Canada, Natural Resources Canada. nance of a micrometeorological station, visibility sensors and the SODAR on ice flow. Snow cover surveys, sampling and snow transport measurements were also implemented by the author. Experiments that involved imaging of blowing snow by video camera and measurements of electrical charging of blown particles were designed and conducted by Mark Gordon. The overall supervision and guidance
23 was provided by Professor Peter Taylor.
Here we describe the research efforts pertaining to meteorological boundary layer studies during the on-ice stage of CASES which took place in January - May
2004 in Franklin Bay, Northwest Territories, Canada (Figure 2.1). We will refer to the on-ice stage as CASES04. The CCGS Amudsen was led into the first year ice about 15 km offshore where it stayed for 5 months, frozen into the ice, serving as a base for the international team of scientists. The seasonal ice was uniformly packed.
The ice floe that hosted the camp was flat, approximately 10 km across. Several research sites were set up in the vicinity of the ship. The sketch in Figure 2.2 shows li.:
LODL\G STRIP ~*r
A.A.1 E D ^
c • >^
A. LANDING STRIPS B ELECTROMAGNETIC & SNOW GEOPKi SIC C GAS CHAMBERS D BIOLOGICAL SAMPLING E WATER SAMPLING MICRO F SNOW FENCING METEOROLOGICAL G SNOW LASER PROFILES OBSERVATIONS
Figure 2.2: Sketch of sampling/activities sites in close proximity to the CCGS
"Amundsen".
24 the relative positions of places of the on-ice scientific activities. In particular, a micrometeorological observation site was approximately 1.5 km east southeast from the CCGS "Amundsen". The snow fencing site northwest and northeast relative to the meteorological towers may have affected air flow from this direction. The
York University team was primarily responsible for two 10 m towers (basically
10 m of 1.25 inch diameter aluminum conduit). One had standard meteorological instrumentation and the other a non-standard setup. Snow particle counters were installed on separate posts as well as visibility sensors. Tower maintenance and snow cover measurements were conducted on a daily basis while snow mass transfer measurements were implemented whenever the weather permitted. Data from two data loggers (one on each tower) were transmitted by radio link to the ship based computer once a day.
2.2 Meteorological towers absolute and relative locations
York University instrumentation was deployed at an ice camp with an electrical generator and a shelter. Two 10 m meteorological towers were installed about
200 m south of the generator along a North - South line with a separation of
20 m. Further south along this line were three flux measuring towers (University of
Manitoba) with eddy correlation flux measurements, snow depth, wind speed and 4 component radiation. A Doppler SODAR system (John Hanesiak group, University
25 of Manitoba) was also deployed near the generator (January 29/30, approximately
50 m south of the shelter). Each of the two meteorological towers was accompanied by a 2 m high post distanced 2 m in a SW direction. They were used to mount
Particle Counters and Cup Anemometers in order to avoid flow distortion around the data logger enclosures. Towers were designated as Tower 1 (northernmost) and
Tower 2. Additional posts were installed for an Electric Field Meter (approximately
15 m west from Tower 2) and for Visibility Sensors (University of Manitoba). The first of these was between the meteorological towers at the top of a 1.5 m high post and the second sensor was located 4 m east from the first at the top of a 3.3 m high post. Geographical coordinates of the towers as well as northward direction were determined by means of a Global Positioning System (GPS) receiver. Table
2.1 lists the coordinates of the towers and main reference objects and in Table 2.2 one can find distances and directions calculated from the GPS locations.
2.3 Instrumentation details
Tower 1 and Tower 2 are based on York University standard 10 m mesonet towers
(Figure 2.3): 3 x 3 m aluminium 1-1/4 inch conduit sections plus aim top section,
3 levels of guy ropes and 4 anchors. 2 m stand-off aluminium posts were frozen into the ice (extra support was added by means of wooden plank attached perpendicular to the post at the ice-air interface level). Posts that housed Visibility Sensors had
26 Table 2.1: Geographical locations of the CCGS "Amundsen" and meteorological towers of York University during ice-camp phase of CASES 2004 experiment.
Point Latitude Longitude Notes
AMUNDSEN A N 70 02.732 W 126 18.059 from ship's GPS
Tower 1 N 70 02.542 W 126 15.894
Tower 2 N 70 02.532 W 126 15.896
Flux Tower 1 (UofM) N 70 02.516 W 126 15.894 closest to Tower 2
Shelter N 70 02.635 W 126 15.873
AMUNDSEN B N 70 02.727 W 126 18.053 starboard side
1 level of guy wires, three in total.
Tower 1 was instrumented January 14, 2004 and taken down on May 7, 2004.
AC power was connected to the data loggers and data collection started on January
15, 2004. The Visibility Sensors had separate 120 VAC power supplies and were installed January 23/24.
Data on Tower 1 were logged on a Campbell Scientific CR10X data logger with a lead acid battery pack plus battery charger in a CR12/14 enclosure mounted at about 1 m. The enclosure contained a 40 W light bulb as a heater. The 100 W
27 Table 2.2: Distances based on GPS locations.
End points Distance Bearing
(degree true)
AMUNDSEN - Shelter 1.32 km 097
Shelter - Tower 1 173 m
Shelter - Tower 2 193 m
Shelter - Flux Tower 1 (UofM) 223 m
Tower 1 - Tower 2 19.8 m 182
Tower 2 - Flux Tower 1 (UofM) 19.6 m 178
heating element used at the very beginning proved to produce excessive heat and was replaced. Power to the light bulb was through a Thermocube outlet to switch on below 2 °C and off at 7 °C. At -30 °C ambient the 40 W bulb was on continuously and held the data logger panel temperature at about —12 °C. An RF400 spread spectrum radio plus Yagi antenna was used to transmit data to the acquisition lab on the ship. Wind profile measurements at four levels were made by means of a
Wind Monitor at 10 m (also providing wind direction) and Gill Cup Anemometers at 4 m, 2 m and 1 m (lower 2 anemometers were on a stand-off 2 m post to avoid
28 V" •••& -K St Figure 2.3: 10 m meteorological tower (Tower 1). Sonic Ranger SR50 to record snow depth is mounted on the horizontal boom. Visibility Sensor at 1.5 m post is at the left of the picture. flow distortion around the data logger enclosure). A Temperature/Humidity sensor in a 12-plate radiation shield was placed at 1.5 m height. A thermocouple pair, in 6-plate radiation shields at 9.5 m and 1.5 m provided AT measurements. A Sonic Ranger - snow depth sensor was attached to a boom arm that in turn was fastened to the tower at approximately 2 m. One Particle Counter was mounted at 0.5 m 29 Table 2.3: Instruments installed at York University meteorological Tower 1. Sensor/Equipment Type/Make Quant. Level Interrogation interval = 2 s; Averaging interval = 5 imin Data logger CR10X, Camp 1 1 m bell Sci. Enclosure CR12/14 1 1 m Wind Monitor RMY 05103 1 10 m Cup Anemometer RMY Gill 12102 1 4 m Temperature/Humidity HMP45C212 1 1.5 m Thermocouple pair Cu/Co 1 9.5 m - 0.5 m Sonic Ranger SR50 1 2 m Spread Spectrum Radio CSI RF400 1 3.0 m with Yagi antenna Particle Counter Post 1 Particle Counter York U. 1 0.5 m Cup Anemometer RMY Gill 2 1 m, 2 m on the stand-off post. Tower 2 was identical in design to Tower 1. Measurements from sensors on the 30 Table 2.4: Instruments installed at York University meteorological Tower 2. Interrogation interval = 1 s; Averaging interval = 5 mm Data logger CR23X 1 1 m Enclosure CR12/14 1 1 m FlowCapt AlpuG 1 0.1 m - 1.1 m "Combox" for FlowCapt AlpuG 1 1 m Thermocouple (single) Cu/Co 6 water, snow/ice in 6-plate interface, 0.5 m, radiation shield 1.5 m, 4 m, 9.5 m Spread Spectrum Radio CSI RF400 1 3.0 m Particle Counter Post 2 Particle Counter York U. 4 0.1,0.2, 1.0,2.0 m Cup Anemometer Gill 12102 1 1 m Visibility posts 1 and 2 Visibility Sensors Sentry 2 1.5 m, 3.0 m Stand-off post 25 m east from Post 2 Electric Field Meter 1 1.5 m 31 tower and stand-off posts (Particle Counters post, Electric Field Meter post and two Visibility Sensors posts) were collected by a Campbell Scientific CR23X data logger. The towers were instrumented and data collection initiated January 20th; problems were noted with the particle counter data, January 21st. Other problems arose due to the visibility sensors (see below). All data except the 1 m Particle Counter are valid as of 28 January. The RF400 spread spectrum radio and Yagi antenna were installed on February 17 to enable transmission of data from Tower 2 to the acquisition lab. A special "Combox" for the FlowCapt sensor was mounted at about 1 m and a CR8/10 enclosure for the Electric Field Meter controller was mounted on the 3 m Visibility sensor post at approximately 1 m. Data from the Wind Monitor at 10 m on Tower 2 were only used for the first few days. The signal was then disconnected to make room for pulse input from additional Particle Counter (installed at 0.1 m). Four Particle Counters (0.1, 0.2, 1.0 and 2.0 m) plus a cup anemometer at 1 m were mounted on the stand-off post. A temperature profile was measured by means of 6 Cu/Co thermocouples: these were located in the water below the ice, at the ice/snow boundary, and at heights of 0.5 m, 1.5 m, 4 m and 9.5 m (the last four units were inserted into 6-plate radiation shields and mounted on the tower). Note that all thermocouples are referenced to a thermistor on the CR23X input panel assuming that panel to be at a uniform temperature. It was not, and temperatures may well be in error as a result. Also any time 32 the enclosure temperature changed abruptly, a false signal was registered for air and water temperature values. These occurred whenever the enclosure was opened and also when the AC power was stopped for generator service. Also, the on/off switching of the thermocube would affect the internal temperature characteristics of the enclosure. Sensors installed on the meteorological towers of York University - Tower 1, Tower 2, Particle Counter posts and Visibility Sensors posts - are itemized in Ta ble 2.3. Note the Snow Depth sensor on Tower 1, Snow Mass Transfer sensor (FlowCapt) on Tower 2 and the stand alone Electric Field Meter. Sensors were interrogated every 2 seconds on the CR10X data logger installed at Tower 1 and every second on the CR23X data logger installed at Tower 2. Individual measure ments were averaged over 5 minute intervals and recorded into data logger memory for later radio transmission or collection by Palm Pilot or storage module. The FlowCapt was interrogated every 3 seconds (smallest interval from the range rec ommended by the manufacturer) and measurements were averaged over 30 minute periods. 2.3.1 Wind measuring devices Anemometers R.M. Young 12102 were used for wind profile measurements for the first 10 m above the ice surface (Figure 2.4). The manufacturer guarantees an 33 (a) Wind Monitor (b) Cup Anemometer Figure 2.4: Wind measuring sensors accuracy of ±0.3 m s_1 for wind speed measurements and ±3° for wind direction measurements of the Wind Monitor Cup Anemometer voltages were filtered to eliminate high frequency noise. Overall performance of the sensors was highly satisfactory (data recovery is more than 90%). Most losses were due to icing. Snow tends to accumulate in the cups of the anemometers during blowing or falling snow events. Cups were cleaned of snow as needed. Hoarfrost grew on the metal and plastic surfaces of sensors in calm, ice fog conditions. With any onset of wind the hoarfrost was removed quite quickly. An occurrence of "stuck cup anemometers" event can be seen on Figure 2.5. A starting threshold of 1.0 m s_1 for the Wind Monitor may be an explanation of wind speed measurements at 10 m (black line) being lower than measurements of the Cup Anemometer at 4.0 m (green line) around 15:30 UTC. 34 10 m Wind Monitor 4.0 m Cup Anemometer 2.0 m Cup Anemometer Figure 2.5: Part of wind speed 1.0 m Cup Anemometer time series on April 05, 2004. 5 —l Cup Anemometers at 1.0 m (pur T3 Deficiencies such as those shown were eliminated during Quality Control of the data. 2.3.2 Temperature/Relative Humidity sensors Along with Cu/Co thermocouples, a Campbell Scientific HMP45C212 Temperature and Relative Humidity Probe was used to provide air temperature and relative humidity measurements of the surface layer. The accuracy of Vaisala HMP-series humidity sensors used in the probe is listed as ±3% in the RH 90 — 100% range (which was the case for most of the experiment's duration). The accuracy of the temperature sensor varies from ±3% to ±5% in the range of temperatures from 0 °C to -40 °C, according to specifications. Six and twelve plate radiation shields 35 were utilized to house the thermocouples and HMP45C, respectively (Figure 2.6). Note that there were fewer problems with snow packing between the plates during January and February then later in the project. (a) Thermocouple (b) Temperature/RH sensor Figure 2.6: Temperature and humidity measuring sensors in radiation shields As has been discussed above, the abrupt change of data logger temperature affects thermocouple measurements (see Figure 2 7 for an example) and conse quently the data recovery rate. The recovery for the thermocouple measurements is slightly lower than 95% (caused by opening the data logger enclosure) while for the HMP45C212 Temperature and Relative Humidity Probe it is almost 100%. 2.3.3 Snow Depth Ranger Stationed at Tower 1 a Campbell Scientific SR50 Ultrasonic Distance Ranger sup plied continuous measurements of snow depth with an accuracy of ± 1 cm. Al- 36 T 18 20 Time (UTC) February 20, 2004 Figure 2.7: Part of temperature time series registered by thermocouples on February 20, 2004. Measurements are affected by data logger enclosure opening around 18:15 UTC though falling snow affected its ability to provide correct distance, the SR50 was able to record the translation of snow dunes during blowing/drifting snow events (see e.g. Figure 2.8). Figure 2.9 shows the SR50 as well as temperature sensors and the data logger enclosure. 2.3.4 Visibility Sensors Meteorological Optical Range (MOR) was calculated from the voltage output of the Sentry™ Visibility Sensor (Figure 2.10). The sensor emits a narrow beam of 880 37 Figure 2.8: Record of dunes passing under the SR50 on April 08, 2004. It 20 £ 18 — took about an hour for an approxi ±= 16 D 14 — . mately 2 m x 3 m x 0.02 m dune 5 A7V c 12 — to pass. 10 m wind speed was 7 - 10 I ' I ' I 1 19 20 21 22 8 m s-1, wind direction was approxi Time (UTC) April 8, 2004 mately 100 degrees true. nm wavelength light, some of which is forward scattered into a north facing, narrow admittance angle detector. The output depends on the amount of light forward scattered from any aerosol. The manufacturer assures an accuracy of ± 10 %. The range of MOR is from 20 m to 16 km. Calibration was performed before the installation with a factory-supplied toolkit. Signals from the visibility sensors were initially installed in the CR23X differential voltage input channels 10 and 11 but channel 10 seemed to desplay significant noise characteristics so we switched to 11 and 12. We also later discovered (with a multimeter) a lot of noise on the shields to the Sentry™ Visibility Sensors. The Sentry manual says "connect the cable shield to either signal ground or earth ground at the data acquisition system". The first visibility sensor was installed on 23 January, following these instructions and it was connected to the signal ground, physically the simpler option with the cable 38 Figure 2.9: Ultrasonic Distance Figure 2.10: Visibility sensor at Ranger 3.3 m post supplied and the data logger wiring panel. Next day we found that we had noise or overflows on at least four of our channels, including battery voltage and panel temperature. The overflow was eventually traced to significant noise (100 mV) in the shields to both visibility sensors which were affecting the analogue ground, and hence bridge and single ended voltage measurements. We added ground connections to the posts holding the two visibility sensors, and separately attached the signal cable shields to the ground stake in the ice at Tower 2. Although this is also 39 connected to the data logger ground it seemed to resolve the problem and visibility sensor signals were reattached at about 2000 UTC on 28 January. 2.3.5 FlowCapt anemo-driftometer Snow mass transport and wind speed measurements by the AlpuG FlowCapt sensor are based on the ability to interpret acoustic pressure induced by saltating snow particles or wind on a pipe that houses transducers. The Fourier Transform of the signal enables separation of energy spectra into parts that afterwards can be related to the impact of particles and of air flow. A one section sensor was installed at an initial height of 0.1 - 1.1 m (Figure 2.11). By 12 February the lowest arm was just touching the snow. On 03 March it was partially buried under a drift after a two day blizzard event (~ 80 cm still visible). On 07 March the sensor was raised and remounted 0 to 1 m (above a 30 cm deep trench). The recovery rate of the FlowCapt measurements still has not been established. In some cases (as for example on Figure 2.12) mass flux provided by the FlowCapt is in a good agreement with the data from other sensors but this is not always the case. 2.3.6 ZEBRA Field Mill An Electric Field Meter of Mission Instruments was used to measure the electric field [V m-1] in the atmosphere during blowing snow events. The meter was in- 40 Figure 2.11: FlowCapt at the bottom of Tower 2, Particle Counter post (left) and Electric Field Meter (far right). stalled near meteorological towers at a height of 50 cm and started recording on February 20 (Figure 2.13). It was disconnected on May 7. During this interval there was sufficient blowing snow (8 major storm events) to measure an electric field output during blowing snow for 34% of the time. Difficulties with heating the recording unit meant that approximately 2/3 of the data have an estimated accuracy of +/- 25%, and 1/3 have an accuracy of +/- 5%. The meter was also used to measure the change in electric field with height from 0 to 2 m four times 41 16 12 ,'V •<— 3.3 m sensor ' i! , V./M a: 8 —I ' 1/ IN o UN t & 1.5 m sensor U*! i—I—i—I—i—I—i—I—r i l i l i I i 8 10 12 14 16 18 20 22 24 40 —i r— 30 0.8 m Particle Counter 03 FlowCapt Mass Flux 30 — O 0) c — 20 ° 20 — 10 3 •H 10 (0 Q. 10 12 14 24 Time (UTC) April 12, 2004 Figure 2.12: Time series of measurements by the Visibility Sensors (top panel) and the FlowCapt anemo-driftometer (lower panel). Particle counts per second at 0.08 m height are also shown. between April 5 and April 9. Analysis of data from the Electric Field Meter was done by Gordon and Taylor (2009a). 42 (a) ZEBRA Field Mill (b) Camera Figure 2 13. Electric Field Meter and Video Camera 2.3.7 Digital Imaging A computer controlled digital camera was used to record images of blowing snow These images were analyzed to provide the velocity, size, and number of particles under varying conditions. The camera is model LU100 from the Lumenera Corpo ration The whole camera system was put together by Precision Camera Inc. (in Toronto). The camera recorded images at the surface using a black background with an image size of 10 cm height by 12 cm width. The camera was used between March 9 and April 12 to record approximately 30,000 images of blowing snow. The 43 recovery rate of this data is as yet unknown due to the difficulty in processing and interpreting out-of-focus particles between the camera and the image plane. The novel method of sizing blown particles employing video camera was combined with particle number density measurements obtained with photo-electric particle counters in Gordon et al. (2009). 2.3.8 Particle Counters Starting from a design of Brown and Pomeroy (1989), Blowing Snow Particle De tectors were redesigned and assembled at York University, Toronto. Detection of particles is based on the drop in voltage generated by a photodiode illuminated by an infrared beam when a particle gets into the path of the light. The distance that light travels in the sampled volume of air is the same for all units (5 in total) and equals 2 cm. A cover on the photodiode has a 0.15 mm diameter hole that allows part of the light beam to reach the active surface of the diode. Two counters installed at the particle post near Tower 2 are shown on Figure 2.14. Note the ver tical orientation of the light beam. The light source is below and the photodiode is above. This orientation was chosen to reduce risk of clogging of the hole at the receiving end by snow particles and to give output independent of horizontal wind direction. In addition, chances of the complete blocking of 0.15 mm diameter sensor hole by snow flake are greater compared to the similar chances for the relatively 44 larger emitting surface of the LED It was speculated that partially blocked LED can still produces sufficient EM radiation for the device to function Figure 2 14 Particle Counters and mobile snow trap in drifting snow The Particle Counters' functionality was checked prior to installation and once during the field stage with the help of an electric motor and a thm wire attached to it All units were capable of recording light beam intersection by the thin wires up to 200 times per second - the maximum that the motor could achieve More comprehensive testing was performed after the field phase, in spring and summer of 2004 Because only 6 Pulse Channels were available on two data loggers (2 on the CR10X and 4 on the CR23X) and two were used by wind monitors, only 4 Particle Counters were deployed at the beginning of the field stage - at 0 2, 0 5, 10 and 2 0m above the snow surface At that time the average snow thickness at the 45 meteorological tower sites was 4 cm. A fifth counter was added at 0.1 m and we disconnected the wind monitor at Tower 2. With snow accumulation during the winter, distance from the counters to the surface changed and the lower level counter eventually got buried under the snow. In such cases the lowest counter was raised. Figure 2.15 depicts the height history for the four counters on the stand-off post near Tower 2. Snow accumulation near the location of the 0.5 m nominal level 2 •SLT -e- o -o 1.5 1 /&- - M*M\- - -A-- --&r--A Q- -- -ri —- o Channel3 Unit 1 •2 0.6 * * * Channel 4 Unit 2 E A- -- -A — —A Channel 2. Unit 3 o J= * * * Channel 1 Unit 5 S 04 + * a- Channel!. Unit 2, 5 c *- W ->&- b 0.2 snow , T 20 40 60 80 100 120 Day of Year, 2004 Figure 2.15: Particle Counters of Tower 2 relative position above snow cover during the experiment. counter (stand-off post near Tower 1) was not as significant and the counter was not moved. 46 2.3.9 Snow Depth, Density and Salinity In addition to the sonic ranger measurements we made snow depth measurements around the area of the meteorological posts using a 1 cm diameter wooden pole. Typically about 15 spots were probed in varying locations. A snow depth transect was done between April 25 - 27 (DOY 116 - 118), 2004 and is representative for the April 5 - May 3 (DOY 96 - 124) low wind period. Surface level snow samples were taken with cutters (see Figure 2.16) constructed following John Iacozza's (University of Manitoba) design which in turn is a varia tion of the Taylor - LaChapelle cutter (see in Conger and McClung, 2009). Sample Figure 2.16: 66.0 cm3 volume snow sampler. volume, 6.0 x 5.5 x 2.0 cm = 66.0 cm3. Snow samples were stored in plas tic bags. With one technique, snow was allowed to melt and the water volume measured and assumed to have density of 103 kg m-3. Snow density = [Water Vol(ml)/N/66.0]xl03 kg m"3, where N is number of scoops that constitute the 47 sample. Another method was to simply weigh the snow contained in the bag and subtract the weight of the bag. A Precision Toploading Balance model P-403 from Denver Instruments was used for weighing. Its capacity is 400 g, readability and repeatability are 0.001 g. During the first three months of the experiment mainly the density of the sur face snow was analyzed. Starting from April more than 30 snow pits were im plemented with density and salinity/conductivity measured every 2 cm within the depth of snow cover. Salinity was analyzed with a portable conductivity meter Cond 330i from Wissenschaft-lich-Technische WerkstAatten GmbH (WTW). The range of conductivity measurements with this device is listed from 1 /u,S to 2 S with an accuracy <5 % of measured value ±1 at temperature -5 ... +80 °C where S stands for Siemens - the unit of conductivity. This results in salinity range of 0.0 ... 42.0 psu (practical salinity units) and an accuracy of ±0.1 psu (for 5 ... 25 °C) and ±0.2 psu (for 25 ... 30 °C). The temperature of the sample is determined with an accuracy of < 0.5 K ±1 digit. 25 °C was set as the reference temperature for the temperature compensation during conductivity measurements. Total Dissolved Solids and units of Practical Salinity Scale were calculated from measured conduc tivity according to Fofonoff and Millard (1983). There were two distinct layers in the snow cover. One apparently appeared at the time when the ice flow formed or shortly after that. Salinity of this layer was around 4 psu in the top part and 48 increased to about 14 psu towards the sea ice. The second layer was on top of the first one and accumulated after the deployment of the ice camp. Its salinity was around zero psu although during blowing snow events of the last month of obser vation the wind-transported snow had some fraction of salt. The salinity of snow captured in snow traps was from 0 to 2 psu. 2.3.10 Snow Traps In the April - May period a snow trap stand was assembled and installed 12 m north of Tower 1. It allowed individual traps (10 x 10 cm catchment area, 50 cm trap extent) to be deployed at 0.04 m through 1.14 m in height from the snow surface, up to 5 levels at a time. In addition, four mobile traps were made to catch snow at levels from 0 to 0.25 m height. Their catchment areas were 10.1 x 5.2 cm, 10.3 x 5.2 cm and 9.1 x 4.9 cm. Mobile traps and the trap stand are shown on Figure 2.17. Another type of mobile trap which is shown in Figure 2.14 did not require a stand so that it was easy to move quickly to where it was needed. Its catchment area was 8.4 x 7.9 cm. Measurements by snow traps were made during four blowing snow events. Mobile traps were especially helpful if only drifting snow (in close proximity to the surface) was present. Total Dissolved Solids / Salinity of blowing snow with respect to height data obtained in the course of the experiment constitutes a 49 mk^ ***~ JZ jtji ^ ** ~. ^si^ (a) Trap stand (b) Mobile traps Figure 2 17 Snow traps valuable addition to scientific knowledge of the Arctic Biological matter observed in snow catchments has also prompted biologists to have a closer look at the aeolian transport contribution to the bio-mass balance of the region 50 3 Snow and its transport in CASES04 3.1 Introduction The snow cover on sea ice is an important physical variable which impacts energy, physical and chemical processes operating across the ocean-sea ice-atmosphere in terface. Blowing/drifting snow events add complexity to the dynamics of fluxes: they change the magnitude of the sublimation rate and therefore the amount and transfer of latent heat; they redistribute snow which causes spatial variability of snow thickness which in turn alters heat and mass fluxes through the ice to the at mospheric boundary. Sublimation of blowing snow is also a factor in the mass/water budget of snow-covered regions. Treatment of snow cover evolution in the land surface schemes of weather prediction and climate models can lead to a better un derstanding of the impact of relevant physical processes such as the nature of snow deposition and aeolian transport. Iacozza and Barber (2010) provide a description of the evolution of snow depth over sea ice for the project site based on extensive snow cover surveys implemented 51 by the University of Manitoba group. In this chapter we present results of snow cover density, salinity and depth observations made by York University researchers in the vicinity of the micrometeorological site. The initial freezing of the CCGS "Amundsen" into the ice did not last long due to the severe storm that caused the break-up of the surrounding ice and forced the ship to find a new spot for wintering over. Some flooding or sea spray drenching of the snow cover may have occurred during the storm. At the time of CASES04 camp deployment the ice floe was covered by hard snow 3-12 cm thick. Snow ac cumulated in the course of the project due to several snowfalls and drifting/blowing snow events. Figure 3.1 presents an evolution of the snow depth as measured by the Sonic Ranger. Since the increase of snow depth with time is apparent it should be interpreted with caution. Snow depth variation at a certain spot is not only due to accumulation during snow fall but also due to snow deposition/removing during blowing snow events and sublimation. Although overall snow depth increased, at spots it varied, following the dynamics of snow ripples and/or dune movement. The initial layer was never eroded, bedforms moved on top of this layer or on top of newly accumulated and hardened wind slab. Sharp spikes on the graph are related to snow fall, blowing snow or bedforms passing under the cone of the SR50 sound beam. The particle flux depicted on the top panel of the figure is an indicator of snow drift and blowing snow. Most blowing events are associated with spikes of the 52 20 30 40 50 60 70 80 90 100 110 120 130 28 i I i ) I E 24 I' i5 ! \ o ?' s 8" 20 Q ;« o "Ts«f.f*v;H«\ V ! 16 2 h £ Ml I 4P! f Figure 3.1: Time series of particle flux at 0.5 m height (top panel) and average snow depth in the cone of the SR50 sound beam (bottom panel). snow depth graph. That it is not so for the early stages of observations is probably because of insufficient supply of snow to form ripples. In late April (day of year 116 - 118) snow depth measurements with a step of 1 m between sampling points were done along a 130 m transect in the vicinity of 53 the meteorological towers. Snow thickness was in the range of 3 to 36 cm with a median value 17 cm and standard deviation 8 cm. The multi-modal shape of empirical snow depth distribution is similar to what was reported by Iacozza and Barber (2010), but their survey included a much bigger area. As they suggested, the form of the distribution reflects the precipitation history and redistribution of snow by wind. 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 Snow Depth (cm) Figure 3.2: Histogram of snow depth measured on April 25 - 27 in the vicinity of the meteorological site. 3.2 Snow density The mass of snow per unit volume is its density. In this work we consider the mass of snow to consist of the mass of ice and the mass of liquid water in some known sampled volume The snow density defines the mass of water per unit volume and 54 can be transformed into liquid water equivalent (height of water per unit area if all snow is melted). Note that snow cover during the period of observation was characterized as dry snow (according to classification of Colbeck et al., 1990). A special interest of the present work pertains to blowing snow. For an indi vidual snow particle, being lifted from the bed by wind means that bonds with surrounding particles are broken. Snow density by itself does not characterize the strength of bonding and resistance to wind. Snow hardness or snow strength would be better parameters to correlate with the onset of blowing snow and particle num ber flux during drifting and blowing snow events. Unfortunately we did not have a proper sensor to measure these parameters. At first glance, the more denser is the snow, the tighter individual grains are packed, and stronger bonding between them expected. But this is not always true, in some cases or at some stages of snow cover evolution relatively dense snow can exist with very few bridges between the individual particles. This can happen, for example, to drifting snow when ice crystals are constantly shattered during collisions and there is virtually no time to form new bonds. Both Shapiro et al. (1997) and Colbeck (1997) in their respective reviews emphasize that it is the number of bonds between snow grains or specific grain contact surface that determines the snow strength and not its density. The term hoarfrost is applied to the ice crystals that grow on a cooled substrate due to freezing of water vapour. This vapour is usually extracted from the air 55 but in some cases it can come from the moisture that is part of the soil, plant, etc. In the presence of light wind hoarfrost that forms on the lee-side of a non- horizontal substrate can reach several centimeters elongated in the wind direction. In CASES04 approximately 5 cm long feathery crystals of hoarfrost on vertical structures were observed after one foggy night. Depth hoar is a designation for crystals within the snow pack usually near the bottom of the snow cover that underwent morphosis and grew to relatively large size because of water vapour flux from the air in pores and from the outside of the layer. 3.2.1 Density of surface snow moved by wind Snow fall crystals in the Arctic are notably smaller compared to those of mid latitudes and they rarely coalesce in part because of relatively small amount of precipitation in individual events but also because they are less cohesive in colder conditions. In CASES04 only on one occasion the daily precipitation totaled 4.0 mm and on two other occasions it reached 2.0 mm. An average value was around 0.5 mm for all registered precipitation events. When deposited crystals are picked up by wind it takes little time to break them into smaller pieces of the size that is characteristic of blowing snow. Because snow fall is often accompanied by wind, the majority of surface snow cover can be identified as formed by wind, so called wind crust. Wind crust can also be formed without precipitation as a result of ice crystals 56 of the surface layer being reworked by the wind in drifting/blowing snow. When the wind subsides the morphological changes in snow cover commence. In order to understand what density of snow can be expected in wind slab at the beginning of calm periods we took 39 samples of snow which was either in motion at the time of sampling (surface of moving dunes, for example) or was freshly deposited in certain places while overall snow drift was still underway. Figure 3.3 is a histogram of surface snow density measured during blowing/drifting snow. The histogram should not be interpreted as an empirical probability func tion because sampling was not random and did not cover all places where snow deposition was possible. On the other hand, it does provide an indication of the magnitude and the range of snow densities for this special case. For the snow densi ties the snow material has come from recent precipitation and wind speed was just above the threshold for which drifting is possible. Snow density for such cases was around 200 - 250 kg m~3. In the case of strong winds with significant duration, the observed density of surface snow still in motion reached 450 kg m^3. By comparison, analogous data obtained at latitudes 58.4° N and 43.8° N, Churchill, Manitoba and Toronto, Ontario, respectively, is presented in the bot tom panel of the figure. At these locations even lower densities were observed probably due to the bigger sizes of snow flakes of lower latitude precipitation that form initial material drifted by wind. The sampled density does not reach as high 57 04 —| g 03 cr _ Franklin Bay, 2004 J= 02 •: *'', i • ..» .'"i" 04 —i Churchill, 2005 Toronto, 2006 O £ °3- 3 o - > N ) - Relativ e fre < ,1, 1 •* 1 1 1 1 1 ' 1 ' 1 ' 1 0 •M50 l 100 150 200 250 300 350 400 450 500 Snow density (kg m3) Figure 3.3: Histogram of snow density sampled from moving or deposited surface snow during blowing events. 39 samples from CASES04 constitutes data for the graph at the top panel. 47 samples behind the histogram at the bottom panel were taken in Churchill, Manitoba or in Toronto, Ontario. values as in the Arctic. An explanation can be sought for in the lower wind speed of drifting events when samples were taken. Air temperature may be a factor but we don't have enough data to investigate temperature influence on snow density 58 3.2.2 Surface snow density In the vicinity of the micrometeorological site, surface snow density was probed throughout the CASES04 period. We present here an analysis of the surface density derived from samples of the top 2 cm of snow cover taken when no drift was present and the surface was settled. Values as low as 50 kg m~3 pertain to the fresh fallen snow. The wind crust layer in some cases exhibits densities in excess of 450 kg m~3. Without hoarfrost or precipitation, the wind crust has density greater than 200 kg m-3. A histogram of density is depicted on the top panel of Figure 3.4. The bi-modal form of the histogram reflects, on the one hand, a surface formed by precipita tion and deposition of moisture in the form of surface hoarfrost and, on the other hand, hardening of the snow cover by wind. In general, the large value part of the histogram of immobile surface (top panel of Figure 3.4) is consistent with the histogram of snow surface in motion (Figure 3.3). They exhibit almost the same range and peak around 300 - 350 kg m~3. Hoarfrost growth on the snow surface has occurred on many windless periods. It was very moderate at the beginning of the campaign under conditions of polar night. As solar illumination increased with time and a diurnal cycle became promi nent the ice-fog at night/morning and hoarfrost become a regular feature of calm 59 o C 02 CD ~r^ i r 100 200 300 400 500 Snow Density (kg m"3) ^_ Hoarfrost Fallen snow, faten snow Surface layer established - no wind -> & |,ght winds during snow drift events 100 200 300 400 Snow Density (kg m"3) Figure 3.4: Histogram of top 2 cm of immobile surface snow density (161 samples, top panel) and time history of 105 cases of density sampling made in the second half of on-ice stage of the project (bottom panel). Snowflake symbol denotes samples of precipitated snow, triangle symbol denotes samples of surface hoarfrost, open circle symbols stands for regular snow surface sampling. 60 periods. Figure 3.5 presents some common types of hoarfrost crystals encountered in CASES04. Note that we do not attempt to give a classification or present all possible types The names of crystal types on the figure are given ad hoc and may not be the accepted scientific terms We distinguish the surface snow hoarfrost from the so called "frost flowers" (Rankin et al , 2002) that grow on thin slush layer on top of open ice. (a) Plate-like (Scales, Leaves) formed (b) Needle-like (Grass, Needles) formed on near on vertical surface (igloo wall m this horizontal snow cover surface case) Figure 3.5: Surface hoar crystals (hoarfrost). Photos by S. Savelyev. A prolonged period of very light winds happened between April 15 and April 27 (days of year 106 to 118). During that time polynyas in the Beaufort Sea and near Banks Island opened It enhanced the flux of moisture into the atmosphere The fast growth of hoarfrost was visible on all exposed surfaces. The group of triangle symbols in the middle part of the bottom panel of Figure 3.4 represents surface snow 61 (including hoarfrost) density measured at this period. At the beginning (DOY 106) measurements of density exhibited a magnitude of 150 - 200 kg m~3 and slightly increased to 200 - 250 kg m~3 at the end of two weeks. It may be that after initial expansion growth a space between newly formed crystals continues to be filled with new ice which led to the increase in density. Snow fall brings an additional mass of snow as well but does not necessarily contribute to the increase of density. A linear regression fit to the data has a slope of 4.5 kg m~3 per day with coefficient of determination R2 = 0.54 (two-tailed p-value = 0.00002). It is a rather large rate of density increase. In order to calculate daily increase of mass of snow one can multiply the volume of the layer where accumulation of the hoarfrost was sampled by the density increase rate. Then for 1 m2 of the surface layer daily increase of mass is 4.5kg m~3 x 0.02m = 0.09kgm~2. One can compare this rate value with measurements of hoarfrost mass collected on several (unfortunately rare) occasions. Those measurements are summarized in Table 3.1. Save for the sampling of hoarfrost formed on vertical substrate, the measurements were taken from the overnight growth at the horizontal surface of a styrofoam board that was cleaned the evening before. The procedure consisted of scraping the hoarfrost from a 20 x 20 cm area in the middle of the board and weighing the collected snow. Growth depends not only on the location of the surface but on the type of surface itself. By no means can we present a systematic study of the subject, but we feel that 62 obtaining at least some numbers would provide us with some reference points. We do not want to carry out comparison of the rate of mass increase in these two cases because of the lack of the systematic research but would like to note that the offset of ice crystal growing on clean styrofoam board is probably hindered compared to the continuation of the growth of existing crystals. On the other hand, samples of the hoarfrost from the snow cover surface may include the snow grains that belongs to layer below the hoarfrost due to fixed dimensions of the sampler. Table 3.1: Measurements of overnight hoarfrost growth made on several occasions during CASES04 Date of DOY Mass Notes sampling kg m-2 April 19 110 0.17 styrofoam, horizontal surface April 27 118 0.05 styrofoam, horizontal surface May 1 122 0.06 trap's mesh, horizontal surface May 1 122 0.41 trap's mesh, vertical surface May 2 123 0.17 styrofoam, horizontal surface After a moderate blowing event during April 27 - 28 (days of year 118 - 119) that removed surface hoarfrost, the next calm period started with new hoarfrost 63 of density comparable to what was observed at the beginning of the previous calm period. 3.2.3 Density distribution within snow pack An area of 5 m x 5 m extent near meteorological Tower 1 was dedicated to the snow density profile measurements. Snow depth at this location was 20 - 24 cm which is where the second mode of the snow depth distribution lies (see Figure 3.2). Each time a snowpit was filled with snow (at the end of the procedure), a new pit was allocated some 0.5 to 1 m distance from the completed one. Two layers or strata could be distinguished : the snow cover that formed during the ice flow formation or shortly after it and accumulated snow on top of the first layer. The storm that caused the break-up of the already consolidated ice field was reported in the late December of 2003. It is possible that intensive sea spray during the storm wetted the snow and increased its salinity. The first layer was the only layer of the snow cover present when the ice camp was established. Figure 3.6 presents 14 profiles made between April 15 and May 6 of 2004. The depth of each of two layers varied by 1 - 2 cm from occasion to occasion so the average value for each layer was calculated and the actual interval for the particular snowpit was cast into the averaged one in such a manner that the top sample for the layer appeared to be at the layer surface. In reality because of the 2 cm vertical 64 span of the cutting tool the top sample should be attributed to the depth of 1 cm below the surface. The surface of the top layer has a density mainly due to 0 —| ^N iV -3BKB- --. 22 - - 2 — 20 4 — 18 o o 0 6 — 16 ST V- ^ + o 0( CD 8 — ffr 14 —* © 3 ^5 10 — 12 in 3 O "£P 12 — 10 c c 0) 14 — 8 -2 o CD gSr* 16 — 3_ - 18 — <*i. «... fpw 20 — %* - „ •3g#»** - 90 £.£. I I I I I I 200 500 Snow Density (kg m~3) Figure 3.6- Snow density profiles taken in the vicinity of met towers. Dashed lines indicate the surface of two distinct layers. Different symbols are used for each of 14 profiles. snowfall and hoarfrost growth. Wind crust was not present continuously although some subsurface samples did indicate the layer apparently formed by the work of wind, some with density in excess of 400 kg m~3. The relatively large range of density (more than 350 kg m~3) in the top strata reflects several sequences of snow deposition, blowing, drifting, dune movement during the time from the setup of the 65 ice camp. Overall this layer can be characterized by the average snow density value of 220 kg m~3. There is a sharp increase (almost by 200 kg m~3) of density from the top layer to the bottom one. The intermediate surface was hard to penetrate to the extent that the cutting tool was in danger of being bent. Immediately below it was a softer layer but with somewhat larger density. The excess of density for the sub-layer was not larger than the error introduced by spatial variability but its trend was consistent. The upper part of the bottom layer is approximately homogeneous density-wise. The top 5-6 cm of this bottom layer has a density of 400 - 450 kg m~3 which is twice the density of the upper layer. In the next 8-10 cm, the snow density decreases almost linearly to the value of 250 - 300 kg m~3. The last 2-4 cm were occupied by a basal layer. Ice crystals in the basal layer are also called the depth hoar but they are bigger than in the middle pack depth hoar and have a distinct structure. Even right above the ice the snow was dry. There were no icy layers encountered within the snow pack. 3.2.4 Pockets of faceted crystals within snow pack Starting from April 9 we became aware of pockets of loose, cohesionless crystals approximately 1 mm in size in the top layer within several centimeters of the snow surface. Snow grains in this snow had a distinct faceted crystalline form with sharp edges and no bonds between crystals. We identified them as belonging to class 66 4fa according to the classification of Colbeck et al. (1990). A similar type of near- surface faceted crystals is reported in many avalanche related research reports, see e.g. Birkeland et al. (1998). In that paper, the authors estimated that such layers were found in almost 60 % of analyzed avalanches. In the Arctic environment the low cohesion layers can provide material for "sand blasting" if they become exposed during drifting/blowing events. In snow drift modelling, the flux of particles from the bed into the flow is thought to be maintained by dislodging of immobile bed grains by impinging of particles already airborne. The response to this impinging depends on the cohesion between bed particles. Now if at some stage of the drift event the layer with loose material is exposed due to eroding of the covering snow then this could lead to a sudden increase of number of saltating and/or suspended particles. It is thought that faceted crystals are formed during rapid growth in the presence of high temperature and water vapour gradients. The confinement of through- pack probing of snow to the relative short period during the late stage of of the ice camp limits our ability to draw conclusions on the extent of faceted crystals layers or processes behind their formation. Here we present a summary of limited information that we collected about these near-surface faceted crystals. The density of such layers (shown in Figure 3.7) is superimposed on the surface snow density measurements. In almost all cases the loose grains were found 2-4 cm below 67 the surface crust and were identified as a snow deposited by recent moderate drift. By moderate drift we call an event with wind speed only slightly above the drift threshold when mostly saltation took place with limited amount of blowing. The extent of the layer was limited by the snow bedform size and it could be designated as a pocket of snow on the side of the old dune or ripple covered by new drift. In one case a new drift was relatively deep, 40 cm of total snow depth at the spot and loose snow was encountered at a distance of 15 - 18 cm from the snow surface. Layer thickness was from 2 to 6 cm. 400 i E 300 — <5 200 Q S w-*** o $ ^ 03 100-1 I 90 100 110 120 130 Day of Year, 2004 Figure 3.7: Time history of the near-surface faceted crystals density probing. The background is the surface layer density shown on Figure 3.4. Solid line represents linear regression fit, coefficient of determination R2 = 0.3. Snow density within layers varied from 140 to 300 kg m 3. A linear regression 68 fit suggests a densification rate of 2.5 kg m~3 per day. Two-tailed p-value for the correlation coefficient equals 0.00072. This means that a null-hypothesis of densification rate being zero is rejected at a 0.001 significance level. 3.3 Salinity of the snow cover The salinity of snow was measured concurrent with snow density probing whether it was a snow pit or the random sampling at the surface. Profiles of salinity shown on Figure 3.8 are related to the density profiles of Figure 3.6. The bulk of the top layer has almost zero salinity and it would be more appropri ate to characterize the Total Dissolved Content rather than Salinity but we choose to show salinity for reasons of comparison with the bottom layer. The surface of the snow pack exhibits the presence of sea salt in snow which we attributed to sea spray from the nearby polynya in the Amundsen Gulf. The bottom of the two layers consists of the salinity homogeneous part at its top and the span of snow with the gradient in salinity near the bottom. Both parts are about 7 cm thick. In the basal layer the salinity is greater then 8 psu and in some cases reaches 15 psu. It decreases to 4 - 5 psu and remains approximately constant towards the border with the top layer of the snow pack. If the basal layer is left out the salinity gradient is estimated to be 2.5 psu per cm of depth. For comparison, Barber et al. (1995) reported the salinity 15 - 20 ppt in the basal layer under 30 cm 69 22 20 18 16 14 12 10 8 6 of a * 4 >5- 20 2 i&SlX; 22 0 AY i l i i l i l i l i 2 4 6 8 10 12 14 16 Salinity (psu) Figure 3.8: Salinity of the snow pack measured in the vicinity of met towers. Dashed lines indicate the surface of two distinct layers. Different symbols are used for each of 13 profiles. Salinity scale is broken between 1.1 and 1.2 to allow for more detailed representation of the surface layer. Note the non-zero salinity at the top of the snow pack. thick snow in winter in the middle of the Arctic Archipelago. This was also for the land-fast first year ice. As was already mentioned the visual observations reveal no water in the basal layer at the time when snow pits were implemented but we don't know if flooding occurred around the time when ice was formed. There were no research activities aimed at the possible cause of the observed salinity distributions. 70 So we cannot pinpoint whether it was flooding, percolation, capillarity suction or a combination of reasons. 3.4 Statistics of the blowing snow events To diagnose whether or not blowing/drifting events occurred a number of indicators were used: snow fall records by the meteorological observer at the ship station, particle counts (number densities) from counters installed at various heights above the snow surface, visibility at 1.5 and 3.3 m levels, and the researcher's field notes. Keeping in mind the definition of blowing snow used by the Meteorological Service of Canada, Savelyev et al. (2006) identified the threshold value of particle number density at 2 m height associated with 9.6 km Meteorological Optical Range (MOR) reported by the 1.5 m level visibility sensor. According to that criterion blowing snow occurred approximately 27% of the time. This particular choice of indicator (at observers eye level) results in not taking into account the occurrence of drift or low intensity blowing snow events. For this study we looked at the number densities at all levels and in particular at the lowest available level. The height of the lowest particle counter varied during the course of the experiment in part due to snow accumulation. Fortunately, the unit at 0.5 m level was functional from start to end and its height above the snow did not change significantly. Arguably, the 0.5 m level counter is above the saltation height and may not indicate the lightest snow drift. 71 From field notes and readings of even lower counters we deduced that in most cases this counter did register the increase in snow particle densities even for the pure saltation mode. For reasons just outlined, the output from the 0.5 m level counter was used in an automated procedure to discriminate blowing from clear periods, i.e. periods with no blowing snow. The threshold value for the number density at the 0.5 m level was determined to be 0.001 particles per cm3. The analysis of data shows that blowing and/or drifting conditions existed for approximately 40 % of the experiment's duration. Apart from the decision as to whether or not it was blowing at the time when measurements were taken, one has to decide if this particular state is a continuation or a change of the previously existing conditions. There can be lulls during blowing snow event or short periods of blowing in the middle of overall calm situation. The overall number of blowing snow events will depend on the accepted definition of the duration of interruptions to the prevailing conditions. For example, in Berg (1986), the blowing snow event was called as such if it lasted more than 2 hours and was separated from another event by no less than 2 hours. We calculated the number of events for different durations of interruptions of the current state. The accepted duration of clear amidst blowing periods does not have to be the same as the accepted duration of blowing amidst clear periods but the results presented in the Table 3.2 are calculated assuming the same limiting duration for both types of 72 interruptions. The number of events and consequently the mean duration of blowing Table 3.2: Dependance of the number of blowing snow events on the accepted duration of clear amidst blowing and blowing amidst clear periods. Duration Number Mean Median Number Mean Median of of duration duration of duration duration interruption Blowing Blowing Blowing Clear Clear Clear (minutes) events (hours) (hours) events (hours) (hours) 30 54 20.0 7.0 54 30.1 8.2 60 32 33.9 30.7 32 50.7 31.7 90 29 37.2 35.8 29 56.2 33.6 120 27 40.0 36.3 27 60.3 39.0 snow events is sensitive to the value of accepted duration of the interruptions of the current state. If the time period of 30 minutes when blowing is detected is enough to consider it an event and interruptions of blowing less than 30 minutes do not change the verdict on the conditions then we counted 54 blowing snow events with mean duration of 20.0 hours. If restrictions similar to those in Berg (1986) are imposed the number of events is reduced to 27 with mean duration of 40.0 hours. Compare this mean duration to the value of 35.6 hours cited in Berg (1986) which was registered in a two year experiment in the mountains near Colorado, USA. 73 One can also conclude that the average blowing condition duration will depend on the frequency of observations and the averaging period. Variability on a time scale less than the averaging period will not be resolved. The result of analysis of hourly data will be different compared to once in 3 hours observations, for example. The effect should be taken into account while comparing model predictions with observations as for example in paper of Lenaerts et al. (2010). To be consistent with hourly observations at stations of the Meteorological Service of Canada we consider the blowing event if our 5 minute averaged data indicated drifting/blowing in consecutive observations for at least 1 hour and if the periods of blowing are separated by at least 1 hour of no drift. With the above criteria in place, the longest blowing/drifting snow event observed lasted almost 4 days while the longest no drift period amounted to 12.5 days. 3.5 Threshold wind speed observations and prediction Each drifting/blowing snow event can be associated with the value of wind speed observed at the very beginning of the event. The choice of whether to take the value of wind speed for the last non-blowing observation or for the first blowing one can result in significantly different threshold velocities. Thus in our project the extreme case of discrepancy is for the DOY 36 as shown in the excerpt of observations below. The 5 minute discretisation introduces more than 1.6 m s_1 difference into the value 74 Table 3.3: Two consecutive records from data file of observations, the first one is taken in no drift conditions while the second one is for the start of the blowing snow event. Day of Time Particle Number MOR at Wind Speed Year HHMM counts density 1.5m (km) at 10m (m s_1) 36 1300 0.0 0.0 16.08 4.60 36 1305 0.077 0.0059 16.08 6.27 of the threshold velocity. In this work we took the 10 m wind speed of the first record deemed to be in the blowing event as the threshold value. Prediction of the onset of blowing snow is of great practical interest. To our best knowledge the only equation that has been used for prognosis of the threshold velocity is the one of Li and Pomeroy (1997). It is a regression formula that uses air temperature as a predictor. It makes a distinction for snow that was exposed to positive temperatures and for snow that didn't undergo thawing. In this work we make an attempt to suggest another algorithm for prediction. The algorithm is based on observations of threshold velocity in CASES04 and as such it is rele vant for the geographical region of the experiment and for dry snow with ambient temperature below zero. The approach can be used to derive similar algorithms for other geographical regions. 75 The factors we assume to influence the onset of drifting are snow surface resis tance to the drag imposed by the wind and the availability of loose material that can facilitate extraction of snow grains from the bed. Snow is deposited to what eventually becomes a snow cover in the form of precipitation: snow fall or hoarfrost deposition. Once on the surface, ice crystals grow bonds between them, and un dergo metamorphosis. The bond development among other factors depends on ice crystal size and shape. Precipitation can coincide with strong wind. In this case initial ice crystals of precipitation are broken by the wind and reach the surface as smaller pieces of irregular shape. In addition, the wind appears to compact crys tals to be much closer in the ice matrix compared to calm conditions. This wind hardening effect can happen not only for precipitated snow but also for snow grains that are extracted from the bed during a blowing event. Wind crust is a term used to describe the hardened surface snow formed under strong winds. Bearing in mind the situation described above, we hypothesize that the onset of blowing snow depends on to what extent the wind in the previous blowing snow event broke the snow grains or precipitated particles and compacted broken pieces together. We hypothesize that the threshold velocity for the new event depends on the maximum wind speed during the previous event. If snowfall or hoar frost depo sition happens after the last blowing snow then the availability of loosely bonded particles on the surface outweighs the wind hardening. In this case the onset of 76 11 —1 10 — CO £ - -a •a 7 — o to * & 6 — O * E - # o 5 — o 4 — 6 8 10 12 14 16 18 10 m Maximum Wind Speed (m s-1) Figure 3.9: Dependance of the threshold wind speed on the maximum wind speed of the previous blowing snow event. Filled circles stand for the regular observations of blowing/drifting; open circles denote cases when snowfall or ice fog were present when blowing begun which made it difficult to accurately determine the threshold velocity. Snow flake and diamond symbols are used for cases when snowfall or ice fog / hoarfrost, respectively were registered within an interval of calm weather preceding the blowing snow event. The solid line is a linear fit to 16 observations denoted by filled circles (R2 = 0.60, p-value < 0.0005). drifting might be dependent mostly on the characteristics of snowfall or hoarfrost and the morphological change of deposited crystals. This prompts us to look into the time elapsed since the snowfall and snowpack temperature gradient history as 77 possible factors of influence. To investigate if there is a dependance we plotted the 10 m threshold wind ve locity diagnosed in the experiment against observed maximum wind speed at the 10 m level associated with the previous blowing event (see Figure 3.9). In several cases it was not possible to accurately determine the onset of drifting due to con current snowfall or ice fog events. These points are also shown but were not taken into account when a regression fit was sought. Threshold velocities that occurred after the snowfall or hoarfrost deposition are presented on the graph although no dependence on maximum wind speed is expected (which appears to be confirmed by the plot). We expect the line that approximates dependance of the threshold velocity on the maximum wind speed to flatten out and reach a plateau. The first reason for this would be an inability of wind to break grains below some minimum size. The smaller the pieces of ice crystals become, the harder it is to further break them down. The second reason is that with increasing wind speed there probably won't be compaction of grains by wind into a wind slab. The loose particles will be in a state of constant motion and formation of the snow cover is only possible when the wind subsides below a certain value. The proposed prediction algorithm for the 10 m level threshold wind speed Uth 78 can be expressed as a following formula 5.5 if hoarfrost deposition preceeded Uth.= \ 6.0 if snowfall preceeded or concurrent (3-1) 0.9 + 0.7 x U%% if 6 m s"1 < U%% < 14 m s"1 where U^^. is a maximum wind speed at the 10 m level registered during the pre vious drifting/blowing snow event. The upper bound of 14 m s_1 on U^x is taken rather arbitrarily, in the data set used to derive the regression fit we do not have any points with a maximum wind speed greater than 12 m s-1. This upper bound can be adjusted if more data become available. In the first two lines of the formula, the effect of morphological changes can be taken into account by introducing terms dependent on time, ambient temperature and snow cover temperature gradient. It may be possible to split the line related to snowfall into two equations; one for preceding and another one for concurrent snowfall. The reason is based on the following arguments, snowfall intensity or the form of precipitated particles may define how snow on the surface will be compacted and so can be considered as a po tential predictor factor if snowfall happens during a calm period. The compaction considerations are not appropriate for snow that has not reached the surface yet. This case can be treated separately. Experience suggests that concurrent snowfall can result in even lower values for the threshold velocity compared to the case when snowfall occurred at some time before the wind picks up. 79 4 Aerodynamic roughness length of a snow covered ice surface based on CASES04 data 4.1 Introduction Surface roughness lengths for momentum ZQU and temperature zot are important parameters of turbulent flow in the surface layer of the atmospheric boundary layer. They are used to express the form of mean wind speed and temperature profiles near the lower boundary. The form of surface layer profiles often serves as a bound ary condition in numerical models. Parameterizations of land-air coupling in atmo spheric models depends on accurate knowledge of surface roughness either explicitly or implicitly via expressions for drag or bulk transfer coefficients (Chen and Zhang, 2009). It is a common approach to assign one number (or a narrow range of values) to a particular surface type so that this number represents a surface roughness value for all atmospheric flows above the surface. The rationale lies in the accepted 80 paradigm that surface roughness for aerodynamically rough surfaces is independent of friction velocity or Reynolds number. Boundary layer meteorologists and wind engineering practitioners are familiar with classification of natural surfaces with respect to their roughness as for example in Wieringa (1993). For the roughness of snow covered sea ice which is the subject of investigation in this paper the most frequently encountered values coincide with the range reported e.g. by Joffre (1982), namely 0.001 - 0.0001 m. Attempts to provide a single value estimate of the surface roughness over snow covered ground resulted in vastly different estimates even for the same geographical region. Notable features of reports of znm are the existence of very small values bordering on the mean free path of molecules in the air and/or a wide range of values computed for the same experiment. When it comes to snow cover there can be a change in flow properties when a simple flow becomes a particle-laden flow. When a threshold friction velocity is exceeded particles can be extracted from a granular bed, picked up by turbulent eddies and become a constituent of the flow. Drag exerted by particles on the fluid leads to a modification of shear stress within the fluid. The issue of surface rough ness for snow cover tends to be investigated separately for these two regimes. For flow below the threshold for saltation it is possible for another change in flow prop erties to occur. In some cases the surface may become classified as aerodynamically smooth. In this case an effective roughness can be considered to be dependent on 81 friction velocity and surface roughness is predicted to increase as friction velocity decreases. In addition, snow surfaces are susceptible to wind erosion and ground topography can change with time. The drag exerted by the surface is directionally dependent because of the peculiar shape of wind erosion forms. This situation has been recognized by researchers. Some try to stay within a particular regime of flow, as in the above mentioned paper of Joffre (1982) where surface roughness was calculated for observations when friction velocity exceeded 0.2 m s_1 (this is the lower end of the estimates of a threshold for saltation friction velocity) while others (see for example Andreas et al., 2005; Naaim-Bouvet et al., 2010) have attempted to provide surface roughness for the whole range of friction velocities encountered in an experiment and analyze results based on flow regimes. Temperature roughness length is usually predicted based on momentum rough ness. An example of such approach is a theory of scalar roughnesses suggested by Andreas (1987). Here we present results of determining momentum roughness for snow covered ice surfaces from observations of wind and temperature profiles made during the Canadian Arctic Shelf Exchange Study (CASES) field campaign near the edge of the Beaufort Sea in January - May 2004. A special feature of meteorological ob servations in CASES04 is the availability of data on snow particle flux and number densities at various heights, obtained by snow particle counters designed and assem- 82 bled at York University, Toronto. First, we introduce regression based curve fitting from the point of view of Maximum Likelihood Estimation. This allows us to put a proper focus on the role of measurement errors. We carry out numerical experi ments to see what can be expected when the results of profile fitting are expressed by points in the u*,.zom plane. We seek to gain some insight on the discrepancy between theoretical predictions and derived values of momentum roughness length near zero friction velocity. The output of applications of profile fitting procedures to observations is analyzed and a representative value for the momentum roughness length is suggested. 4.2 Site location and profile measuring instrumentation in CASES04 The on-ice stage of CASES04 took place in January - May of 2004 when the ice breaker "Amundsen" was frozen with the ice near the entrance from the Arctic Archipelago into the Beaufort Sea. During this period solar illumination went from none at all to 20 hours of daylight. Thus the diurnal cycle was absent at the beginning of the period, so temperature and atmospheric stability variability were predominantly advection induced. The diurnal cycle was pronounced from the mid dle stages of the experiment nearly up to its end. An ice camp was established on 83 land-fast ice in Franklin Bay, Northwest Territories, Canada. Seasonal ice cover was relatively uniform over an area about 10 km across. At the time of camp de ployment the ice was covered by hard snow 3-12 cm thick. Snow accumulated in the course of the project due to several snowfalls and drifting/blowing snow events. In late April snow thickness was in the range of 3 to 36 cm with a median value of 17 cm and a standard deviation of 8 cm. The initial snow layer was never eroded, dunes moved on top of this layer or on top of newly accumulated and wind hardened snow. A full description of the project's instrumentation can be found in Chapter 2. A wind direction chart constructed from 10 min averaged data recorded over the Wind Speed range (m s""1) 270 90 • >5-10 • >10- 15 • >15-20 180 Figure 4.1: Wind chart of 10 m level wind based on 10 min averaged observations during the on-ice stage (January 15 - May 7, 2004) of CASES04. Size of the directional bins is 11.25 degrees. 84 period of the experiment is shown in Figure 4.1. The distribution is bimodal; east erly and westerly winds have the dominant contribution. Due to sheltering effects from the masts and the ice camp structures sectors from 0 to 67.5 and from 157.5 to 191.25 degrees true were excluded from profile analysis. A threshold value of particle number flux was established to separate periods of blowing snow from no drift conditions. This information was used to study dependence of roughness on particle number density. According to Savelyev et al. (2006) blowing snow occurred 27% of time. In April - May 1971 Langleben (1972) conducted an experiment involving cal culation of surface roughness over first year ice in the Beaufort Sea at the same latitude (70° N) just 250 km west of the CASES04 site. Comparisons will be given below. 4.3 Monin-Obukhov Similarity Theory (MOST) form of mean wind speed and temperature profiles Monin-Obukhov Similarity Theory for flow in the Atmospheric Surface Layer as sumes that in addition to z and «* an additional parameter, the so called Obukhov length, L, is a relevant scale. It is the height where production of turbulence due to buoyancy (related to temperature variations) equals production due to wind shear 85 (mechanical turbulence production). For consideration of the velocity profile, two independent dimensionless products can be assembled from the list of variables involving the velocity gradient dU/dz, u*, z and L. KzdU z n ——, n = -. (4.1 1 = u* oz 2 L Note that von Karman's constant K is included in the first product making it close to unity. Application of Buckingham-Rayleigh theory (Hutter and Johnk, 2004) results in Hi = tyijl-z) or KZ dU (z \ , A „. ^ = ft(i)' (4"2) where the subscript u is added to convey notion that this relation is for mean wind speed. For the mean potential temperature profile the analysis may be repeated with the result that KZ86 (z\ ,„ „. x&=Ki> (4-3) Here 9* is a temperature scale defined by 0* = —u'6'/u±. Sometimes it is argued that the turbulent Prandtl number should be included in the equation above to render the dimensionless product close to unity, i.e. K z 89 (z\ . 86 Functions ipu and ipt are to be determined from experiments. The Obukhov length is calculated according to L=-f~, (4.5) K— Vm where u* is a friction velocity, 9m is a virtual temperature scale, g is an acceleration due to gravity and K is a von Karman's constant. 6VQ is a reference potential virtual temperature. The temperature scale used in the formulae is that for virtual poten tial temperature, i.e. with moisture effects included. Integration of the respective functions gives the mean velocity and temperature profiles. In general form these are U(z2) - U{Zl) = ^\FU(Z2/L) - Fu(Zl/L)\ K l J (4-6) 6{z2) - 0(Zl) = ^Ft(z2/L) - Ft(Zl/L)\, n ( m Z where Fu(() = J v?m(C)^O C) and Ft(C) = / P<(C)°^( C) with C = /L. In the case of mean wind speed, level z\ is usually chosen to be where a plot of U versus ln(z) crosses the ln(z) axis and U = 0. This height is called the momentum roughness length and denoted as zo„. The general form of the wind profile is then U(z) = ^IFU{Z/L) - Fu(z0u/L)\. (4.7) Mean potential temperature in the surface layer can increase or decrease with height or even be constant. To come up with a roughness length for temperature which is similar to the momentum roughness length and would parameterize interaction 87 with the interfacial sublayer, the notion of the surface potential temperature 9S is introduced. Then, the temperature roughness length 2nt is the height where tem perature coincides with the surface temperature. A general form of the temperature profile can be expressed as 9(z) = 9S + ^ht(z/L) - Ft(zot/L)\. (4.8) For flux-profile functions tpu and ipt we used empirical relations as in Hogstrom (1988) : tp»(z/L) = l + 6.0y, 0 ipt(z/L) = 1 + 8.2^, 0 Similar forms were proposed by Businger et al. (1971) with slightly different nu merical coefficients. Upon integration of the empirical expressions (4.9) one arrives at the result x>-l FU(Q = In -—- + 2 arctan(p), -2 < ( < 0, Fu(() = ln(C) + 6.0C, 0 < C < 1, (4.10) F (() = ln^, -2 Ft(C)=ln(C) + 8.2C, 0 p = (1 - 19.3C)1/4 and s = (1 - 11.6C)1/2. Equations (4.7) and (4.8) together with Equation (4.10) allow estimation of mean wind speed and temperature at various heights within the surface layer pro vided the Obukhov length, roughness lengths, velocity and temperature scales and surface temperature are known. A historical account of MOST and its modern state can be found in Foken (2006). 4.4 Maximum Likelihood approach to fitting curves to ob servations The profile of some physical variable is understood to be a set of measurements of this variable at various heights made in such a manner that observations are considered to be simultaneous. Because measurements intrinsically involve mea surement errors it is desirable to take this fact into account when trying to find a curve (model) that best approximates the observations. A Maximum Likelihood approach provides such an algorithm together with a criterion as to what to consider the best fit. The choice of criterion is grounded in the experience that measure- 89 ments concentrate around the "true" value. Errors of large magnitude are less frequent than small deviations or in other words, the probability of observations to be close to the true value is higher than for those farther away. To deal with a set of observations that form a profile one considers a random experiment to consist of multiple parts - individual measurements made at several heights. Then the notion of the product model from probability theory is invoked to combine several parts into one probability model. If measurements at different heights are statistically independent then a product model can be used for these multiple parts. Overall probability in this model is calculated as a product of probabilities of individual parts. Thus it is possible to assign the probability value to a set of observed numbers based on the distances of each observation from the respective true value provided it is known. As true values one takes the prediction of the model. For the profile they are the values predicted for the measurement heights, that is points on the fitted curve at those levels. This probability value is used to judge whether or not the choice of model was good in the first place. A small probability raises a concern that the model is not correct. Note that as the measurements are made already, one cannot alter them. The model on the other hand can be replaced by another one. Another probability value is calculated and compared to the previous number. The model that gives the maximum value of the associated probability is the one 90 the researcher will accept as the most probable for the given set of measurements. So there is a need for an efficient algorithm to try different models The first step is to decide upon what type of model will be tried. In other words, what is the general form of the relationship from which, at each step, a specific realization will be chosen. For the purpose of this paper we fit profile measurements of wind speed and/or temperature into the MOST form of the profile. There are three parameters, namely it*, znm and L in the MOST wind profile. Setting them to particular numerical values, for example 0.3 m s_1, 0.001 m and 100 m, respectively fixes a specific model as an approximation to a certain set of observations. This model predicts value y(z%) at a height of measurement z% where the observed value was yz. As long as the model is fixed the values predicted by the model are treated as "true" values. We assume that yl is a measurement made with random error of a true value y(z%). Next we assume that errors are normally distributed with the mean value of y(z%) and variance a\. The probability density function (PDF) f(y) for any value from its domain reflects relative frequency of occurrence of this value. With the above assumptions, for the value yt to appear as a result of measurement the relative frequency is assumed to have the PDF (4.11) According to the product model for statistically independent random variables the PDF of a composite experiment is a product of individual PDF's. Then the rel- 91 ative frequency of occurrence of the composite set yi,y2,...,yN obtained from N individual parts of the experiment is related to fcKVl, V2, • • • , VN) = \\ r- o eXP -9 (4.12) where fc(yi,y2, • • • ,VN) is a PDF of the composite experiment calculated at the point ( 2/1,2/2, • • • ,VN)- The choice of the test model influences the value y(zt) which is a mean of the individual normal distributions. Now the objective is to find the combination of the model's parameters that results in the maximum value of /c(z/i) 2/2) • • •) 2/JV)- As it is easier to deal with the logarithm of this function, one wants to find the maximum of 1 2 (4 13) .nW„fc...,m))^EK7=?)-^(^ ) ' The first term on the right hand side does not depend on the model so it could be discarded from the procedure. The maximization is replaced by minimization of the negative of the functional. As a result, one seeks to find a minimum of i;(*7(z,))2 (4.i4) in a space defined by the model parameters. Different strategies are developed to find the minimum of the function. One way is to take derivatives of the Equation (4.14) with regard to each of the model parameters, equate them to zero, find the critical point as a solution to the system 92 of resulting equations and check that it is really a minimum (e.g. not a maximum or a saddle point). The system of equations to solve are i(^)^=°,_, a (415) where each mq is one of Q parameters of the model. Recollect that y(zt) is a prediction of the model and as such it depends on the model parameters. 4.5 Fitting data to MOST profiles An algorithm for deriving turbulent scales from observations of mean flow param eters at various levels is referred to as a profile method. The alternative method being the so called flux method (see for example Sun, 1999). The latter method is applied when an observation of momentum and/or temperature flux and a mean flow parameter is available at some height above the surface. An assumption em ployed in this case is that the flux measured is an observation of surface layer flux and the mean flow parameter is an observation of a point of a vertical profile described by the MOST form. Then the aerodynamic roughness lengths can be uniquely determined from Equations (4.7) and (4.10). The temperature roughness length follows from Equations (4.8) and (4.10) provided the surface temperature 9S is known. The profile method is based on curve fitting. A Maximum Likelihood approach 93 described in the previous section is used often in geophysics. In meteorology the profile method is introduced with a slightly different appearance called least-square fitting. What often lacking in this case is proper attention to measurement errors which could be distinct for different sensors. It is not uncommon to have propeller wind monitors and cup anemometers from diverse manufacturers to be used in a project. So that a different amount of trust can be put into measurements of indi vidual sensors, each observation can be assigned a distinct weight. Those weights are taken into account when some profile curve is tried as a fit to observations. A least-square fit can be found in papers of many researches, including the work of Zilitinkevich (1970) where some distinct ideas are introduced. Profile curves are sought for wind speed and temperature simultaneously. In addition, constraints are imposed on the friction velocity and temperature scale. They are related to each other via the expression of Obukhov length (Equation 4.5). Fitting is performed iteratively until a constraint is fulfilled. Instead of surface temperature defined at the height of temperature roughness it has been suggested to use temperature at the momentum roughness height. This temperature is called sometimes aerody namic temperature (Huband and Monteith, 1986; Sun, 1999). In the case of the temperature profile it is not possible to find the temperature roughness length if surface temperature is not known. These two parameters are combined in the fi nal result of the profile method. Setting one defines the other. The idea of the 94 aerodynamic temperature allows us to use the profile method even without knowl edge of the surface temperature. The profile method as in Zilitinkevich (1970) can be found in papers of many scientists investigating momentum and temperature roughness above various natural surfaces. Molder (1997) augmented the method by introducing a displacement height which is necessary to consider for flow over a canopy. It should be mentioned that the possibility of including a displacement height into the procedure was recognized very early, see e.g. Lo (1979). In what follows we present an algorithm of curve fitting very similar to least- square regression but in more general form based on Maximum Likelihood argu ments. Errors pertaining to each individual sensor can be accounted for. The other distinction from the method of Zilitinkevich (1970) is the possibility to fit a curve to any available profile (not just wind speed and temperature) separately. The MOST model of the wind speed profile depends on three parameters: Zou, u* and L. Let us denote the difference between the observed and predicted by model value of the wind speed at the level z% as MJX = Ut-^(FU(ZJL) - Fu(z0u/L)\. (4.16) A system of equations to solve to find the minimum of the Equation (4.14) for some set of observations U% at levels zt, i = 1,...,N is 95 E".A^K = °> F E{^r ( U(ZJL) - Fu(z0u/L)^J }=0, (4.17) If the restriction of the first equation is introduced into the second and third equations the system simplifies to AT EA*7^ , = °> „^i * N ^2^Fu(zt/L)=0, (4.18) \AU, Y=r*nWL) = o. For convenience we introduce notation N 6== 1 by„ »Ut bFn ^Fu(f) a ^(D^d) 2^' -l^^ -l^—^-' ^FF~2^ -2 i=l » i=l * t=l * j=l » JLTJF(^) JLZF'(^) JLUZF'(^) ^FF = 2^ —3"—' ^f = 2^ —^2~~' ^z*" ~ 2^ ^2 ' t=l * i=l J i=l * 96 and rewrite system (4.18) as SY-^(sF-F0s)=0, SYF-^(sFF-FoSF\=0, (4-20) 1 SYZF ( SFzF' — F0SzF' J = 0. From the first two equations of (4.20) follows the result (we assume that denomi nators are not zero) U* _ SySp — SYFS _ SySpp — SFSyp K, OpOp — OppO Oyop — ijypiJ which we put into the third equation to get (&p — SFFS)(3YFF'S — SySzF'j + (SySp — SyFS)(SpSzF' — SFzF'S) = 0. (4.22) This is an equation of the general form f(L) = 0. It can be easily solved numerically. After finding L, parameters u* and Fo are calculated from (4.21), ZQU follows from FQ = Fu(zou/L) as a numerical solution. For the MOST temperature profile a set of model parameters is z§u0* and L. Surface temperature may not be available but it is still possible to fit a curve to observations. We rearrange terms in Equation (4.8) for potential temperature 9(z) as d 9(z) = ^FtU)+A0 (4.23) 97 where A0 = 9S — (9*/K)Ft(zot/L). Assume that the model parameter set consists of A0,9* and L. After taking derivatives of 9(z) modeled by Equation (4.23) with regard to parameters one arrives at system of equations similar to (4.18) i=\ l JT^Ft(Zl/L) = 0, (4.24) i=i * N Aft J2^F;(ZZ/L) = o. In a similar fashion solutions for #*,L and AQ can be obtained from this system. What is different in this case is a coupling of z0t and 9S via the parameter AQ. Note that the vertical profile is uniquely defined by 9*, L and A0. In the case of a known surface temperature, zot is calculated from AQ — 9S = —(9*/K)Ft(zot/L). When 9S is not available it is possible to take ZQU as a reference height for temperature and consider aerodynamic temperature instead. Thus far we have shown a method of fitting curves to profiles of measured points of one parameter (for clarity we denote Lw as the Obukhov length derived from wind speed profile and LT as the one derived from temperature profile). The result of fitting is the curve that best approximates measurements based on some criteria. The drawback though is the absence of information on the other parameter and this can sometimes lead to a result that is unreasonable from the point of view of MOST. To illustrate this point we present MOST profile curves for wind speed and potential 98 temperature on Figure 4.2. The line (U*/K) \n(z/zom) could be the neutral stability limit in the case of wind speed, provided the friction velocity is held constant. In this case, curves corresponding to different values of Obukhov length lie on either side of logarithmic profile. The case of potential temperature is quite different. The line (9*/K) \n(z/zot) can not be the neutral stability limit unless 9* = 0. When atmospheric stability approaches a neutral state the potential temperature curve approaches vertical line, 9* approaches zero. Potential temperature curves for stable stratification can only have 9* greater than zero and for unstable stratification 9* should be negative. If 6* is held constant then the only possible curves for varying Obukhov length are those shown on Figure 4.2, above (9*/K) ln(z/zot) line on the left hand side of the figure if L < 0 and below that line on the right hand side of the figure if L > 0. Those restrictions are not incorporated into the fitting procedure. Due to errors in measurements it is quite possible that the best fit MOST curve for potential temperature obtained in one profile case will have the Obukhov length and 9* of opposite sign which is prohibited by theory. To circumvent this drawback additional information should be taken into account. When wind speed and temperature profiles are known at the same time a con straint in the form of Equation (4.5) can be used as suggested by Zilitinkevich (1970). In the framework of the Maximum Likelihood approach developed in our work this restriction is incorporated as follows. An expression for U*/K is derived 99 10 Unstable stratification L<0 0. Stable 01 -= 01 — stratification L>0 0.>O 0 01 0 01 4 6 8 242 242 5 243 5 244 244 5 Wind Speed (ms1) Potential Temperature (K) Figure 4.2: MOST profiles for different atmospheric stability situations. Left : Wind Speed. Right : Potential Temperature. Each curve is calculated with different value of Obukhov length L. Friction velocity «* or temperature scale 0* are fixed, as well as momentum and temperature roughness lengths, Zom and ZQt. Dashed lines represent (U*/K) ln(z/zom) and (#*/«;) ln(z/z0t), respectively. from the first two equations of the system (4.18) as Equation (4.21). Similarly, an expression for 0*/K is derived from the first two equations of the system (4.24). Inserting formulae for u* and 9* into the equation for the Obukhov length (4.5) we obtain an equation of the general form f(L) = 0 and solve it numerically. With L determined, u* and 9* follows from their respective equations. We will denote the Obukhov length obtained by this two profile method as L2F. Note, that the third equation of the respective systems is not used because L is not an independent variable in this case. The statistics of the Equation (4.14) for the wind speed and 100 air temperature are minimized in u*, ZQ and 9t, AQ space. Often times only the A9 parameter is measured at a meteorological station and not the temperature profile. This information can be used in place of a profile. From the second equation of (4.6) it follows 9, A0 (4.25) K Ft(z2/L)-Ft(Zl/LY With this 0* and u* from Equation (4.21), Equation (4.5) becomes 9VQ f SySp — OypO \ LA9 (426) g \SFSF-SFFSJ Ft(z2/L)-Ft(Zl/L) °' Again, this is an equation of the form f(L) = 0. We denote Obukhov length obtained from it as LdT- A similar path can be followed when the temperature profile and wind speed at two points in the vertical are measured (L^u in this case). In both of the latter cases the result provides a curve that fits the available profile, and another curve that goes directly through two measured points. There is no way to account for measurement errors or how a parameter not represented by its profile varied between two points in vertical. It is possible to employ this procedure even when only two temperature and wind speed points are available. The equation to solve is then W At/ V LA9 Q 9 \Fm(z2w/L)-Fm(zlw/L)J Ft(z2t/L)-Ft(zlt/L) Obviously the accuracy of the method when AU and/or A9 is involved is suspect. 101 4.6 Application of the fitting method to artificial profiles An understanding of the result of some procedure applied to real data depends on the ability to assess the influence of measurement errors and errors associated with the procedure itself. To get an idea of what errors to expect we simulated artificial profiles of wind speed and potential temperature at four points in the vertical for each parameter. 1000 profiles were calculated for stable and unstable atmospheric stratifications characterized by Obukhov length equal to 50 m and -50 m, respectively. Roughness lengths were chosen to be zom = 1.0E-04 m and ZQt = 1.0E-05 m. The friction velocity u* was 0.155 m s_1 for L = 50 m and 0.156 m s_1 for L = -50 m while the temperature scale was 0.03 and -0.03, respectively. The surface temperature (at ZQt) was set to -30 °C. A reference temperature 0VQ was calculated for an atmosphere with no moisture as an average potential temperature within the layer where measurements supposedly took place. One can check that this choice of scales satisfies the equation for Obukhov length. Heights for wind speed measurements were set to be 1.0 m, 2.0 m , 4.0 m and 10.0 m and 0.5 m, 1.5 m, 4.0 m and 9.5 m for temperature. The choice of levels was made based on actual measurement levels in the CASES04 experiment. Errors of measurements for each sensor were assumed to be normally distributed around "true" MOST value for the particular level with standard deviation of 0.01 102 m s_1 for wind speed and 0.01 °C for air temperature. With the help of a random number simulator "measurements" were calculated for each point of the respective profiles independently. Then profiles for a specific stability situation were combined and subjected to fitting procedures. We will present results for several different methods: • one profile is given only (resultant L : Lw or LT), • two profiles are given (resultant L : L2p), • wind profile is given plus temperature at two points in vertical (I^x)- For the last method temperature points were taken as the lowest and highest levels. Table 4.1 presents the statistics for stable atmospheric stratification, . Obviously the two-profile method performs better than one profile and the range of variations of derived parameters is noticeably less for all parameters. Although the roughness length varies by an order of magnitude in the two-profile method, for the one profile method scatter is roughly two orders of magnitude and it is ln(zo) that matters. Mean or median values are reasonably close to original values. With the temperature profile as the only source of information some derived Obukhov lengths are negative. This should not occur for a positive temperature scale. The fitting procedure applied to a wind speed profile with a constraint in the form of A9 performs almost as well as the two profile method. This can be partially explained 103 by the fact that profiles are assumed to be from the universe where MOST is imposed. The only disturbance in the profiles comes from random "measurement" errors. Temperature points that are discarded when one switches from the full profile to two points only do not carry significantly more information on how close points are to MOST. This information is contained in two remaining points as well. The real comparison of these two methods can be only made on real world profiles. For unstable stratification of the atmosphere (Table 4.2) one profile methods perform with less success when compared to the stable stratification case. The scatter of derived parameters becomes larger. But the two-profile method gives slightly better results than in the stable case. Momentum roughness length varies by less than one order of magnitude although the range of temperature scale variations increases. It is customary to investigate relations between turbulent scales of atmospheric flow. In the situations where scales are derived by one of the profile methods errors associated with the procedure propagate to some extent into all scales. So some behavior can be attributed to procedure errors only and not to any real physical relationship between variables. It is instructive to investigate in what way procedural peculiarities manifest themselves in the results presentation. For this purpose we plot derived momentum roughness against derived friction velocities for the two-profile method in Figure 4.3. Box-whisker plots are drawn on top of scatter 104 plot points, so some points can be hidden behind boxes. Plots are combined in such a way that each box represents all points that lie to the left of it in a vertical strip between lines that go through the centers of adjacent boxes. For example, the box centered at 0.15 m s_1 represents points that belong to u* bin 0.1 - 0.15 m s_1. The whole range of roughness values falling into a particular friction velocity bin is depicted with the help of "whiskers" and box itself shows where 50 % of the bin points reside. The horizontal line inside the box is where the median value of the ZQm for that bin is. The reason behind presenting the box-whisker plot along with the scatter plot is to gain understanding of how the two plots relate to each other. The box-whisker plot is often the method of choice to illustrate or to investigate the relationships with a wide range of variation of one parameter for a fixed value of the another. In the particular case we considered above, the box-whisker plot does not offer more insight and is probably redundant but it can be useful as a descriptive method for the field project data. In particular, the relationship between the flow friction velocity and the surface roughness length is often presented with the help of a box-whisker plot. In this figure we plotted boxes for any bin with points in it. In what follows we will only depict boxes for bins with more than 10 values in them. Note that for the data represented on this figure random profiles were gen erated with bigger errors. Standard deviation of errors are 0.1 m s_1 for wind 105 speed and 0.05° for temperature. These values are estimates obtained in post CASES04 calibration of sensors. Langleben (1972) estimated standard deviations of cup anemometer measurement errors to be 0.05 m s_1. Larger errors resulted in larger variation of derived parameters. There is significant difference between stable and unstable stratification cases. For the unstable case, the scatter of u* and ZQm is much less compared to the stable one. Momentum roughness values span 10 orders of magnitude when L = + 50 m and close to 5 orders of magnitude when L = - 50 m. The scatter of friction velocity values is also larger. The tendency of derived profiles with smaller u* to have smaller zom is as ex pected. Random errors to the MOST profile do not change the magnitude of values significantly but may alter the slope of the curve. Curves with smaller u* (bigger slope) will cross the vertical axis (height) lower than the original curve. This gives a smaller value of zom- The opposite happens to curves with a smaller slope. This explains the characteristic shape of the znm via u* plot in Figure 4.3. Although the range of variations in a particular bin could be large, it is mainly due to the fact that the friction velocity bin spans a range of values. The points are pretty compact, they clump close to the line that approximates the scatter plot. To sum marize, the application of the profile method to a set of random realizations of a particular MOST profile resulted in a set of znm, «*, L points. In the Zom - u* plane, the point cloud is spaced in such a manner that some pairs are in close proximity to 106 0.01 -m 0.01 0.0001 -m 0.0001 -a 1E-006 -s 1E-006 -s L = - 50 m 1E-008 -• 1E-008 -a 1E-010 1E-010 0.15 0.2 0.1 0.15 0.2 0 25 u. (ms1) u.(ms-1) Figure 4.3: Scatter plot and box-whisker plot of momentum roughness and friction velocity derived by application of the two-profile method to a set of wind speed and temperature profiles. Left : Stable stratification. Right : Unstable stratification. Profiles were generated by adding random, normally distributed errors to MOST curves. Standard deviation of errors are 0.1 m s_1 for wind speed and 0.05° for temperature. Cross and circle symbol shows coordinates of the original MOST curve. Bin size is 0.05 m s_1. the "true" MOST point with a significant number of points dispersed but following the general rule smaller M* - smaller znm and bigger u* - bigger znm. Now let us consider the case when several MOST curves are used to generate sets of random error curves. Application of the fitting procedure gives rise to several sets of derived parameters which we place in the Zom - u* plane on the same plot. Again we concentrate on the small interval around some particular 107 value of u*. Each M, region of the plot consists of points that comes from different original MOST curves. Seed curves with their u* bigger than the one for the region considered will contribute points from their " smaller it* - smaller zom " subset while curves with smaller u* will contribute points from their " bigger u* - bigger Zom " subset. This would lead to a greater dispersion of points around the approximating line. Contributions from different sources would account for the majority of the dispersion and not the size of the «* bin as it was in the case of one seed curve only. For a real project the contribution to the plot would come from curves with different values of parameters. One can think of the project's scatter plot as a collection of points sampled from different populations and added together. 4.7 Momentum roughness in CASES04 After gaining some understanding of what to expect from the result of the profile method of deriving turbulent scales, we apply the procedure to the data set of measured wind speed and temperature profiles obtained during the overwintering stage of the CASES04 expedition. We start with 10 minute average data. After the Quality Control stage there are 9677 legitimate pairs of wind speed / air tem perature profiles. Out of this number of pairs the two-profile method produced 9659 results with z0m > 1E-07 m, so 18 cases were discarded on the basis that this value is close to the molecular mean free path in the atmosphere (Andreas et al., 108 2005). Results in a form analogous to the one considered in the previous section are plotted in the left panel of Figure 4.4. Note that this is a different scenario from what was presented in Figure 4.3 where all points originated from one profile with fixed u* and znm. Now each point can be considered as just one sample from a set of all possible observations of some "true" profile form. Different points may or may not be from the same population. For each observed (M*,znm) point the correct profile that gave rise to it can have u* bigger or smaller than derived. For small friction velocities there is a large number of points with small rough ness length. Some points have zom > 0.1 m. There is a characteristic "dip" in the median value of roughness length when zero friction velocity is approached. Compared to mid-range friction velocities where points can have their origin from profiles with both smaller and larger it*, in the low u* region of the plot random error contributions come mostly from profiles with bigger "true" friction velocity, the ii* is limited by zero on the left. These most often contributing random error profiles have smaller than "true" friction velocity and consequently smaller than "true" Zom- This feature becomes even more evident when a selection criteria of wind speed > 2 m s_1 is applied to the source data set. The result of the two-profile method on this data set is presented in the right panel of Figure 4.4. The num ber of source profile pairs is reduced to 8143. The majority of eliminated points belonged to profiles with derived u* < 0.35 m s~J. There was no change in the 109 01 02 03 04 05 06 07 01 02 03 04 05 06 07 u, (m^1) u, (ms-1) Figure 4 4: Momentum roughness via friction velocity derived by application of two- profile method to a set of 10 minute averaged wind speed and temperature profiles measured during overwintering in Canadian Arctic (CASES04 project). Results -7 with znm < 1.0 x 10 m were discarded. Left : All measurements when wind speed and temperature profile were available were processed. Right Only pairs of wind speed / air temperature profiles with wind speed exceeding 2 m s_1 were processed. number of points after w* > 0.45 m s"1. The number of results discarded due to the znTO > 1E-07 m restriction remained unchanged The decrease in median values of zrjm near ut = 0 is more prominent since the contribution of random realization of small u* "true" profiles is taken away What remains is a contribution from the region to the right in the form of "smaller u* - smaller z0m". Note that there far fewer points with low it* and large znm in the right panel plot. This gives us a reason 110 to think that large momentum roughness values are due to decreasing accuracy of wind speed measurements for low winds. Two restriction criteria (wind speed less than some threshold or derived zom is too small) upon which it is decided whether or not a measured profile or result of application of the method to the profile can be accepted are of common occurrence (e.g. Konig, 1985). We can consider the first as a pre-process criterion and the sec ond as a post-process one. Another example of pre-process restriction is exclusion of profiles due to katabatic flow over glaciers. Considerations of flow steadiness are of great importance because it allows us to seek MOST profiles only when the theory is valid. There is a good examination of the subject in Joffre (1982). There it is sug gested to exclude periods of measurements when the temperature field undergoes rapid changes. Joffre (1982) also suggested that the post-processing criterion of eliminating results with too small znm helps us to exclude most non-steady periods as well. Commonly employed post-processing criteria are based on the correlation co efficient of a least-square fit when only results with large enough value of this coefficient are accepted; for an example see Denby and Snellen (2002). In the Max imum Likelihood approach this is equivalent to setting some value of the chi-square statistic (Equation 4.14) as a threshold of acceptance. Note that in this case the uncertainties associated with each sensor are properly accounted for. Still this is 111 an integral criteria. An acceptance of the measurement from some sensor depends upon performance of the others. An alternative would be to impose restrictions on each sensor separately, namely exclude the sensor measurements that have too small a probability to occur assuming the fitted curve represents the "true" model. This can be done in terms of the standard deviation of errors associated with each sensor. When analyzing the u* - znm relationship presented in the form similar to that of Figure 4.4 the region near u* = 0 should be excluded from consideration for reasons outlined above. If outliers in the figure are discarded then one can see that starting from u* = 0.35 m s~x the median values of roughness length of snow-covered ice in CASES04 was close to 0.001 m. The range of z0m values spans two orders of magnitude up to u* = 0.6 m s_1. The range diminishes even further with increasing friction velocity but this may be the effect of not having enough data points. Note that, for our data set, a friction velocity over 0.35 m s_1 corresponds to neutral or near neutral stability. The range and median value from our analysis is similar to what was reported by Inoue (1989) for neutral stability flow in the katabatic region of the Antarctic. In addition, from 17 values of surface roughness of Antarctic snow cover derived from papers of other researchers reviewed in the above mentioned article 10 fall within the interval from 0.0008 m to 0.002 m, though in a more recent paper of Nishimura and Nemoto (2005) the value of z0m = 6.3E-05 m is reported for 112 the same region. From 30-min observations of wind and temperature profiles over a melting glacier in Iceland, Denby and Snellen (2002) derived an average zom = 0.001 m with a standard deviation of 0.0004 m. The surface roughness of snow covered ice flows in the Baltic Sea under near-neutral conditions was reported to lie within the 0.001 - 0.0001 m range (Joffre, 1982). These values were derived from 10 min averaged profile measurements and correspond to friction velocity greater than 0.2 m s_1. 0.1 -3 0.1 -= 0.01 -= E . 0.001 -= _ • '.-iLi- %Xv MMQ 0.001 0.0001 0.0001 -5 " _l_ 1E-005 I I I I I I I I 1E-005 0.|5 0|2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.C u.fms1) u. (ms-1) Figure 4.5: Momentum roughness via friction velocity derived from 1 hour averaged wind speed and temperature profiles measured during overwintering in Canadian Arctic (CASES04 project). Results with zom < 10E-07 m were discarded. Left : Result of the two-profile method. Right : Result of wind speed profile fitting with a constraint imposed by measured A9. 113 Figure 4.5 is intended to show effects of the data averaging process (left panel) and further application of the method to hourly data when only the wind speed profile is fitted with Obukhov length definition constraint in which 0* is expressed through the temperature difference at two levels (right panel). A smaller friction velocity range is apparent. The range of znTO is also smaller but this could be due to 6 times fewer points to compose the picture. The median value of momentum roughness didn't change compared to the 10 min average case, znm ^ 0.001 m for u* > 0.35 m s_1. Surprisingly the one profile method with a A9 constraint performs overall as well as the two-profile method in the case of hourly averaged data. There is even a decrease in the znm range in the small friction velocity region mainly because of elimination of very small values. This may be an argument in favor of attributing the appearance of some very small znm values to the application of a fitting procedure when MOST is not valid, during the periods of transition of the temperature field from one form of stability to another. Langleben (1972) calculated the roughness length of first year ice from 1 hour averaged wind profiles chosen to represent neutral stratification. That experiment was carried out in nearly the same geographical region. The season corresponds to the late stage of CASES04. Roughness lengths over smooth ice were found to vary from 0.0002 to 0.002 m with an average value of 0.00052 m. Our value of 0.001 m compares favorably with the above result. However, it has to be mentioned that 114 the spread of values in our case is bigger, two orders of magnitude compared to one order in Langleben (1972). 4.8 Influence of snow drift on momentum roughness The surface roughness of an aerodynamically rough surface is generally considered to be independent of flow properties and to be a characteristic of the surface itself. The criterion to determine whether a surface is rough is based on the so called roughness Reynolds number Re = u*d/v, where n* and v are the friction veloc ity and kinematic viscosity of the fluid, respectively and d is some characteristic height of the roughness elements. Often it is taken to be proportional to the surface roughness znm. Flow is considered to be aerodynamically smooth if the roughness Reynolds number does not exceed some threshold value. For this regime of at mospheric flow Znm depends on the flow properties. The functional form of the dependence can be obtained by comparing the equation U(z) = — In — (4.28) K Zom with the law of the wall for smooth flow of an incompressible fluid 1 z U(z) = ±]n ^ + a (4.29) K V It follows that zom = — exp(-AcC). (4.30) M* 115 The coefficient exp(—K,C) depends on K and C which were found from experimental data. The numerical value of this coefficient in most cases is taken to be 0.135 although if K = 0.4 and C = 5.1 as it is in Coles (1956), for example, then C\ = 0.130. It is clear that with u* small enough the roughness Reynolds number would be less than a threshold so that surface is aerodynamically smooth. According to Equation (4.30) z0m should increase with u* approaching zero. If friction velocity increases then at some point particles that comprise the underlying surface can be lifted and be entrained in the flow. An increase of mo mentum roughness length due to particles of the underlying surface entering the fluid flow is an accepted paradigm. The rationale lies in the necessity to spend some energy to propel particles in the direction of the flow as well as in an act of extracting particles from the bed. The partitioning of wind shear stress between the underlying surface and airborne particles occurs mainly in the so called saltation layer close to the surface. Momentum gained by airborne particles is lost at the end of their trajectories - at the surface. This confinement of fluid momentum loss to a relatively thin region allows us to extend the parametrization of a momentum sink in the viscous layer to include a saltation layer. The effect of airborne particles on the mean wind speed profile can be modeled as an increase of surface roughness. The idea seems to originate from works of Bagnold (1941) and Owen (1964). It was 116 suggested that in the presence of saltation u2 z0m = a- (4.31) g being acceleration due to gravity and the coefficient of proportionality a is of order 0.01. For a historical account and rationale of deriving this formula see e.g. Andreas et al. (2005). In an attempt to arrive at a relationship that describes znm behaviour over a wide range of friction velocity Andreas et al. (2005) combined Equations (4.30) and (4.31) and also suggested an additional term to represent what they called fundamental macroscale roughness. As was shown in the previous section, our analysis of CASES04 data indicates that there is no increase of surface roughness as friction velocity increases. Friction velocity is related to the number of particles entrained into the flow but in some cases particle number flux could vary significantly for the same value of friction ve locity (especially in the region close to the saltation threshold of friction velocity) due to properties of the underlying surface that include bonds between snow par ticles, temperature and snowfall history, snow availability, etc. Besides comparing derived roughness length with derived friction velocity we have an opportunity to investigate dependence of roughness length on measured particle number flux or the particle number density derived from it. An exploratory technique in the form of the combined box-whisker and scatter plot is shown in Figure 4.6. There were no restriction on minimum wind speed 117 imposed. All points with number density larger than 0.25 x 106 m~3 are plotted. The median value of roughness length is approximately 0.001 m and does not exhibit statistically significant variations with particle number density. The number density of snow particles at 0.5 m height according to our measurements varies from 0 to 3 x 106 particles per m3. It compares well with results of Mann et al. (2000). 0.1 0.01 E" ~ 0.001 0.0001 1E-005 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 Number Density (crrr3) Figure 4.6: Aerodynamic roughness length derived by the profile method as a function of snow particle number density. Number density is calculated from 10 minute averaged particle flux measured at 0.5 m nominal height above the snow surface and wind speed interpolated to that level. 118 Table 4.1: Summary statistics of fitted parameters resulting from application of several profile fitting techniques to a set of wind speed and air temperature pro files under stable atmospheric stratification, L = 50 m. Profiles were generated by adding random, normally distributed errors to MOST curves. "Seed" column indicates parameters of original MOST curve. Method Fit Min Max Seed Median STD Wind Speed 26.1 81.9 50.0 49.9 7.4 Profile 0.11 0.18 0.16 0.16 0.008 Zom 3.0E-06 3.2E-04 1.0E-04 1.0E-04 4.6E-05 Temperature -284.7 309.9 50.0 43.0 35.5 Profile 9, 0.013 0.072 0.03 0.030 0.006 Two L2P 31.8 61.1 50.0 50.0 3.4 Profiles 0.13 0.17 0.16 0.16 0.004 z0m 1.5E-05 2.2E-04 1.0E-04 1.0E-04 2.7E-05 0.027 0.034 0.030 0.030 0.0007 Wind Speed 29.3 61.6 50.0 50.1 3.5 Profile and 0.12 0.17 0.16 0.16 0.004 A9 Zom 9.9E-06 2.2E-04 1.0E-04 1.0E-04 2.8E-05 9, 0.027 0.034 0.030 0.030 0.0008 119 Table 4.2: Summary statistics of fitted parameters resulting from application of several profile fitting techniques to a set of wind speed and air temperature profiles under unstable atmospheric stratification, L = - 50 m. Profiles were generated by adding random, normally distributed errors to MOST curves. "Seed" column indicates parameters of original MOST curve. Method Fit Min Max Seed Median STD Wind Speed -6493.1 7913.9 -50.0 -47.3 384.5 Profile 0.12 0.45 0.16 0.16 0.028 ZOm 8.1E-06 8.0E-03 l.OE-04 9.9E-05 5.2E-04 Temperature LIT -29623.1 42334.8 -50.0 -15.0 1727.5 Profile 0* -0.313 -0.012 -0.030 -0.029 0.018 Two Li2P -75.2 -39.9 -50.0 -50.1 3.9 Profiles 0.15 0.16 0.16 0.16 0.003 z0m 5.9E-05 1.6E-04 l.OE-04 l.OE-04 1.7E-05 0* -0.038 -0.018 -0.030 -0.030 0.003 Wind Speed -70.2 -39.7 -50.0 -50.1 4.1 Profile and 0.15 0.16 0.16 0.16 0.003 A9 z0m 5.8E-05 1.7E-04 l.OE-04 l.OE-04 1.7E-05 0* -0.038 -0.020 -0.030 -0.030 0.003 120 5 Light beam interruption counter There are number of devices both in research and in the industrial field that are intended to detect and/or size individual items crossing a light beam. For the purpose of this thesis we consider particle counters based on the effect of reduction of the energy of light reaching the detector if particle blocks the light path for some amount of time. The detectors used are light sensitive sensors: photodiodes, phototransistors or photoresistors. The light source could be monochromatic (emit electromagnetic waves in a narrow band around a certain frequency) or have a broad range of frequencies of emitted waves. In the former case the receiver is usually chosen to be most sensitive in the band of frequencies of emitter. If snow grains are the primary target of detection it is beneficial to work within one of the water absorption bands where electromagnetic wave energy reduction would be the biggest for water based particles crossing the beam. There are several water absorption bands in the infrared regions of light and there are emitters available that work within those bands. All photoelectric counters reviewed in Chapter 1 121 including the York University counter use infrared emitter-receiver pairs. 5.1 Basics of individual particles light shadowing detection The characteristic feature of light beam counters is sensing based on the area or the volume of a detected particle. Particle mass has no influence on the changes in the portion of light energy reaching the sensor. Nevertheless many photoelectrical counters (Gubler, 1981; Sato et al., 1993; Schmidt, 1977) output mass flux as well as particle sizes. Mass flux is calculated from size distributions and in some cases involves a calibration procedure. Figure 5.1 illustrates the cycle of particle detection. The fully illuminated pho- todetector will have a current flowing through it. The current is converted into voltage by circuitry and voltage is monitored. When a spherical particle intrudes into the light beam some of the light energy is prevented from reaching the sensor and the current and consequently the voltage will change. The voltage decreases until the whole particle is in the beam or the beam is blocked completely if the particle is bigger then the sensor field of view. If the particle is smaller than the light beam there will be a period of time when the particle moves within the beam but the area of shadow it casts on the sensor does not change. The voltage during this period is shown as a constant in Figure 5.1. For this to happen two conditions must be fulfilled. First, the light intensity should be constant throughout the beam 122 I I I Light Photo- Time source detector >o Light Photo- Time source detector + W/M6? \ /T Particle 0 & • Light vl/ Photo- Time sou rce dete ctor Figure 5.1: Sketch of a particle moving through a light beam and corresponding voltage monitored at the sensor. cross section. Second, the sensitivity of the detector has to be constant over its surface. These conditions are important not from the point of view of keeping the voltage constant (this is just a manifestation of conditions fulfilled) but from the point of view of getting the same result no matter at what portion of the beam the 123 particle travels across. A particle of the same size but in different areas of the beam and casting a shadow on different areas of the sensor would intercept a different amount of light energy if the first condition is violated or the current change at the sensor would be different if the second condition is not fulfilled. In both cases the voltage drop would be different for the same particle (or the particle of the same size). The first condition was not achieved in the Schmidt (1977) counter because of the state of technology at the time and that resulted in a high error level. Sub sequent counters conditioned the light beam to make it collimated and to have a homogeneous light intensity. The sampling volume - particle concentration relationship is of great importance for the kind of detection we deal with. If two (or more) particles are in the sampling volume at the same instant of time they are seen as a single particle which size is determined by the relative position of the particles but at least as big as the biggest one. This results in a smaller number of particles being detected and an increase in the number of bigger particles registered at the expense of smaller ones.From the argument above, it is clear that there is a limit on the sampling volume size to ensure correct detection and that this limit depends on the particle concentration. This in an important design consideration. From the opposite point of view, given the sampling volume dimensions, one can determine the range of concentrations amenable for correct detection and from it establish the range of wind speeds and 124 heights above the surface the device can operate correctly. For example, Sato et al. (1993) calculated that for the sampling volume of their counter and a wind speed greater than 20 m s_1 two or more particles are in the light beam for all heights below 5 m. There is a so called edge effect related to the detection of particles that enter the light beam only partially. Some particles will never be detected because of too small a shadow cast by the part that came into the beam. Others will be detected as smaller size particles depending on the area of shade. The number of particles reported by the sensor is smaller and/or the size distribution is altered. At the same time the detection of particles partially outside the beam means that the effective area of detection is bigger than the beam area (and is variable!). This in turn means that the correction to the sampling volume due to clipping particles is needed. The corrected value should be used for example, for calculation of • the limit of particle concentration above which two or more particles are probable in the sampling volume, • the particle number flux from the registered number of particles per unit time. One algorithm of correction is suggested in Brown and Pomeroy (1989). It requires knowledge of the parameters of the particle size distribution. Savelyev et al. (2006) pointed out another implication in the case of particles 125 just clipping the beam. Even when the shade is big enough for the voltage drop to be detectable the time of travel through the beam could be smaller than the electronics can handle - the particle will not be registered. The limit of speed attainable by electronics will also effect the results of detection if the separation between the two consecutive particles is too small. Depending on the actual design the second particle could be missed or two particles can be counted as one (of bigger size). Obviously, this leads to a decrease in the upper limit of particle concentration under which the correct detection is possible. 5.2 Parameters suitable for detection Although it is possible to employ a photovoltaic cell as a detector in a photoelectric counter and have the voltage as the signal the accuracy considerations dictate that the output current directly depend on the energy of incident electromagnetic waves. A current to voltage converter is the first stage in the circuitry after the sensor with the rate of change of voltage monitored. The sketch in Figure 5.2 helps to visualize the relationship between the change in area of shadow cast by a particle on the sensor surface and the time variation of voltage. The bottom panel of the figure shows the sensor area that remains illuminated as particle progresses. The shape of the curves gives us an indication of the possible shapes for the voltage waveform. The sensor voltage is proportional to the illuminated area which can be 126 ^ •*• •• • • • ••^ Sensor eCDn "1 "I ro - — "\_ ^ ^7 •5 1 : > - 1 1 1 11 II I I I 1 1 II 1 11111 1 1 1 1 1 1 1 1 1 Time Time Time Time Time Time Time instant: tl tl.5 t2 t3 u „ 8 — tl t E 2 t3 u 00 fa 6 — Particle Diameter 1 4^ 1 U (XI11 - 100 urn T3 _ . .12- - 200 urn £ t - 300 urn I I J i 1 ' 1 C) 10 20 30 40 Time (us) Figure 5.2: Particle moving through the light beam. Top : Succession of particle positions along the trajectory. Middle : Time variation of the voltage at the sensor. Each graph ends at the time instant corresponding to the position at the top panel. Bottom: Time change of the lit area due to shadow cast by particles of different diameters on the sensor surface. Particles move with 15 m s_1 velocity. Sampling area is of 300 (j,m diameter. Time instants are shown for the 100 //m diameter particle (blue line on the graph). obtained by subtracting the extinction cross section area of the particle from the total sensor surface area. For now we will consider the the extinction cross section 127 to be equal to the particle's cross section and discuss their differences later. The voltage at the sensor decreases to the value determined by the particle size or to the minimum value if the whole beam is covered. This relationship suggests we monitor the absolute value of the voltage drop in order to size the particle (e.g. Gubler, 1981). The procedure will only work for particles smaller than the sensor field of view. Almost all particle counters developed monitor whether or not voltage decreases below some threshold. If this happens then it is assumed that a particle was sampled. Some devices only count the number of particles in the sampling area during a time interval (Brown and Pomeroy, 1989; Savelyev et al., 2006). More complicated counters use two sampling volumes in the line of particle movement to register a sequence of appearances of the same particle. The time between appearances is measured and is used together with other parameters to calculate particle speed (Sato et al., 1993; Schmidt, 1977). The time between the start and the end of the voltage change is related to the combination of the sensor field of view dimensions, the particle size and speed. This time interval can also be monitored. With sensor dimensions known and particle speed estimated the particle size can be calculated. This technique is used in the third generation counter developed at York University and reported in this thesis. 128 5.3 Limitations of beam interruption detection The variation of the electromagnetic energy reaching the sensor is due to intercep tion of a fraction of the energy by the particle. The particle may absorb, reflect or refract some of the energy. For this to happen the path of the electromagnetic wave should go through the space occupied by the particle. There is yet another process that will lead to energy of the source not reaching the destination. It is a diffraction of electromagnetic waves by particle edges. Diffraction involves the energy around the particle. So the cross sectional area of space that includes all affected waves is slightly bigger than the geometrical cross sectional area of the particle and it is called the extinction cross section. The ratio of the extinction cross section area to the geometrical area of the particle is an extinction coefficient Qext- For big enough particles (this condition can be stated fairly precisely) the extinction coefficient can be around 2. This means for example that a 300 /mi diameter sensor will be completely shaded from the light source by 212 /mi diameter particle (provided no light is scattered into the sensor). The extinction coefficient is wavelength de pendent. Pomeroy and Male (1988) calculated the value of the Qext based on Mie scattering theory for different wavelengths of incident electromagnetic radiation. It is evident from Figure 2 of their paper that due to oscillation of the value of Qext in the small radius region of particle sizes there could be situations when a smaller 129 particle causes a larger extinction than a slightly bigger particle. The situation becomes more pronounced as wavelength increases. This means that estimation of particle size based on the shadowing of the electromagnetic wave loses accuracy in the small size region and the extent of the low accuracy region increases with the wavelength. Some of the electromagnetic energy intercepted by particle with a certain effec tive cross section may reach the detector surface due to diffraction and refraction of the electromagnetic waves. In this case, the extinction coefficient Qext has to be corrected for those processes. This results in an effective extinction coefficient Qeff- Apart from the wavelength the impact of diffraction and refraction depends upon detector size (and geometry), the particle size and its position in the sampling volume. These effects can be estimated. For examples of calculations for simple particle - detector geometries, see Brown and Pomeroy (1989) or Mishchenko et al. (2009). Note that the result is highly oscillatory depending on the position of the particle in the light beam. In addition to the particle extinction cross section, the shape of the voltage drop waveform is also influenced by the electrical characteristics of the sensor and circuitry. A certain level of irradiation is needed for the output to change state, say from low to high, that is for a pulse to be produced. This limitation manifests itself, for example in the voltage starting to decrease when some portion of the 130 particle is inside the sensor field of view instead of in a position when the particle just touches it. An analogous situation happens when a particle leaves the field of view. As a result, the time interval between the start and the end of the voltage change is smaller than the time actually needed for particle to cross the field of view. A different situation happens when a particle is almost as big as the field of view. At the bottom panel in Figure 5.2, the illuminated area of the 300 /mi diameter sensor is zero at the instant when the 300 /mi diameter particle is exactly at the position in front of the sensor and we expect voltage to be at its lowest. As discussed above this actually can occur with a smaller diameter particle. Because of sensitivity limitations, the voltage drops to its minimum a bit earlier, when a smaller area of the sensor is still illuminated. From the point of view of the illuminated area, particles with an extinction diameter bigger than the field of view are indistinguishable. But because of the sensitivity implications the upper limit of distinguishability is even smaller. Yet another limitation imposed by the sensitivity results in particles smaller than a certain threshold not being detected at all because they do not cause a measurable voltage decrease. Figure 5.2 (bottom panel, purple line, 10 /mi particle) suggests that small particle will cause little decrease in output voltage. The line corresponding to the illuminated area for a 10 /mi particle is almost flat compared 131 to lines related to particles of a bigger size. The voltage drop waveforms may not retain the same scale of the relationship because the extinction coefficient is not linearly dependent on the particle size in the infrared region. Still the difference in voltage waveform for small and big particles warrants provisions in the counter design that facilitate the detection of small particles. One way to achieve the wide range of size detection is to use a logarithmic scale when converting current into the photodiode to output voltage. The photodiode in this case is used in photovoltaic mode (Placko, 2007). 5.4 Electronics design of the York University particle counter After receiving a berth at the CCGS "Amundsen" to participate in the CASES04 expedition, we were confronted with the necessity to build particle counters on a fairly short notice. Thanks to John Pomeroy we were given one of the particle counters described in Brown and Pomeroy (1989) and its schematic. Unfortunately, some of the key electronic components had been out of production for some time already. Specifically, the light emitting diode (LED) and the photo-detector com prised of a detector diode and transimpedance amplifier were not available. So the counter schematic was redesigned taking into account that photo-transistors are now used as photo-detectors and the current to voltage converter (transimpedance amplifier) is implemented on a separate operational amplifier. 132 +12V Q2,Q3 2N3904 U1A U1B U2A LM158 LM158 LM158 Photo- Current-to-Voltage Comparator Output Detector Converter Figure 5.3: Circuit schematic of the particle counter used in CASES04. Figure 5.3 depicts the electronic design solution of the counter that was used in CASES04 save for the part responsible for conditioning of the power supply. The emitter of the phototransistor is negatively biased against the virtual ground of the collector. A 9 V battery was used to provide a bias and a negative polarity power to dual supply operational amplifiers. A positive 12 V supply to the operational amplifiers was taken from the data logger battery. The output voltage VOUT of the transimpedance amplifier in this configuration is given by expression VQUT = Ic x RI where Ic is the collector current of the photo-transistor and i?x is a feedback resis- 133 tance. The dependance of output voltage on the irradiation intensity is near linear in the small irradiation intensity region. 5.5 Physical realization of counters Figure 5.4: Physical dimensions of particle counters (in millimeters). Counters are shown in operational position, mounted on vertical post. The insert shows a nozzle with an aperture that limits photo sensor's field of view. The diameter of the aperture on devices used in CASES04 was 150 /mi. 134 Mechanical realization of counters has to satisfy two conditions - provide as little wind flow interruption as possible and be sturdy enough to maintain LED - photo detector geometrical coupling throughout the measurement cycle. Units were designed and assembled at the York University's Faculty of Science and En gineering machine shop. An aluminium frame supports the circuitry box with a nozzle attached to it and the Light Emitting Diode on the opposite side. The LED beam and the opening in the nozzle are aligned along a common optical axis and are 20 mm apart. There is a provision for LED holder alignment. The hole in the nozzle limits the portion of the light beam that reaches the photo sensor. With this arrangement, the sampling volume is a cylinder with a base determined by the hole size and a length of 20 mm. Counters used in CASES04 had 150/wn aperture diameter. Figure 5.4 depicts two counters in the field installation. Major physical dimensions are presented. The hole was drilled in the nozzle and was cleaned from small scales formed during drilling. There was a concern of the hole coming clogged by snow particles but this was not observed to happen. Note that the aperture is at the top of the sampling volume. 5.6 Calibration of photoelectric counters The quantitative utility of measuring devices relies on their calibration. Only when the output number from the sensor can be referenced to some known quantity can 135 it be used in analysis. The photoelectric counters are usually tested with spinning wires and their snow mass transfer measurements are calibrated against the filter- fabric traps. The latter make sense not only for those devices that measure particle sizes directly but also for devices that count the number of particles, such as the counter type of Brown and Pomeroy (1989). It is customary in field experiments to relate several similar devices to one that is either factory calibrated or considered to produce accurate data. If there is uncertainty with respect to all instruments, the intercalibration is still useful especially if the instruments are planned to be installed to give simultaneous, profile measurements. Several calibration runs were performed with particle counters in winters 2004/05 and 2005/06 on the ice of a freshwater lake in Churchill, Manitoba. A typical installation is shown on Figure 5.5. An example of particle counter time series from a calibration run on January 29, 2005 is presented in Figure 5.6. Readings from three units are quite different at the beginning and at the end of the blowing snow event when there is little snow in the air. At higher winds Units 2 and 5 measure similar number flux while Unit 4 output is significantly lower. Nevertheless, data from all units is well correlated as it can be seen from Figure 5.7. The coefficient of determination is better than 0.96. This gives support to the assumption that a correction coefficient can be used in each case to relate the output from all units to a particular one. The discrepancy 136 Figure 5 5: Calibration arrangement of several units at the same height above the ice. Churchill, Manitoba. Winter 2005/06. in the output of different units can be related to the different minimum detected by each unit particle size. Each unit outputs the sum of number of particles in their actual distribution counted starting from a certain minimum diameter. The upper limit of detected particle diameters can be considered the same for all units. If one unit has a larger minimum detected diameter than the other then the sum of counts for this unit does not include a portion of small size particles that the other 137 unit is able to count. At the beginning and at the end of the calibration run the wind speed was low and only small size particles were in suspension. In this case the difference in the minimum detected size had a bigger effect on the discrepancy in the total number of particles registered by two units because the fraction of large particles common to the sum counted by each unit is smaller. 29 29.5 DOY, 2005 Figure 5.6: Time series of particle counts from three detectors installed at 50 cm above the ice. 2005/01/29, Churchill, Manitoba. A post-CASES calibration experiment at a Trent University (Peterborough, Ontario) wind tunnel was aimed at providing correcting coefficients similar to those 138 0 20 40 60 0 20 40 60 Unit 5 counts Unit 5 counts Figure 5.7: Scatterplots of data from different units against each other. mentioned above. Units in pairs were inserted into the air stream that carried plastic particles simulating snow. It was discovered from the counters output, despite the fact that units were placed close to each other, that the difference in flow at the two positions was significant. This prompted us to run comparisons twice for each pair switching places of the units between runs. Employing the assumption that output from a particular unit is proportional to the particle concentration in the air and that the coefficient of proportionality is constant, the correction coefficients were calculated. We did not actually use these coefficients to correct data from CASES on the grounds that artificial snow size distribution differ from the actual snow particles size distribution. In addition, we later discovered that the minimum size detected by a counter depends on the wind speed. This latter fact 139 partially invalidates the assumption of the constant proportionality coefficient. 5.6.1 Spinning wire calibration It appears that all developers of counters reviewed in this work used a spinning wire of fixed diameter to simulate a particle crossing the light beam in order to check the ability of the devices to register beam interruption. The only quantitative assessment was of the maximum frequency of interruption that the particular device was capable of registering. This estimate was obviously valid only for the size of wire used. The ability to handle a certain frequency of interruption that was significantly higher than expected in the measurement environment was taken as a proof that the device will count without much error in all environmental situations. One can easily see that utility of the wire test can be extended by employing wires of various diameters. Taking into account the discussion presented in section 5.3, it can be realized that the size of the wire and the actual position where it crosses the sampling volume can have a significant impact on the result of the test. By repeating the test with wires of increasingly smaller diameter one can expect to approach the threshold of counter sensitivity. It would be important to know the minimum size of the particle moving with a specified velocity that can be detected, and whether this threshold size varies with position of particle in the sampling volume. In order to provide more accurate calibration information we devised a 140 series of tests with wires of different diameters. We were fortunate to get samples of wires as small as 40, 25.4, 12.7, 10.16, 7.62, 5.08, 2.54 /xm diameter and be able to put them on supporting frames (wheels) of different sizes and design. Table 5.1 helps to set reference points to sizes we used in calibration. 2.54 /xm diameter is about the limit of what we could see and handle. Table 5.1: Characteristic sizes of some physical objects in 2 - 70 /xm range Object Size (/xm) Smallest blowing snow particle 1-5 Human hair thickness 50 - 70 White blood cell 25 Talcum powder granule 10 Red blood cell 8 Bacteria 2 Martian dust 2 To relate the wire thickness with the diameter of a spherical particle we take into account that the sensor voltage drop is related to the amount of electromagnetic energy not reaching the sensor. Recollect that in one of the preceding sections the shading of energy was discussed by considering first geometrical, then extinction and finally effective extinction area of the obstructing particle. If a cylindrical 141 wire is considered, the geometrical area of its intersection with the portion of the light beam that reaches sensor, AWXb will be at maximum at the position shown in Figure 5.8. The maximum geometrical shade A™t cast by a wire when placed into the light beam from the LED equals the area of the ABCD shape and is close to the product of wire thickness and sensor diameter. The spherical particle that casts the same geometrical shade when in the center of the light beam would have a diameter Deq equal to /4 \!/2 /4 \V2 Deq=(-A™l) ~(-Dpovxdw) , (5.1) where Dpov and dw are field of view and wire diameters, respectively. We call Deq a diameter of equivalent sphere or equivalent diameter. Table 5.2 lists diameters of "equivalent" spheres that give the same shade area as the wires for two sizes of the sensor field of view. Although the wires are small, when this area was compared to the area of the shade cast by the spherical particle it became clear that, with the set of wires at hand, we could not cover particle diameters smaller than 25 /tm even for a 200 /xm diameter aperture. The exact correspondence of a spherical particle diameter to the size of wire that causes the same amount of electromagnetic energy reaching the sensor re quires calculation of extinction and effective geometries of the wire as well as a spherical particle. This calculation was not done for the wire. We proceed with empirical measurements bearing in mind that the correction to conclusions based 142 on geometrical dimensions due to diffraction and refraction are warranted. Figure 5.8: Sketch of wire in serted into the center of sensor's field of view. At this position the area shaded by wire (outlined by Sensor c Field of red line) is maximized. View Wire Wire diameter Sensor diameter Table 5.2: Diameters of "equiva (microns) 200 300 lent" spheres (microns) that cast 2.54 25.44 31.14 the shade of the same geometrical 5.08 35.96 44.04 area as thin wires. Two sensors of 7.62 44.04 53.94 different diameter are considered. 10.16 50.86 62.30 12.70 56.84 69.64 25.40 80.32 98.44 143 5.6.1.1 Minimum detected particle size Ideally, with a set of wires of any required size available the minimum detected size can be found. One can simply spin wires of progressively smaller diameters until the smallest detectable is established. In reality one can hardly go below a 2 /mi thick wire and even this size results in equivalent particle diameter significantly bigger than 2 /xm as was demonstrated above. In the following we present a procedure intended to mitigate the limitation imposed by the smallest available size of wires that could be installed on the frame. Two factors can be considered to potentially limit the smallest detectable size - the minimum electromagnetic energy reaching the sensor required to cause the change of state of the device, and the signal to noise ratio. In the following discus sion we assume that the signal to noise ratio is high enough and that the sensitivity of the device is the limiting factor. The sensitivity itself can be separated into limi tations of the photo-detector and limitations of the monitoring part of the circuitry that signals the decrease in voltage. Let us direct our attention to the monitoring part of the circuitry first. It takes the voltage from the current-to-voltage converter (refer to Figure 5.3) as an input. To measure the minimum voltage required for the monitor to change its state, we emulate the output from the detector-transimpedance amplifier with the help of 144 a signal generator. The photo-detector is completely covered from the light beam but remains connected. This ensures that the dark current is present as it would be during the measuring cycle. The pulse generator should provide the ability to change the pulse amplitude. The amplitude of the signal is decreased until pulses at the counter output cease to be produced. This amplitude is taken as a minimum required drop in voltage AVmin at the detector output. Now we turn our attention to the detector and try to find out the size of the particle that would result in the minimum (discernible by monitoring part) voltage drop measured on the previous step. To accomplish this we measure the voltage drop by placing obstacles of known size into the sampling volume. Having several empirical pairs of (AV, ASh) where AV is a drop in voltage caused by an obstacle of area ASh one can establish the empirical relationship denoted in the general form as AV = f(Ash). (5.2) From Equation(5.2) we can find the Amm corresponding to AVmm of the previous 1 step, namely Amin = f~ (AVrmn) . Finally, converting Amm into dmm we find the diameter of the smallest detectable particle. The actual calibration assembly is shown on Figure 5.9. The wheel with wires of different diameters is attached to the motor with a tachometer - an instrument that allows measuring of the angular speed of rotation. The latter is not needed for 145 the test we are about to describe but will be used in another calibration procedure. A micrometer is used as a translation table when rotating the wheel manually in order to place the wire precisely into the center of the light beam. The drop in voltage caused by beam interruption is measured by a precision voltmeter. The assembly allows us to accurately put the wire in front of the pin hole and find the position when the sensor output voltage is minimum. It is the position sketched in Figure 5.8. We know that the amount of energy still reaching the sensor depends upon the position of the obstacle in the sampling volume as well as on the geometry of the obstacle. So the value of AV will be different for the same wire but at different positions and thus the experiment should be repeated to find out the threshold detected size at various places of the sampling volume. Figure 5.10 presents a summary of the first part of the procedure for Unit 8. Each set of A V, Ash pairs taken at the same position in the sampling volume is approximated by a polynomial. Data sets and respective polynomials are shown together. AV is plotted against wire diameter instead of Ash because for a given sensor area Ash is proportional to the wire diameter. Note that dependance (the form of Equation 5.2) is not linear. Also comparing measurements made with sets of wires at different locations of the sampling volume it is clear that when an obstruction is closer to the light source it shades comparatively more energy. One can expect that farther from the light source the sensitivity of the device decreases. 146 Figure 5.9: Calibration assembly consisting of the wheel with thin wires, DC motor with tachometer, micrometer as a translation device (front of the picture), pulse generator (on the right). The minimum detected wire thickness resulted from the two-part test are pre sented in Table 5.3. At the position closest to the light source the voltage drop due to shadowing by 1.9 /xm diameter wire is enough for the counter to change state. While at the farthest from the source position a wire of 4.9 /xm is needed for the same event to happen. The test described here allows us to determine the threshold of detection even when we do not have a wire as small as the device sensitivity warrants. Moreover 147 2 mm 500 3 mm 5 mm 400 7 5 mm 9 mm > 11 mm 14 mm E, 300 oa. y 16 mm u_ 18 mm Q 0 -i 10 15 20 Wire diameter (u.m) Figure 5.10: Drop in sensor voltage produced by wires of different diameters put into the light beam at different distances from the sensor. Similar symbols denote results of the experiment with different wires at the same position in the sampling volume. Solid lines are polynomial fits to respective experiments. even when the sensitivity is such that a set of available wires allows us to directly test detection by rotating wires through the sampling volume, the discretization error introduced by the difference in consecutive wires thicknesses could be too large. In such a case, the present test can provide more accurate estimates. The relationship that we assumed to exist is between the voltage and the energy 148 Table 5.3: Minimum detected wire diameter (calculated) at various positions in the sampling volume. Results of the two-part test for Unit 8. Distance from LED (mm) 2 3 5 7.5 9 10.5 13.5 16 18.5 Diameter (/xm) 1.9 2.1 2.5 3.2 3.5 3.7 4 4.7 4.9 reaching the sensor expressed by the effective extinction area. In other words, the variable Asu in the Equation (5.2) should be the effective extinction area. It has to be calculated from the geometrical area of the wire projection on the sensor area employing the theory of electromagnetic wave propagation. Then the result of the test will be the minimum possible effective extinction area of the wire and we take it as the threshold effective extinction area of the spherical particle. The latter should be converted into the geometrical area of the particle and ultimately into its diameter. The procedure we followed to get the results presented in Table 5.3 was altered slightly. The variable Ash was a geometrical area of the wire shade. An implicit assumption was that the geometrical area is related to the effective ex tinction area and thus the empirical relationship between voltage and geometrical area is meaningful. As a result we have obtained the threshold geometrical area. To calculate threshold spherical particle diameter one has to calculate the thresh- 149 old effective extinction area of the wire first, equate it to the threshold effective extinction area of the spherical particle and then calculate the minimum detected particle diameter. In the following we present a summary description of the test and emphasize the differences between two approaches. Minimum detected particle diameter test Part 1 Use the signal generator to emulate the output from the detector. Feed the signal to the decision making part of the circuitry. Decrease the signal amplitude until the device stops detecting the input voltage variation. Take the minimum signal amplitude as a minimum required drop in voltage AVmin at the detector output. Part 2 Place a wire of known thickness into the particular location in the sampling volume such that it covers the largest area of the field of view. Measure the voltage at the output of the current-to-voltage converter. The shade is maximized when the voltage is at a minimum (the voltage drop is the largest). For the set of wires at hand obtain empirical pairs of (AV, dw) where AV is a drop in voltage and dw is a wire diameter. Branch A Branch B 150 Use GL and field of view size to cal culate the geometrical area of the shade. Calculate the effective ex- Aeff J J tmction area As h . e f Using (AV,A /h ) pairs es- • Using (AV, dw) pairs establish em tablish empirical relationship pirical relationship e f AV = f(A /h ). AV = e l m • Find A H = f- (AVmm) where • Find <% = r\^Vmm) where Vm,n was measured in Part 1. Vmm was measured in Part 1. • ... • Calculate the threshold effective ex tinction area A^n for the wire of diameter d™m. Assume that A^n is a threshold effective extinction area of the spherical particle. Calculate the corresponding geometrical area of the spherical particle and then its threshold diameter. 5.6.1.2 Dependance of the minimum detected size on particle velocity The sensitivity of the photoelectric counter or its ability to detect beam interruption is also limited by the speed of the signal processing. Small particles crossing the beam on its periphery remain in the field of view for a very short period of time. 151 One can hypothesize that even small particles with trajectories through the beam center can be missed if their speed is too high for the circuitry. With spinning wires we can assess the speed limitation for particles with through-the-center trajectories. The corrections then can be developed to account for partial interruption of the beam periphery. The calibration assembly consisting of DC motor with tachometer and wheel with wires was used to assess the influence of the particle velocity on the ability of the counter to detect particles. The tachometer provides us with reasonably accurate estimates of the angular speed expressed as RPS - rotations per second. The linear speed of the point on wire where it crosses the beam is calculated as U = 2TT x r x RPS (5.3) where r is the distance from the point of beam crossing to the center of rotation. Knowing the number of wheel rotations per second and number of beam inter rupting objects Ngpikes (wires and wheel arms) on it one can predict the maximum number of counts per second that a detector could possibly register, Ncounts = Nsplkes X RPS. (5-4) If the actual number of counts the device output is smaller than this number then one can infer that some of wires were not counted. Wires were put on the wheel in 152 groups each containing N^ wires of identical thickness di so that i where 2 is due to the number of wheel arms. When the speed of the beam crossing exceeds the threshold speed of detection of certain diameter wires from the ith. group, the output number of counts decreases sharply by A^, x RPS and is easy to notice. Equation (5.4) still holds but with Nsphkes decreased by A^. An example of speed test is presented on Figure 5.11 for two devices of similar design but implemented on electronic components with different parameters. Unit 7 detects all wires until the linear speed of the crossing point exceeds 23 m s_1 when counts drop to the value indicative of the number of wires for the combination of bigger diameter groups. Note also that around 20 m s_1 the counts start to deviate from the maximum possible number. This can happen if some wire in the 10.16 /xm group is slightly thinner than the rest. Unit 16 does not detect the 10.16 /xm group at all and it is clear that its performance started to degrade at a relatively slow crossing speed. For this particular unit a change in design or choice of different components is indicated. At the end of the speed test we have a set of crossing speed numbers related to a discreet set of wire diameters. In order to get a continuous functional dependance of crossing velocity allowing the detection on the object's size we can fit the curve 153 0 5 10 15 20 25 Velocity (ms^) Figure 5.11: Counters readings of beam intersection by wires of different diameters for various speeds of crossing. Unit 7 - circle symbols, Unit 16 - diamond symbols. There are three groups of identical diameter (10.16 /xm, 12.7 /xm, 25.4 /xm) wires in each group placed on the wheel. Solid lines are maximum possible counts if all wires in groups with wire diameters indicated next to the line are detected. to pairs of (speed, size) points we've got from the test, i.e. to find an empirical relationship. Now for every value of the particle velocity we are able to calculate the minimum detected particle size. Of course, the conversion of wire size into the effective extinction size and ultimately into the particle geometrical diameter as 154 explained in the previous section has to be done. 5.6.2 Calibration for specific purpose For some specific applications one may not need the detailed calibration of the counter and only an empirical relationship between the counter output and mea surements of a different parameter would suffice if those measurements come from a calibrated device. As an example of this approach is the use of counters to give information on visibility. Visibility or Meteorological Optical Range (the term used by the Me teorological Service of Canada) is defined by the maximum distance the object of 1° angular span can be discernable by an observer. A more objective criteria is given by requirement of a minimum 2% contrast between a black object and white background. Airborne particles may absorb a fraction of the optical energy and scatter the remainder of it. This leads to the reduction of light energy reaching the observer and to the decrease of the contrast between objects. The end result is a decrease of visibility. The process of light leaving the object, travelling through the air, being absorbed and scattered, and finally reaching the observer takes so little time that it can be considered to happen in an instant. There won't be detectable change in airborne particle population or their positions during this time. The vis ibility can be considered to depend on the instantaneous state of the particle cloud. 155 The output from the optical counter on the other hand results from a succession of individual detections in a certain period of time. If there is a correlation between number of detections, i. e. particles (and their distribution if size is measured) reg istered during the measuring cycle and the number of particles and size distribution of the volume of the instantaneous particle cloud (which can be taken as an average during the measuring cycle) then parameters provided by counter can be used as an approximation to parameters that determine the visibility sensor readings and ultimately be used to approximate visibility. 10- O 1 0.1 -I—I—I I I I I n—i—i i i ii ii 1—i—i i i i i u 0.001 0.01 0.1 Number Density (cm-3) Figure 5.12: Relationship between Meteorological Optical Range measured by vis ibility sensor at 1.5 m height and number density calculated from particle counter data at 2.0 m height. Measurements are made during CASES04. Power fit (solid line) is for the number densities greater than 0.01 cm-3. Coefficient of correlation R2 = 0.93. 156 Figure 5.12 shows the relationship between the Meteorological Optical Range (MOR) expressed in kilometers and data from Unit 2 as was established during a calibration run in February 2004 in CASES. An exponential formula MOR = 0.13 x (ND)-1-01 (5.6) is a parameterization of the visibility that uses ND (number density) derived from particle counts and wind speed at 2 m height. The coefficient of determination R2 = 0.93. Post experiment evaluation of the relationship (based on data from the whole experiment) showed that the value of R2 is somewhat lower but still better than 0.85. 5.7 Modifications to the original counter design After realizing that the original design of the York University particle counter may not provide consistent measurements for all wind speed velocities that can be en countered in the intended applications, a change in the electronic and mechanical design was implemented. As a mechanical improvement we considered placement of an optical fiber into the counter nozzle. The optic fiber carries light from the opening of the nozzle hole to the photo-detector. This provided us with a field of view size consistent between units. The fiber that we use now has a 200 ± 2 /xm core diameter and it is the size of the fiber core not the size of the hole that determines 157 the size of the detector field of view. The clogging of the hole is not a problem any more. The optical fiber also alleviates difficulties related to the alignment of the nozzle hole axis which had to be done very precisely without the fiber. Now the optic fiber and the photo-detector are coupled using techniques well developed in optical communications. The phototransistors (they were used in the original design) have a rise/fall times on the order of microseconds. This is the time needed for an output to reach its 90% magnitude starting from 10%. Obviously the rise/fall time determines the time scale of the fastest output pulse, and in doing so the maximum frequency of the input signal that can be handled by the detector. It was decided to replace photo- transistors with photodiodes that have rise/fall times on the order of nanoseconds. The performance of a photodiode depends on whether it is used in photovoltaic or photoconductive mode (Johnson, 2003). In photovoltaic mode the noise is low and the output is linear. In photoconductive mode an reverse voltage is applied across the diode which lowers its capacitance and allows for faster speed. So the former is used in situations when precision is of importance and the latter when speed of operation is more important than accuracy. There are two qualities one would want to have in optical an photodetector: high sensitivity to detect small particles and high speed of operation to detect fast moving particles or to avoid missing closely spaced particles when the concentration 158 is high. Often the solution to gain one quality leads to the degradation of the other. Photodiodes have an internal capacitance. Capacitance slows the speed of operation. The smaller sensitive area has a smaller capacitance. To achieve a high speed one chooses photodiodes with a smallest possible sensitive area. At some point this area can become smaller than the light beam cross section. The solution to this problem can be achieved by collecting the light energy of the beam by a relatively large lens and then directing it to a sensor with a small area. In the design of the second generation devices depicted in Figure 5.13, the reverse voltage is applied to the photodiode. The capacitance decreases and so does the speed but a large reverse voltage results in an increase of the reverse current. A reverse current through the diode increases noise. A high noise level (low signal to noise ratio) will bury the signal from small particles making their detection impossible. The variable resistor VR2 allows us to set the threshold for detection of the signal to be bigger than the noise level and thus prevent false counting. Note also the faster, compared to the previous design, operational amplifiers powered from one polar source. All post-CASES particle counters of York University are of the design discussed in this section for which a speed of operation is the first priority. 159 CI Rl +9V 4.7pF .. 100k D2 1N4148 Dl U1A U1B U2A Q2, Q3 OPF480 TLC082AIP TLC082AIP TLC082AIP 2N3904 Photo- Current-to-Voltage Comparator Output Detector Converter Figure 5.13: Circuit schematic of the second generation particle counter. Photo diode detector is used in photoconductive mode to gain speed of operation. 5.8 Counter with ability to measure particle time-of-flight The counters of Brown and Pomeroy (1989) and York University have a small number of components, are inexpensive, and can be run in remote locations because of low power consumption, output data suitable for recording by a station data logger, are robust, and do not require daily maintenance. Their deficiency is an inability to measure the particle size distribution; the number flux is the only output parameter. We decided to develop our counter into a device that can measure the particle size in addition to counting individual particles. The idea was to use 160 the existing counter as a front end with no mechanical and as little as possible electronics change. A sizing part was developed as an addition to the existing circuitry that we can put either together with the front end or at some distance from it. As discussed earlier, the parameters that can be monitored are the magnitude of the voltage drop which depends on the particle size and time needed for a particle to cross the field of view (time-of-flight). Because of the requirement to have no more than one particle in the sampling volume the field of view is small. Any particle with a size equal or greater than the field of view causes the same voltage drop. This means that the range of sizes that can be monitored is narrow and limited by the field of view dimensions. The time-of-flight is reflected in the duration of detector voltage being lower than the voltage produced by the unobstructed light beam. If the output of the decision making part changes state when voltage begins to drop and remains in this state until the voltage is almost restored and then switches again then we have a pulse duration which (almost) equals the time-of- flight. Sensitivity limitations will cause the pulse duration to be slightly less than the time of beam crossing. Time of crossing can be related to the particle size only if one knows the particle's speed. The field of view dimensions are assumed to be known. For the time being, we rely on the accepted paradigm that mean speed of the blowing snow particles 161 is the mean flow velocity. The flow speed should be measured simultaneously by some other sensor. We would like to mention at this point that if an independent particle velocity estimates can be made then the assumption regarding relationship between particle and fluid speed can be investigated depending on the accuracy of the device. Although the small field of view limits the range of sizes that the counter can monitor one can still at least measure the size of small particles and, with the time-of-flight measured as well, compare mean wind speed with particle's velocities. Time interval measuring is usually done by filling the interval of unknown du ration with pulses of fixed length. The latter is produced by a fixed frequency oscillator. The diagram on Figure 5.14 explains how measurements of pulse dura tion are done and stored by the third generation of York University counters. There are 32 bins that divide the range of durations into equal intervals. Based on the actual pulse duration the circuitry determines which bin it belongs to and signals to increment the number of occurrence pertaining the particular bin. The microcon troller keeps watch and allows measurements to proceed for 30 seconds. At the end of the 30 second interval the content of all bins is output and bin counters are reset to zero. Two protocols can be used to wrap up data into packages, RS-232 and RS-485. On the other side of the communication link, the computer with software that understands either one of protocols is expected. For simple tasks of monitoring 162 1 r TRIMMING nnnn ADDRESS BIN# MAKING BASED ON 1 INPUT PULSETRAIN LENGTH 2 jinmRjirui PULSE TRAIN 32 GENER. MEMORY CELLS ONE PULSE PROCESSING N, N2 M I k DATA w k N3 PACKAGING ^ INPUT OUTPUT 30 seconds of N INDIVIDUAL 32 INPUT PULSES MEMORY PROCESSING CELLS SEQUENCE OF PULSES PROCESSING Figure 5.14: Signal processing flow chart. Each pulse is measured in terms of pulses of known duration generated by processing circuitry. Signal pulse duration is assigned to one of 32 bins based on its length. The counter of the respective bin is augmented. This sequence is carried out for 30 seconds. The accumulated counts in all 32 bins are output at the end of a 30 second interval in one of two available serial port protocols. 163 the program called HyperTerminal can be used (it is standard on Windows based computers). I-12V GND DA2 -jvi uvo| C1 ; DA1 l-12V 470M .100W MCP101 LM2931Z-05 C5 C6 BOI M 2P M47 M47 GND 22118 KHZ 2 GND aji C9 DD5 :i+ C2 + DD3 I :i- C2- M47 C7 oc V 22P •CC CLK cm 2 DD4A M- 19 T1I ^_ 3_ ID 1Q 18 Tie 20 20 17 +5V 2 £ 3D 30 C8 T21 T20 4 ~~ IS ^ 4D 40 16 M47 +5V S 6 50 5Q J5 __ ?1B « 7 R11 8 6D 60 70 70 13 SN74AC02N •1I C 9 Mr w m 80 12 GND ST232 GND AT89C2051 -24 74HC574S GND" +5V 74AC4040S +5V GND liliJULUlii DD8 2 , I XT2 "S" * ^ . ... oc DD7 | R1 XT3 I 50 0'(19 660)Tfe ac "- CLK 1K8 U •+; 6V8 2 ^Slf , 3 ID 10 1 4 2D 20 GND , 5_ 3D 30 VD2 4D 40 R2 C10 15 6 /™L 7 50 5Q D "* XT4 60 60 *• || GND ,33P SiT1 8 7D 70 +5V GND 74HC574S 10KV +5V COUNT_ DIGITAL SCH GND VCC Sun Jun 13. 2210 Figure 5.15' Circuit schematic of the time-of-flight measuring device. The electronic schematic of the digital part of the counter is presented on Figure 5.15. The design is based on an Atmel AT89C2051 microcontroller. It is an 8-bit low-voltage microcomputer. Operating temperature is rated down to -55 °C which makes it an ideal candidate for low temperature applications. An on-chip amplifier for our purpose is configured to serve as an oscillator with a quartz crystal as a resonator. Power supply voltage to the microcontroller is held at 5 V by voltage stabilizer MCP101. There is a primary voltage stabilizer built on the LM2931Z 164 chip that provides + 5 V and + 12 V power supply. All logic chips used in the design require only one supply voltage. The hex inverters of SN74AC02 provide logic necessarily to cut the fixed frequency pulse train into pieces of length equal to the signal pulse length. The CLOCK signal is also generated to indicate the end of the input pulse. The truncated piece of the pulse train is processed by the 74AC4040 binary ripple counter. As a result, the input signal pulse duration is coded. When the CLOCK signal indicates the right time, the code formed by the ripple counter is written into the high speed logic flip-flop 74HC574S. Here code is translated into a memory address according to the programmed bins start-end pairs. The binary counter 74AC4040 registers are zeroed on CLOCK and ready for the next pulse train. The ST232 and AD485 components are RS-232 and RS-485 serial port drivers-receivers, respectively. RS-485 protocol not only allows a longer communication link (maximum length close to 1200 m compared to 3 m of RS-232) but also the connection of several devices to the same computer. 5.9 Possible development of York University counters The second generation of the York University particle counters are designed to achieve high detection efficiency in fast moving particle-laden flow. There are also applications when the monitoring of particle load in almost motionless fluid is de sired as, for example, in ice fog. The ice fog particle size is on order of microns and 165 even smaller. High sensitivity is a priority in this case. Changes to the existing de sign are possible to fulfil requirements of low noise high precision applications. The photodiode should function in photovoltaic mode (Johnson, 2003; Placko, 2007). The comparator part of the electronics scheme changes the output state when ever voltage drops below a reference point. This reference point is taken to be relative to the maximum voltage attainable with an open optical path at the mo ment of measurement. The maximum voltage may vary depending on the working temperature. Fixing the comparator switching level would have resulted in a vari ation of the minimum detected particle size with temperature. That is why we employed a design that allows for the switching level to be referenced relatively. The drawback of this particular design is its inability to detect slow moving parti cles. For the ice fog application, the changes to the comparator part implementation are necessary as well. To eliminate, or at least to reduce, the dependence of detection on temperature we suggest another approach. We propose to modify the continuous light emitted by the LED to a train of high frequency pulses. The voltage to the LED can be modulated to produce pulses of light. If a particle blocks the light path for an amount of time needed to cross the light beam, some of the pulses will not reach the detector. On the receiving end, we can place circuit that counts the number of missing pulses. If the detection of a particle is the only goal, then we only need to 166 establish the absence of pulses at certain moments of time. The number of required components in this case will be relatively small although significantly larger than in the existing design. This approach may not be the best from the point of view of accuracy to cost ratio but it can be attractive if particle size determination is intended. Time-of-flight is given by product of the number of missing pulses and pulse period. The third generation of the York University particle counters have the ability to measure time-of-flight. With the addition of minimum voltage detection circuitry, the particle size can be deduced for particles with an effective extinction diameter less than the sensor field of view. Some of the microcontroller memory can be allocated for the particle size bins although at the expense of the time period bins. This design would be helpful in testing the fluid and particle velocity relationship. 167 6 Summary and Discussion The blowing snow phenomenon in the Atmospheric Surface Layer links a simple fluid situation with multicomponent flow. Below a certain threshold of wind velocity (or friction velocity) the flow in the surface layer involves only one component fluid, the air. When the threshold is exceeded, particles entrained from the underlying surface mix with air, and the flow becomes particle-laden. In the scenario just described, the source of the particle can be considered to be external to the flow. It has been long recognized that blowing snow is a multiphase flow Schmidt (1982a). where water is present in the air in particulate form. The phase change into solid form (and vice versa) is possible under the right conditions. In this case, the source (and sink) of particles is from within the fluid itself. The Canadian Arctic Shelf Exchange Studies experiment in winter of 2003 - 2004 provided us with the opportunity to carry out a complex investigation of a particle-laden flow (blowing and drifting snow) together with monitoring the con ditions and evolution of the underlying snow cover. During the on-ice stage of 168 CASES a system of micrometeorological and turbulent flux measuring sensors was deployed on land-fast first year ice in the Canadian Arctic. Specialised sensors were dedicated to measurements of different aspects of blowing and drifting snow. The instruments included particle counters, snow traps, visibility sensors, a snow depth sonic ranger, a snow mass transfer sensor FlowCapt, a video camera system and an electric field meter. Daily sampling of snow cover to determine profiles of snow density, salinity and layer thickness were implemented in the course of the experiment. Snow traps, a video camera system and the electric field meter were operated during drifting/blowing if the security of observers was within established limits. Standard meteorological observer activities at the ship station and on the ice complemented the instrumented observations. The author of this work was responsible for the preparation, testing, calibration and deployment of the mete orological masts, standard and specialised equipment save for the video camera and electric field meter which were primary instruments for Mark Gordon. The snow traps were designed and hand manufactured by the author. Shortly before the CASES04 on-ice stage the photoelectric particle counters were made at York University, Toronto. They were designed by Jim Hodges and Harvey Emberley of the electronics shop of the Faculty of Science and Engineering with participation of Sergiy Savelyev and Professor Peter Taylor. Because of time shortage only the simple spinning wire test was performed on the counters prior to field deployment. 169 The attention to the snow cover properties and their evolution in the experiment devoted to the studies of blowing snow is not surprising. The snow cover is the source of the particle constituent of the flow. On many occasions it is the only one. Snow availability is a condition of developed snow transport. The snow matrix properties define the onset of blowing snow when wind speed increases and are thought to comprise the major influence on the magnitude of near surface shear stress. The mean flow speed profile near the surface (which in numerical models is often taken to be the boundary condition) is believed to be altered due to particle load. The ice camp and meteorological measurement site was located on a relatively flat ice flow with little obstruction to the wind. At the beginning of the observational period (DOY 15) snow thickness did not exceed 12 cm and at some places was no more than 3 cm. The severe storm at the end of 2003 that interrupted the first attempt to freeze in the ship broke the initially homogeneous sea ice. It apparently caused the wetting of snow cover by sea spray and lead to the observed increase in salinity. This layer of snow, formed prior to the experiment, served as an underlying substrate for the new precipitated snow. It was hard to penetrate and it was observed to not eroded. The density of the top 5-6 cm of this layer was around 400 - 450 kg m~3. It decreased to 300 kg m~3 towards the ice surface. The top part of the layer had a noticeable salinity, 4-5 practical salinity units compared to 170 almost zero salinity of the subsequent accumulated snow that came as precipitation or was blown into the area. Salinity increased to almost 15 psu towards the ice. Snow depth variations in the course of the project were caused mostly by pre cipitation, hoarfrost deposition and snow redistribution by wind. Sublimation was not measured nor estimated. It is estimated that densification due to gravity or metamorphism was not a factor in snow depth alteration. Almost all occurrences of precipitation coincided with or shortly followed wind strong enough to cause blowing or drifting. The snow redistribution followed. In certain circumstances the bedforms (snow ripples and/or dunes) developed, moved along the surface and immobilized when wind subsided. The histogram of the snow depth survey made at the late stage of the experiment (DOY 116 - 118) is bi-modal reflecting the vari ation of depth due to dunes. The median snow depth was 17 cm. The density of the precipitated and not yet altered by wind action snow was in the range of 40 to 140 kg m~3. Phase transformations of water contributed to the snow particle population. Ice fog was a regular nighttime and early morning occurrence during periods of calm weather. Hoarfrost also formed on snow and any other available surface. The density of the top snow layer, comprised mainly of hoarfrost crystals was measured to be 150 - 200 kg m-3 when the hoarfrost first formed. One 12 day long calm period in April allowed us to estimate an average rate of hoarfrost layer density increase to be 4.5 kg m-3 per day. At the end of this calm period the hoar- 171 frost crystals were removed when the wind caused drifting. The next deposition of hoarfrost also produced a top surface layer of similar density. To investigate what range of snow densities could be observed in the top layer due wind, 39 samples of snow were taken from surface snow either still in motion or being just deposited while the drift was still in progress. In these particular circumstances there are virtually no bonds between snow grains. Snow density varied from 200 to 450 kg m~3 with the lower values attributed to light wind situations. Regular snow sampling was done during calm periods. Bonds between grains that started to develop or had been developed depend to a great extent on the time passed since the last drifting. The range of surface snow density variation encompasses densities associated with precipitation, hoarfrost deposition and the action of wind deposition. A few samples had densities in excess of what was observed in drifting snow but this may be a random deviation. The snow density profile probing made near the meteorological site exhibited two distinct layers in snow cover, one was apparently formed at the early stages of the ice flow prior to the camp deployment and another layer on top of the first that was a result of snow deposition after the ice flow consolidated as a permanent interface. The salinity of the upper layer was near zero throughout its depth during almost the entire experiment duration. Only at later stages when polynyas opened in the area was the snow caught in snow traps observed to have a salinity from 0.1 to 2 psu. 172 Surface snow had a salinity of at most 0.3 psu. There is a sharp decrease in snow density from the first layer to the second one. While the top part of the first layer has density 400 - 450 kg m~3 the adjacent lower part of the second layer has density 200 - 250 kg m~3. And as was noted above, the snow salinity changes here from 4 psu to near zero. We observed that snow metamorphism inside the snow pack resulted in the existence of volumes of snow grains with very little bonding between them. The approximately 1 mm long faceted crystals were identified as belonging to class 4fa of the Colbeck et al. (1990) classification. The volumes of loose grains did not form continuous layers but instead were confined to "pockets" of snow 2 to 4 cm below the surface of newly deposited snow or snow dunes. The origin of this snow was traced to moderate intensity drift. In the vertical these volumes extended 2 to 6 cm. The median value of loose snow density is close to 200 kg m~3. The densification due to metamorphism with a rate of 2.5 kg m~3 per day was deduced from the set of snow pit probings carried out for 24 days. We speculate that, when exposed, the loose snow grains can facilitate further erosion of the snow surface which in turn will lead to the increase of snow mass transport. The climatology of blowing snow events is of obvious interest to researchers, de cision makers and to the general public. The comprehensive set of instrumentation that we were able to deploy in CASES04 and carefully planned observations allowed 173 us to accurately determine whether or not particles are entrained into the flow at any particular instant and to identify the source of the particles. This allowed us in particular to define the set of criteria of the drifting/blowing and as a result to de termine the start, the end and duration of the drifting/blowing snow events. It was concluded that drifting/blowing was in effect during the course of the experiment for approximately 40% of time. The number of events and their mean duration depends on yet another criterion related to the duration of the interruption to the existing conditions that is deemed to be not long enough to signal the end of the period. If for example one considers the blowing to happen if it lasted no less than one hour and the separation from the previous event is at least one hour then in CASES04 there were 32 drifting/blowing snow events and their median duration was 30.7 hours while the longest lasted almost 4 days. The dependence on criteria is clearly demonstrated. This should be taken into account when the climatology of blowing snow is reported or compared with model predictions. Being able to pinpoint the start of drifting we analysed the flow velocity as sociated with the start, namely the threshold velocity. The threshold velocity is expected to depend on snow surface conditions, drag imposed by wind and the availability of loose particles to start initial bombardment of the snow surface. The obvious source of loose particles is precipitated snow and ice fog. There is no veg etation at the site of the experiment so there were no loose particles from snow 174 trapped on vegetation. The hoarfrost and unbroken precipitated snow flakes on the ground cannot be characterized as loose particles, there are bonds between crystals and they are part of the snow skeleton. But they are easy to break, even by a light wind. The snow cover in general, and the snow surface layer in particular undergo a constant metamorphosis. The result of this metamorphosis at the end of a calm period depends on the temperature and moisture history, both of the fluid and the snow cover. There are other causes of the change of surface conditions. They were not observed in CASES04 so we do not consider them in this work. A thin icy crust can develop at the very top of the snow due to melt-freeze cycles caused by solar radiation. Short spells of warm weather can cause melting or it may be ac companied by freezing rain. The snow surface comprised of blowing snow particles (snow grains) that are the end result of drifting/blowing is the third type of surface snow if we count the precipitated and hoarfrost crystals as the other two types. During blowing snow events, snow grains are being broken into increasingly smaller pieces and compacted into the snow skeleton at the deposition stage. Both actions depend on the wind speed - the stronger the wind, the smaller the size of snow grains and the greater compaction of grains in the wind crust. Smaller and more closely situated snow grains will develop a greater number of bonds between each other and ultimately will cause more resistance to the wind when the next increase in wind speed happens. After analysis of data on blowing snow occurrence col- 175 lected in the experiment we propose a linear regression type relationship to predict the threshold velocity based on the maximum wind speed of the previous blowing event. We speculate that the dependance on the maximum wind speed is only valid for a certain range of wind velocity. The further increase of velocity will not result in smaller grains if their size is already small, and there won't be any compaction because very strong wind prevents deposition. Unfortunately, we do not have ap propriate data to verify our hypothesis. The methodology also makes provisions for precipitation or hoarfrost deposition that may take place during a preceding calm period up to the very onset of the drift. These provisions are also rooted in the observations. Although our approach is strictly valid for the geographical region and the season of the CASES04 experiment we think that it can be expanded or be a part of the methodology if a prediction procedure for the different time/space situation is sought. Under the assumption of the validity of MOST in the Surface Layer, the turbu lent scales of flow are often derived from measured profiles of wind and temperature. The fitted profiles define the normal to the surface derivatives of the respective pa rameters. The normal derivative of a parameter can be considered as a boundary condition in a boundary value problem. It is believed that although the form of the profiles in the particle-laden flow may not be explained from the point of view of MOST but the similarity theory can be extended for a multicomponent fluid at 176 least to give an indication how mean profiles should look in the presence of solid particles in the flow (Taylor and Dyer, 1977). We outlined a curve fitting procedure based on the Maximum Likelihood ap proach. Although it is possible to fit wind speed or temperature profiles alone this may lead to violation of the similarity theory. Information on both wind speed and temperature is needed to fulfill the constraints imposed by the Obukhov length formula. In the absence of full profile measurement it will suffice to have measure ments at two points in the vertical for the parameter whose profile is not available (or for both parameters, wind speed and temperature if neither profile was mea sured). The Maximum Likelihood approach allows us to account for uncertainties associated with each individual sensor while not only finding the best fit but also during post-procedure control of the results. Application of the method to artificially constructed sets of profiles allowed us to investigate how normally distributed random errors of measurements propagate into the derived parameters and lead to a specific shape of the ZQm versus u* scatter plot. We think that for u* close to zero, the effect of random errors introduces too much noise into the results of the profile method so that it is impossible to make conclusions about the actual friction velocity - roughness length relationship. Because of the specific shape of the MOST wind profile, random errors can lead to unrealistically low values of roughness length, more so when friction velocity 177 approaches zero. This can be aggravated by eliminating low wind speed measure ments from the analyzed data set. The form of the points cloud in the u* - z^m plane in the low M* region can be dominated by these two effects. That is why we excluded this region from our analysis of real data. After the analysis of CASES04 data it was found that the median value of momentum roughness length over first year snow covered ice was 0.001 m with a scatter around this value that spans two orders of magnitude. The roughness length was derived from pairs of wind speed and temperature profiles with a condition that derived friction velocity exceed 0.35 m s-1. In our case, this restriction also means that profile pairs belong to flow under near-neutral atmospheric stability. We found no dependency of zom on suspended snow particle number density either u by analyzing the derived zom via * relationship or by investigation of zom via measured particle number densities. The modeling of the multicomponent flow requires quantification of each con stituent of the flow. The particle load in the control volume can be described by its mass or volume fraction. Depending on the case of interest the total fraction may not provide a full information. The distribution of the constituent's mass over the range of its particle sizes could be sought. The absorption or scattering of electromagnetic waves by airborne particles is a foundation of photoelectric sensors aimed at quantification of the particle load. Back-scattered, forward-scattered or 178 straight-through radiation can be monitored. In this work we consider devices that sense electromagnetic energy propagating straight-though from emitter to sensor. The amount of energy reaching the sensor is reduced if a particle blocks a portion of the sensor field of view. The parameter depending on the electromagnetic energy is taken to be the voltage of the sensor - current-to-voltage converter combination. The voltage change waveform is linked to the amount of sensor surface shaded by a particle at various positions along its trajectory. Various time/space parameters of the waveform can be monitored to derive information. The maximum drop in voltage caused by an obstruction can be measured and related to the particle's di mension. Some devices register only the voltage reduction below a certain threshold to establish occurrence of a particle crossing the beam. In this case, the information about particle dimension is not retrieved. The time-of-flight of a particle through the field of view depends on the particle's velocity and size as well as on sampling volume geometry. The number, mass, or volume of detected particles has to be referenced to the sampling volume to derive a meaningful quantity. There are two important issues associated with the sampling volume. First, the volume should be small enough to avoid ambiguity related to more than one particle being simultaneously in the sampling volume. The condition of being small enough depends on the particle concentration that is, this condition can be fulfilled in certain situations and fail in 179 others. Second, the detection of a particle that only partially enters the field of view means that the effective sampling volume is greater than the geometrical dimensions of the field of view. Thus the sampling volume is variable and its determination becomes a complicated task sometimes without an accurate solution. Yet another source of detection error is linked to the finite speed and sensitiv ity of the instrumentation electronics. Closely following particles or particles just clipping the sampling volume may not be properly resolved because of too short a response time. The sensitivity limitations manifest themselves not only in poor de tection of small particles but also in a voltage waveform not exactly corresponding to the particle's position in the field of view. It results, for example, in the time scale of the voltage waveform being smaller than the actual time-of-flight. The photoelectric particle detectors used in CASES04 was designed and built at York University, Toronto. The prototype was a similar device described in Brown and Pomeroy (1989). In addition, we received a working unit and recommendations with regard to detector design from Professor J. Pomeroy. In the first generation of our counters, a phototransistor was used as a sensing device. The phototransistor was replaced by a photodiode in the second generation of counters together with a choice of faster operational amplifiers. There were also improvements related to mechanical design. Only detection was targeted, no sizing of particles was consid ered. The third generation of counters measure the particle's time-of-flight through 180 the field of view which enables the calculation of the particle size if wind speed measurements are available as well and certain assumptions with regard to particle velocity are made. Assessing the capabilities of instruments and their calibration is an essential step in the interpretation and assimilation of data obtained with their help. A certain amount of consistency in interpretation of data can be achieved with inter calibration of several units even if no reference device is available. We performed a post CASES04 calibration of particle detectors in the field experiment on a frozen freshwater lake near Churchill, Manitoba. For some applications, a reference to a sensor that measures a different parameter from the counters but utilizes the princi ple of light attenuation by suspended particles is possible and beneficial. Visibility sensors are in regular service for industry and research. The procedure of their calibration is established. As was deduced from concurrent time series of visibility and particle counts obtained in CASES04 the correlation between data from these two sensors is quite high. The coefficient of correlation is greater than 0.85. This fact can be used to argue in favor of particle counters when visibility monitoring in blowing snow is needed. The current models of visibility sensors require a signifi cant amount of electrical power to operate while particle counters of our design are very energy efficient. The ability of counters to detect the obstruction to the light beam is easy to 181 check by inserting any object into the beam. A spinning wire test did exactly this plus it confirmed the ability to detect fast moving objects. We made an obvious extension of the test by assembling the set of wires of progressively smaller diam eter on the supporting frame in the shape of a "wheel". Two calibration schemes were developed. One procedure resulted in estimates of minimum detected particle diameters for different positions of a particle in the sampling volume. This was a two-step operation. First, with the help of a signal generator the minimum ampli tude of the input signal still resulting in detection was found. Then the empirical relationship between wire diameter and the magnitude of the voltage drop it caused was established. From this relationship it is possible to find the wire diameter that produces the drop equal to the minimum detected input signal. This diameter is taken as the minimum detectable wire size. To relate the wire diameter with the spherical particle size, calculations based on Mie scattering theory are needed. The second calibration procedure allowed us to estimate the maximum particle speed at which the counter output was not dependent on particle size. Alternatively, it identified the minimum detected particle diameter for a certain speed of propaga tion. The third generation of York University particle counters have a provision to measure time scale of the voltage drop waveform in order to make a connection to the particle size that causes this voltage drop. 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