Regional-Scale Distributed Modelling of Glacier Meteorology and Melt, southern Coast Mountains, Canada
by
Joseph Michael Shea
B.Sc., McMaster University, 2001 M.Sc., University of Calgary, 2004
A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
in
The Faculty of Graduate Studies
(Geography)
THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver) April 2010 c Joseph Michael Shea 2010 Abstract
Spatially distributed regional scale models of glacier melt are required to as- sess the potential impacts of climate change on glacier response and proglacial streamflow. The objective of this study was to address the challenges as- sociated with regional scale modelling of glacier melt, specifically by (1) developing methods for estimating regional fields of the meteorological vari- ables required to run melt models, and (2) testing models with a range of complexity against observed snow and ice melt at four glaciers in the south- ern Coast Mountains, ranging in size from a small cirque glacier to a large valley glacier. Near-surface air temperature and humidity measured over four glaciers in the southern Coast Mountains of British Columbia were compared to ambi- ent values estimated from a regional network of off-glacier weather stations. Systematic differences between measured and ambient conditions represent the effects of katabatic flow, and were modelled as a function of flow path length calculated from glacier digital elevation models. Near-surface wind speeds (ug) were classified as either katabatic or channelled, and were mod- elled based on Prandtl flow (for katabatic winds) or gradient wind speeds. Models for atmospheric transmissivity, snow and ice albedo, and incoming longwave radiation were tested and developed from observations of incident and reflected shortwave radiation (K↓ and K↑) and incoming longwave (L↓) radiation. Data from a regional climate network were used to run a degree-day model, a radiation-indexed degree-day model, a simple energy balance model (including tuned parameters for turbulent exchange) and two full energy balance models (incorporating stability corrections, with and without cor- rections for katabatic effects on air temperature and humidity). Modelled
ii Abstract melt was compared to mass balance measurements of seasonal snow and ice melt. Models were also compared based on their ability to predict date of snow disappearance, given an initial snowpack water equivalence. The degree-day model outperformed the simple energy balance and radiation- indexed degree-day approaches, while the full energy balance model without katabatic boundary layer corrections yielded the lowest errors.
iii Table of Contents
Abstract ii
Table of Contents iv
List of Tables viii
List of Figures xii
List of Symbols xvi
Acknowledgements xx
1 Introduction1 1.1 Glacier Melt Modelling...... 2 1.2 Meteorological Inputs for Melt Modelling ...... 4 1.3 Melt Model Selection...... 5 1.4 Thesis Objectives and Outline...... 6
2 Study Area and Data Collection9 2.1 Meteorological Data ...... 9 2.1.1 Glacier Meteorological Stations...... 9 2.1.2 Ambient Meteorological Stations...... 17 2.1.3 Meteorological Data Post-Processing...... 17 2.2 Mass Balance and Snowline Retreat Observations ...... 18 2.2.1 Winter Balance...... 20 2.2.2 Summer Ablation...... 21 2.2.3 Snowline Retreat...... 21
iv Table of Contents
3 Distributing Meteorological Fields, Part 1 28 3.1 Introduction...... 28 3.2 Methods...... 31 3.2.1 Temperature ...... 31 3.2.2 Vapour Pressure ...... 33 3.3 Results...... 35 3.3.1 Temperature ...... 35 3.3.2 Vapour Pressure ...... 48 3.4 Discussion...... 57 3.5 Conclusions...... 58
4 Distributing Meteorological Fields, Part 2 60 4.1 Introduction...... 60 4.2 Methods...... 62 4.2.1 Data Preparation and Modelling Approach ...... 62 4.2.2 Katabatic Wind Speed Modelling...... 64 4.2.3 Non-katabatic Wind Speed Models...... 68 4.3 Results...... 68 4.3.1 Glacier Wind Characterization...... 68 4.3.2 Surface Winds in Katabatic Flow...... 73 4.3.3 Surface Winds in Non-Katabatic Flow...... 79 4.3.4 Modelled Surface Wind Speeds...... 79 4.3.5 Comparison of Wind Speed Models...... 88 4.4 Discussion...... 89 4.5 Conclusion ...... 92
5 Distributing Meteorological Fields, Part 3 93 5.1 Introduction...... 93 5.2 Methods...... 95 5.2.1 Temperature ...... 99 5.2.2 Vapour Pressure ...... 99 5.2.3 Wind Speed...... 100 5.3 Results...... 101
v Table of Contents
5.3.1 Temperature ...... 101 5.3.2 Vapour Pressure ...... 106 5.3.3 Wind Speed...... 109 5.3.4 Application...... 113 5.4 Discussion...... 116 5.5 Conclusions...... 118
6 Radiation Modelling 119 6.1 Solar Radiation and Transmissivity ...... 119 6.1.1 Background and Objectives ...... 119 6.1.2 Methods and Data...... 121 6.1.3 Results ...... 125 6.1.4 Discussion...... 137 6.2 Albedo...... 138 6.2.1 Background and Objectives ...... 138 6.2.2 Methods...... 140 6.2.3 Results ...... 143 6.2.4 Discussion...... 147 6.3 Longwave Radiation ...... 150 6.3.1 Background and Objectives ...... 150 6.3.2 Methods...... 151 6.3.3 Results ...... 153 6.3.4 Discussion...... 169 6.4 Recommendations ...... 170
7 Melt Model Test Data 172 7.1 Background and Objectives...... 172 7.2 Data and Methods...... 176 7.2.1 Snow Density Modelling ...... 176 7.2.2 Interpolation of Initial SWE ...... 178 7.2.3 Mass Balance and Snowline Retreat Data ...... 179 7.2.4 Error Analysis ...... 179 7.3 Results...... 181
vi Table of Contents
7.3.1 Snow Density Modelling ...... 181 7.3.2 Initial SWE Interpolation ...... 186 7.3.3 Surface Temperature Loggers and Snowline Retreat . 188 7.3.4 Error Analysis ...... 193 7.4 Discussion and Recommendations ...... 194
8 Melt Modelling 197 8.1 Introduction...... 197 8.2 Study Areas and Climate Data ...... 199 8.3 Melt Modelling Methods...... 200 8.3.1 Degree-day Model ...... 200 8.3.2 Radiation-indexed Degree-day Model ...... 200 8.3.3 Simplified Energy Balance Model ...... 203 8.3.4 Full Energy Balance Model ...... 208 8.4 Meteorological Inputs ...... 213 8.4.1 Temperature ...... 214 8.4.2 Vapour Pressure ...... 214 8.4.3 Wind Speed...... 215 8.5 Melt Model Comparisons ...... 218 8.6 Results...... 218 8.6.1 Modelled Melt and Benchmark Evaluations ...... 218 8.6.2 Full Energy Balance Model Analyses ...... 224 8.7 Discussion...... 227 8.8 Conclusions...... 229
9 Conclusion 231 9.1 Summary of Key Findings...... 231 9.1.1 Glacier Meteorology ...... 231 9.1.2 Radiative Fluxes...... 233 9.1.3 Melt Model Test Data...... 233 9.1.4 Glacier Melt Modelling ...... 234 9.2 Suggestions for Future Research ...... 235
References Cited 238
vii List of Tables
Table 1.1 Glacier energy balance studies ...... 8
Table 2.1 Location and instrumentation of glacier AWS . . . . . 10 Table 2.2 Summary of on-glacier AWS periods of operation . . . 16 Table 2.3 Meteorological instrumentation specifications...... 16 Table 2.4 Ambient AWS locations and data source ...... 17
Table 2.5 Dates of initial snow water equivalence (SWE0) mea- surements for mass balance and snow course sites . . . 19 Table 2.6 Snow course locations and ID...... 19 Table 2.7 Specifications of submersible temperature loggers used in this study ...... 22
Table 3.1 Mean ambient and observed temperatures at glacier AWS...... 40 Table 3.2 Piecewise temperature model parameters ...... 41 Table 3.3 Elevation of 0◦C isotherm...... 47 Table 3.4 Mean ambient and observed vapour pressures at glacier AWS...... 49 Table 3.5 Vapour pressure model parameters...... 53
Table 4.1 Directional constancy (dc) and mean observed wind −1 speeds (ug, in m s ) at glacier AWS...... 70 Table 4.2 Optimized eddy diffusivities and model errors for Prandtl wind speed model ...... 77 Table 4.3 Surface wind speed models for channeled katabatic flows 78
viii List of Tables
Table 4.4 Surface wind speed model coefficients and modelled errors for channeled flows ...... 79 Table 4.5 Mean (x, m s−1) and standard deviation (σ, m s−1) in
observed and modelled uNK , uK , and uKc...... 87 Table 4.6 Modelled wind speed errors using E-P methods and a representative station ...... 88
Table 5.1 Fitted coefficients for estimating Tg, eg, and ug, ob- tained from glacier boundary layer analyses ...... 98 Table 5.2 Summary of models for estimating piecewise temper- ature transfer functions from topographic indices . . . 103 Table 5.3 Temperature transfer function coefficients estimated from meteorological observations (obs) and from to- pographic indices (est) for withheld AWS sites . . . . 104 Table 5.4 Errors in modelled temperatures and vapour pressures 105 Table 5.5 Model summary for vapour pressure transfer functions and FPL...... 107 Table 5.6 Vapour pressure transfer function coefficients estimated from meteorological observations (obs) and from topo- graphic indices (est) ...... 108
Table 5.7 Model summary for fitted eddy diffusivities KH and
KM ...... 110
Table 5.8 Eddy diffusivity coefficients for estimating uK observed from meteorological observations (obs) and estimated from topographic indices (est) ...... 111 Table 5.9 Errors in modelled wind speeds ...... 111
Table 6.1 Atmospheric transmissivity models ...... 125 Table 6.2 Radiation and transmissivity correlations ...... 127 Table 6.3 Errors in modelled daily transmissivity ...... 131 Table 6.4 Errors in modelled daily solar radiation totals . . . . . 132 Table 6.5 Fitted model parameters for daily precipitation-adjusted
∆T1 transmissivity models ...... 135
ix List of Tables
Table 6.6 Hourly transmissivity model coefficients and errors . . 136 Table 6.7 Errors in modelled hourly radiation ...... 137 Table 6.8 Snow albedo parameterizations...... 139 Table 6.9 Simple correlations (r) between snow and ice albedo station pairs...... 145 Table 6.10 Snow and ice albedo models ...... 147 Table 6.11 Clear-sky emissivity parameterizations ...... 158 Table 6.12 Cloud factor (F ) models ...... 160 Table 6.13 Summary of hourly and daily L↓ model errors . . . . . 164
Table 7.1 Snow density model summary ...... 182 Table 7.2 Snow density summary by site ...... 185
Table 7.3 Summary of Loess and polynomial fitting of SWE0 data versus elevation...... 187 Table 7.4 Snowline retreat sensor locations and estimated day of snowline retreat (DOY), Place Glacier ...... 190 Table 7.5 Snowline retreat sensor locations and estimated day of snowline retreat (DOY), Helm Glacier ...... 191 Table 7.6 Snowline retreat sensor locations and estimated day of snowline retreat (DSR), Weart Glacier ...... 192 Table 7.7 Snowline retreat sensor locations and estimated day of snowline retreat, Bridge Glacier ...... 192 Table 7.8 Winter and summer balance error statistics ...... 194
Table 8.1 Melt model parameters and constants for degree-day, radiation-indexed degree-day, and simple energy bal- ance models...... 201 Table 8.2 Summary of previous RIDD model parameter values . 203 Table 8.3 Melt model parameters and constants for the full en- ergy balance model...... 210 Table 8.4 Coefficients for kabatatic boundary layer corrections, based on results from Chapter5 ...... 216 Table 8.5 Mean ablation season glacier wind speeds ...... 217
x List of Tables
Table 8.6 Melt model errors ...... 220
xi List of Figures
Figure 1.1 Glacier melt models overview...... 3
Figure 2.1 Southern Coast Mountains study area...... 11 Figure 2.2 Place Glacier AWS locations...... 12 Figure 2.3 Weart Glacier AWS locations...... 13 Figure 2.4 Bridge Glacier AWS locations...... 14 Figure 2.5 Example of the on-ice meteorological stations (a) and a close-up view of the Gimbel joint used to mount pyranometers horizontal to the surface (b)...... 15 Figure 2.6 Helm Glacier mass balance and snowline retreat ob- servations...... 23 Figure 2.7 Place Glacier study area, mass balance and snowline retreat observations ...... 24 Figure 2.8 Weart Glacier mass balance and snowline retreat ob- servations...... 25 Figure 2.9 Bridge Glacier mass balance and snowline retreat ob- servations...... 26 Figure 2.10 Method for calculating column-averaged snow density 27 Figure 2.11 Example of the surface temperature logger being de- ployed on the ice surface, Bridge Glacier 2006 . . . . . 27
Figure 3.1 Conceptual piecewise regression model...... 32 Figure 3.2 Conceptual model for KBL vapour pressure analyses . 35 Figure 3.3 Hourly temperature gradients...... 37 Figure 3.4 Testing horizontal variability in ambient temperature and vapour pressure ...... 38
xii List of Figures
Figure 3.5 Temperature extrapolations for an independent station 39 Figure 3.6 Piece-wise temperature models...... 42 Figure 3.7 Boxplots of predicted near-surface temperature residuals 45 Figure 3.8 Synoptic types ...... 46 Figure 3.9 Vapour pressure gradients...... 51 Figure 3.10 Vapour pressure estimation for an independent ambi- ent station ...... 52 Figure 3.11 Vapour pressure models...... 54 Figure 3.12 Vapour pressure residuals by hour of day and synoptic type...... 56
Figure 4.1 NCEP grid used in calculation of flow indices...... 63 Figure 4.2 Logic for glacier wind speed modelling...... 64 Figure 4.3 Theoretical Prandtl profiles...... 66 Figure 4.4 Glacier AWS wind direction histograms ...... 71 Figure 4.5 Hourly glacier wind speeds versus ambient temperatures 72 Figure 4.6 Ambient temperature - wind speed hysteresis . . . . . 74 Figure 4.7 Wind speed and temperature cross-correlations . . . . 75 Figure 4.8 Error analysis, katabatic flow optimization ...... 76
Figure 4.9 Global model for estimating uKc from southerly flow strengths V ...... 77 Figure 4.10 Global models for non-katabatic flows ...... 80 Figure 4.11 Time-series of observed and modelled wind speeds, PM2 82 Figure 4.12 Time-series of observed and modelled wind speeds, WM1 83 Figure 4.13 Time-series of observed and modelled wind speeds, BM1 84 Figure 4.14 Wind speed residuals, PM2...... 85 Figure 4.15 Wind speed residuals, WM1 and BM1...... 86 Figure 4.16 Predicted wind speed profiles...... 91
Figure 5.1 Morphometric parameters calculated for Place Glacier. 97 Figure 5.2 Models for estimating KBL temperature transfer func- tions from topographic indices ...... 102
Figure 5.3 Observed and modelled Tg at independent testing sites.104
xiii List of Figures
Figure 5.4 Models for estimating j1 and j2 from FPL ...... 106
Figure 5.5 Observed and modelled eg at independent testing sites. 108
Figure 5.6 Estimating eddy diffusivity coefficients KH and KM from flow path lengths...... 109
Figure 5.7 Observed and modelled uK at independent testing sites.112 Figure 5.8 Application of boundary layer development models of temperature, vapour pressure, and wind speeds . . . . 115
Figure 6.1 Coefficients of variability for hourly and daily solar radiation ...... 126 Figure 6.2 Scatterplot matrix of daily transmissivity observed at four mountain stations...... 128 Figure 6.3 Scatterplot matrix of hourly tranmissivity observed at four mountain stations...... 129 Figure 6.4 Transmissivity model fits with and without precipita-
tion adjustment for S∆T1,ea at each site ...... 133 Figure 6.5 Transmissivity model residuals ...... 134 Figure 6.6 Daily K↓ residuals...... 134 Figure 6.7 Modelled and observed hourly solar radiation fluxes . 136 Figure 6.8 Fisheye photo of the field of view of an inverted pyra- nometer...... 141 Figure 6.9 Time-series of observed albedo ...... 143 Figure 6.10 (a) PDD snow albedo model, (b) snow albedo residuals versus daily atmospheric transmissivity ...... 147 Figure 6.11 Time series of observed and predicted daily albedo . . 148 Figure 6.12 Comparison of off-glacier and on-glacier L↓ ...... 154 Figure 6.13 Differences in on- and off-glacier L↓ ...... 156 Figure 6.14 On- and off-glacier emissivities ...... 157 Figure 6.15 Predicted versus observed clear-sky emissivities at (a) hourly and (b) daily timescales ...... 159 Figure 6.16 Modelled and observed cloud factor F ...... 161 Figure 6.17 Time-series of observed and modelled incoming long- wave radiation ...... 165
xiv List of Figures
Figure 6.18 Boxplots of hourly L↓ residuals by hour of day . . . . 166 Figure 6.19 Modelled L↓ residuals versus ambient T ...... 167 Figure 6.20 Modelled versus observed L↓ for test cases ...... 168
Figure 7.1 Accumulated PDD snow density model and residuals . 183 Figure 7.2 Difference maps of snow density ...... 184 Figure 7.3 Comparison of polynomial regressions and Loess curve fitting ...... 188 Figure 7.4 Tidbit temperature records ...... 190 Figure 7.5 Dates of snowline retreat versus elevation, for all sites and years...... 191
Figure 7.6 Observed specific net balance (bn) versus date of snow- line retreat obtained at Place and Helm Glaciers, 2006 - 2008 ...... 193
Figure 8.1 Modelled and observed bs for various melt models . . 221
Figure 8.2 Modelled and observed MTB for various melt models. 222 Figure 8.3 Melt model residuals versus observations...... 223 Figure 8.4 Observed and modelled (a) hourly and (b) daily net radiation at PM2, 2007 ablation season ...... 225 Figure 8.5 Modelled snow pack temperatures ...... 226 Figure 8.6 Mean monthly energy fluxes for full energy balance models with (left) and without (right) KBL corrections 226
xv List of Symbols
bn net mass balance
bs summer mass balance
bw winter mass balance C surface temperature deficit
Ca specific heat capacity of air
CD total drag coefficient
CE bulk latent heat transfer coefficient
CH bulk sensible heat transfer coefficient
d0 initial snow depth
df final snow depth
ea ambient vapour pressure
ef surface vapour pressure
eg glacier near-surface vapour pressure
es saturation vapour pressure F cloud factor
Fm modified melt factor G goodness-of-fit index g gravitational acceleration h surface height k von Karman’s constant K ↓ incoming shortwave radiation
K ↓cs potential clear sky insolation K ↑ outgoing shortwave radiation
KH eddy diffusivity for heat
KM eddy diffusivity for momentum
xvi List of Symbols
ki Degree-day melt factor for ice ks Degree-day melt factor for snow L↓ incoming longwave radiation L↑ outgoing longwave radiation
Lf latent heat of fusion
Lv latent heat of evaporation
Ma molar mass of dry air
Mi ice melt
Ms snow melt PDD accumulated postive degree days p atmospheric pressure p0 mean sea-level pressure Q∗ net radiation
QA advected turbulent heat fluxes
QE latent heat flux
QG ground heat flux
QH sensible heat flux
QR heat flux from precipitation
∆QS change in snowpack heat storage R rainfall
Rb bulk Richardson stability number
Rg ideal gas constant RH relative humidity
Rig bulk Richardson gradient number ri radiation factor for ice rs radiation factor for snow
SWE0 initial snow water equivalence T ∗ critical ambient temperature
Ta ambient air temperature
Tg glacier near-surface air temperature
T d mean daily temperature
Ts surface temperature
TZ=0 sea-level temperature
xvii List of Symbols
T0 threshold temperature for melt U westerly wind speed ug wind speed uK katabatic wind uKc channelled katabatic wind uNK non-katabatic wind u(z) wind speed profile V southerly wind speed V ∗ critical southerly wind speed Z elevation z measurement height
∆zs snow depth for ∆QS calculation zx roughness length of temperature and vapour pressure z0 roughness length
α surface slope
αf fresh snow albedo
αi ice albedo
αs snow albedo β parameters for KBL modelling
a atmospheric emissivity
cs clear-sky atmospheric emissivity
s surface emissivity
0 effective atmospheric emissivity
γe vertical vapour pressure gradient
γT vertical temperature gradient λ length scale µ momentum scale Θ wind vector and stability correction θ potential temperature θ(z) temperature deficit profile
θZ solar angle of incidence
xviii List of Symbols
ρi ice density
ρs snow density σ Stefan-Boltzmann constant τ atmospheric transmissivity
xix Acknowledgements
First and foremost, this work would not have been possible without the guidance and support of my advisor, Dan Moore. His insights, scientific curiosity, and attention to editorial detail are hopefully manifested in this thesis, and his committment for this project was unwavering. I also thank my thesis committee, comprised of Dr. Garry Clarke, Dr. Ian McKendry, and Dr. Tim Oke, for their feedback and contributions. University examiners, Dr. Andreas Christen and Dr. Mike Novak provided numerous insights and suggestions. Special thanks go to Ellen Morgan, Roger Hodson, and Natalie Stafl, whose assistance in the field was central to obtaining both data and mem- orable field trips. Other people who generously volunteered their time and their backs include Faron Anslow, Chris Borstad, Rob Burrows, John Chap- man, Jeff Kane, Derek van der Kamp, John Richards, Rich So, and Brett Wheler. Ivan Liu created the portable weather station tripod, which made the field loads bearable. Kerstin Stahl provided data, collaboration, and early inspiration, the British Columbia Ministry of the Environment provided the opportunity to do research at Weart and Helm Glaciers, and Blackcomb Helicopters never failed to pick us up from the field. Many thanks to a strong supporting cast in the Geography Department at the University of British Columbia for much-needed discussions and distractions, including Josh Caulkins, Emily Davis, Marwan Hassan, Derek van der Kamp, Scott Krayenhoff, Sonya Pow- ell, Joanna Reid, Russell Smith, Amanda Stan, and Andr´eZimmerman. Funding for this research was provided by both NSERC grants to JMS, and NSERC and CFCAS grants to RDM through the Western Canadian Cryospheric Network. The opportunity to collaborate and receive feed-
xx Acknowledgements back through WCCN meetings was incredibly beneficial. Mike Demuth at the Geological Survey of Canada provided invaluable LiDAR data for the study sites, in-kind-support through shared helicopter flights, and has single-handedly maintained the Canadian glacier mass balance monitoring program. Finally, I acknowledge the patience and understanding of my wife Shelley, who has tolerated my PhD mistress and encouraged me throughout. This thesis is dedicated to Connall and Tate, who provided cheerleading when I needed it most. Any remaining errors and shortcomings in this thesis are, unfortunately, my own.
xxi Chapter 1
Introduction
Glacier fluctuations are significant at local, regional, and global scales, with impacts on the hydrology and ecology of alpine streams [Fagre et al., 2003; Fleming, 2005], geomorphic hazards and water quality [Moore et al., 2009], regional water supplies [McCarthy et al., 2001; Barnett et al., 2005] and hy- droelectric power generation [Tangborn, 1984], and global sea-level changes [Oerlemans and Fortuin, 1992; Raper and Braithwaite, 2006]. Glacier mass balance is the sum of accumulation (inputs) and ablation (outputs) on an annual basis, and interannual mass balance variability is determined by cli- mate [Moore and Demuth, 2001; Shea and Marshall, 2007]. Glacier mass balance is also the driving variable in dynamic glacier and ice sheet models, which are necessary for modelling the evolution of glacier area and volume. Glacier mass balance thus provides a critical link between climatic change and glacier responses [Marshall and Clarke, 1999], which are of global inter- est. Despite the significance of glacier mass balance, a maximum of only 90 sites worldwide have been monitored for mass balance changes in any given year [Dyurgerov, 2002]. Declining summer streamflows in British Columbia have been linked to glacier retreat [Stahl and Moore, 2006], yet only two glaciers in the southern Coast Mountains are currently monitored for an- nual mass changes. The total area of these monitoring sites (ca. 5 km2) represents less than 0.1% of the total glaciated area in the southern Coast Mountains (ca. 8000 km2). Developing glacier mass balance models that can be applied with confidence to unmonitored regions thus represents an important goal that is complicated by the fact that processes which gov- ern glacier fluctuations (accumulation and ablation) vary in both time and space. Research presented in this thesis focuses on ablation, and on ablation
1 1.1. Glacier Melt Modelling modelling methods.
1.1 Glacier Melt Modelling
Regional analyses of glacier melt are required to identify the impacts of cli- mate change in glacierized basins. However, distributed melt models have typically focused on a single glacier with detailed climatological measure- ments [Arnold et al., 1996; Klok and Oerlemans, 2002; Hock, 2005; Klok et al., 2005]. Two important issues regarding model performance are porta- bility and complexity. The performance of different melt models has been previously compared for individual glaciers [Hock, 1999; Pellicciotti et al., 2005; Pellicciotti et al., 2008; Gudmundsson et al., 2009], but the portability of a given modelling approach between glaciers has only recently been exam- ined [Carenzo et al., 2009]. In snow hydrology, melt model portability and the relation between complexity and performance has been addressed numer- ous times, most notably by the Intercomparison of Snow Models project or- ganized by the World Meteorological Organization [WMO, 1986], and more recently by Essery et al.[1999], Strasser et al.[2002], Etchevers et al.[2004] and Franz et al.[2008]. Each of these studies attempted to address the performance of a given model in relation to its input parameters and as- sumptions. Approaches to glacier melt modeling range in complexity from lumped statistical models to empirical temperature-index and energy balance models (Figure 1.1), which can operate at scales ranging from point melt estimates to fully distributed models. The surface energy balance of a melting glacier can be expressed as:
∗ QM + ∆QS = Q + QH + QE + QR + QA (1.1) where QM is the energy involved in melting (QM > 0) or refreezing (QM < ∗ 0), ∆QS is the change in energy storage within the snowpack, Q is the net radiation, QH and QE are the turbulent fluxes of sensible and latent heat, respectively, QR is the sensible heat flux supplied from rain, and QA is the
2 1.1. Glacier Melt Modelling local advection of sensible heat from surrounding snow-free terrain (all in units of W m−2). In this formulation, fluxes directed towards the surface are positive, and fluxes away from the surface are negative. A summary of energy balance studies conducted at mid-latitude glaciers (Table 1.1) indicates that net radiative fluxes tend to dominate the surface energy balance, though turbulent fluxes represent between 5 and 50% of the net energy at the surface. At maritime sites, the contribution from turbulent fluxes tends to be greater than that observed at continental locations, and on shorter time-scales turbulent fluxes of energy can contribute substantial amounts of melt energy [Hock, 2005]. All other modelling approaches are essentially simplifications of the en- ergy balance approach, where melt determined by the surface energy balance is parameterized through air temperature [e.g. Ohmura, 2001], or air tem- perature and solar radiation [e.g. Hock, 1999], or atmospheric circulation [Shea and Marshall, 2007].
Figure 1.1: Glacier melt models overview.
The success of temperature-index approaches to melt modelling is due mainly to the relation between air temperature and fluxes of longwave ra- diation and, to a lesser degree, sensible heat [Ohmura, 2001]. High air temperatures are also correlated to clear-sky conditions during the summer,
3 1.2. Meteorological Inputs for Melt Modelling providing a further link between temperature and solar radiation. To deter- mine which melt model is most appropriate for regional melt modelling, it is necessary to examine the meteorological drivers required for each approach.
1.2 Meteorological Inputs for Melt Modelling
Energy balance melt models require measurements or estimates of shortwave and longwave radiation, and observations of near-surface air temperature
(Tg), vapour pressure (eg), and wind speed (ug)[Hock, 2005]. These vari- ables may be measured directly on the glacier surface [van de Wal et al., 1992; van de Wal and Russell, 1994; Hock and Holmgren, 1996; Brock and Arnold, 2000; M¨olgand Hardy, 2004; Pellicciotti et al., 2005; Anslow et al., 2008], at stations adjacent to the glacier [Munro, 1991, 2004; Machguth et al., 2006], or extracted from regional climate networks [Greuell and Oerlemans, 1986; Oerlemans and Fortuin, 1992] or mesoscale atmospheric models [Cook et al., 2003; Box et al., 2004]. Distributing meteorological fields on melting glaciers, regardless of the source data, is problematic due to katabatic flows and the development of a katabatic boundary layer (KBL) during melt peri- ods. In contrast, a temperature-indexed approach requires only regional air temperatures [Braithwaite, 1977; Shea et al., 2009], which serve as an index of the total energy available for melt. The KBL is a well-documented phenomenon of melting glaciers and ice sheets [Holmgren, 1971; Munro and Davies, 1978; van den Broeke, 1997b; Hock, 2005]. At mid-latitude glaciers in the ablation season, ambient air temperatures (Ta) typically exceed snow- or ice-surface temperatures (Ts = 0◦C). Cooled air near the surface and the resulting density gradient pro- duce katabatic flows, which are typified by strong down-glacier wind speeds [Munro and Davies, 1978; Ohata, 1989; Obleitner, 1994; van den Broeke, 1997b; Greuell et al., 1997; Strasser et al., 2004]. Katabatic winds reinforce the sensible heat exchange and cooling of the near-surface layers, creating a shallow but intense temperature inversion [van den Broeke, 1997b]. As this situation arises when conditions for melt are favourable, assumptions of a constant environmental lapse rate or reference wind speed based on either
4 1.3. Melt Model Selection on- or off-glacier data may be unsuitable for parameterizing temperatures, wind speeds, and incoming longwave radiation over a melting glacier surface [Greuell and B¨ohm, 1998; Greuell and Smeets, 2001; Klok et al., 2005]. In the snow hydrology literature, numerous studies have demonstrated methods for generating fields of T , ea, and u for distributed energy balance melt modelling [e.g. Susong et al., 1999; Garen and Marks, 2005]. However, these schemes do not account for modification of air temperature, humidity and wind speed by the development of katabatic flows, and thus are generally not applicable to glacier settings. Few glaciological studies have compared on-ice meteorological quantities to those measured off-site [Stenning et al., 1981; Lang, 1986; Oerlemans, 2000], and even fewer have directly examined relations between meteorological variables measured within the katabatic boundary layer at the same glacier [Greuell and B¨ohm, 1998; Strasser et al., 2004; Marshall et al., 2007]. To enable regional energy balance melt mod- elling, methods for transforming regional climate data to on-glacier fields of
T , ea, and u are required.
1.3 Melt Model Selection
It is important to reconcile the complexity of a given model with both (a) portability and (b) input data requirements. While energy balance ap- proaches theoretically offer the most portability due to the complete descrip- tion of surface energy fluxes, the generation of appropriate regional climate fields has been neglected in the glacio-meteorological literature. Conversely, while temperature indexed models are the simplest approach, model porta- bility is a concern [Shea et al., 2009]. Walter et al.[2005] demonstrated that a heavily parameterized energy balance approach achieved greater accuracy than a degree-day approach for predicting snow melt at four open and level measurement sites across the United States, whereas Franz et al.[2008] suggested that degree-day snowmelt models are preferable due to the large uncertainty in energy balance approaches. Radiation-indexed degree day model (RIDDM) coefficients are fairly stable between sites and years within a limited geographic region [Carenzo et al., 2009], but for substantially dif-
5 1.4. Thesis Objectives and Outline ferent climates RIDDM coefficients require local optimization [Schneeberger et al., 2003; Pellicciotti et al., 2005]. To date, there have been no inter- comparisons of glacier melt models of varying complexities at a range of locations.
1.4 Thesis Objectives and Outline
The processes that govern snow and ice melt on temperate glaciers have been well studied, and both empirical and physically based melt models have been used to successfully model glacier melt at the scale of individual glaciers (Table 1.1). However, modelling skill depends to great degree on the quality of the input data, and glacierized regions are typically devoid of high-altitude climate stations. Physically based approaches for modelling melt furthermore require the input of meteorological data that represent conditions near the surface, as the development of the katabatic boundary layer precludes the use of standard meteorological extrapolation techniques. Research presented in this thesis is focused on two main themes: the estimation of meteorological quantities for glacier melt modelling, and the portability of melt models of varying complexities between sites. Analysis of observational data forms a significant portion of this research, and field data collection and instrument specifications are described in Chapter2. Techniques for estimating near-surface meteorological variables within katabatic boundary layers are developed and tested in Chapters3 through 5. Chapter3 presents models for estimating near-surface temperature and vapour pressure, constructed with meteorological observations made at four glacier sites in the southern Coast Mountains of British Columbia. Chapter 4 describes the nature of near-surface wind speeds on melting glaciers, and suggests methods for estimating wind speeds. The results of Chapters3 and 4 are re-examined in relation to the topographic characteristics of each site in Chapter5, which provides models for estimating the effects of katabatic boundary layer development on near-surface meteorological variables based on digital elevation data. Methods for distributing radiative fluxes for energy balance modelling
6 1.4. Thesis Objectives and Outline are explored in Chapter6, which focuses on atmospheric transmissivity, snow and ice albedo, and longwave radiation using surface observations. A description of methods used to generate datasets for testing melt models is given in Chapter 7, which includes the application of temperature loggers for monitoring snowline retreat. The final research chapter (Chapter 8) outlines four melt models of varying complexity, and examines model performance at four sites in the southern Coast Mountains of British Columbia. Individually, each chapter represents an important contribution to the fields of glaciology and climatology. Together, this research provides the foundation for future investigations into the effects of climate change on both individual glacier melt totals and regional glacier melt, as well as guidelines for regional modelling of glacier melt in hydrologic models.
7 1.4. Thesis Objectives and Outline
Table 1.1: Energy flux contributions from mid-latitude glacier studies, ex- pressed as a percentage of total melt energy. M = maritime glacier, and ∗ QM = Q + QH + QE. The quantity (QH + QE)/QM describes the contri- bution of turbulent fluxes to total melt energy.
∗ Lat Elev Q QH QE QH + QE Date ◦ Source ( ) (m) (%) (%) (%)QM (d) Snow Surfaces a 46.0N 2876 87 13 0.13 Jul-Aug (20) b 46.8N 2500 91 10 -1 0.09 Jul (10) b 46.8N 2630 93 20 -10 0.10 Jul (18) c 51.7N 2500 65 34 1 0.35 Jun-Jul (20) d 51.7N 2510 43 8 48 0.56 Jul (14) e 46.4N 2540 95 8 -3 0.05 May (18) e 46.4N NA 53 48 -1 0.47 Summer f 47.1N 2945 76 19 4 0.23 Jun-Aug (46) f 47.1N 3225 78 20 1 0.21 Jun-Aug (46) g 46.8N 3420 61 40 0.40 Aug-Sep (28) h 45.8N 3550 100 24 -23 0.01 Jul (25 d) i (M) 54.8N 810 33 44 23 0.67 Aug-Sep (31) j (M) 43.4S 2150 61 39 0.39 Mar (4) k 43.1S NA 52 30 16 0.46 Jan-Feb (53) Ice Surfaces f 47.1N 2310 73 22 5 0.27 Jun-Aug (46) a 46.0N 2876 85 15 0.15 Jul-Aug (13) c 51.7N 2300 51 41 7 0.48 Jun-Jul (15) l 51.7N 2280 49 22 29 0.51 Aug (6) m (M) 43.4S NA 21 55 25 0.80 Feb (4 d) n(M) 67.9N 1375 66 29 5 0.34 Jul-Aug (39) Snow and Ice Surfaces o (M) 48.3N 1650 62 29 9 0.38 Jun-Aug (92) f 47.1N 2420 72 23 4 0.27 Jun-Aug (46) p 27.7N 4956 85 10 5 0.15 May-Sep (125) p 27.7N 5245 94 9 -1 0.08 May-Sep (125) q (M) 69.3N 1715 71 25 5 0.30 May-Aug (85) r (M) 61.6N 1570 76 17 8 0.21 Season r (M) 60.6N 1450 65 25 15 0.25 Season aWillis et al.[2002]; bvan de Wal et al.[1992]; cMunro[1990]; dF¨ohn[1973]; ePl¨uss and Mazzoni[1994]; f Greuell and Smeets[2001]; gAmbach and Hoinkes[1963]; hde La Casini`ere[1974]; iKonya et al.[2004]; jKelliher et al.[1996]; kHay and Fitzharris[1988]; lDerickx[1975]; mIshikawa et al.[1992]; nHock and Holmgren [1996]; oAnslow et al.[2008]; pKayastha et al.[1999]; qKlok et al.[2005]; rGiesen et al.[2009]
8 Chapter 2
Study Area and Data Collection
Four glaciers in the southern Coast Mountains of British Columbia were chosen as observation sites (Figure 2.1). Site selection was based on the existence of ongoing or previous glaciological studies (Place, Helm, and Bridge), as well as glacier size and accessibility. This chapter details the meteorological observations, mass balance and initial snow water equiva- lence measurements, and the snowline retreat observations.
2.1 Meteorological Data
2.1.1 Glacier Meteorological Stations
Automatic weather stations (AWS) were operated on glacier surfaces be- tween May and October at Place Glacier (Figure 2.2), Weart Glacier (Fig- ure 2.3), and Bridge Glacier (Figure 2.4). Handheld GPS coordinates were used to locate the station at approximately the same location each season, though in 2008 two stations at Place Glacier were relocated in order to docu- ment lateral variability in observed weather data (Figure 2.2, Table 2.1). At Weart Glacier, station WM1 was located in the same location in 2007 and 2008, and WM2 was in operation only in 2007. One climate station (BM1) was operated at Bridge Glacier in 2008 to test assumptions about the scale dependence of katabatic boundary layer development. An illustration of the floating station design is given in Figure 2.5. Station locations and elevations are given in Table 2.1, and periods of record for each station and season are given in Table 2.2. Weather stations
9 2.1. Meteorological Data used in this study were based on a portable tripod design, with wooden feet that prevented the station from melting into the snow or ice surface. With a floating station, sensors remained at a relatively constant measurement height (ca. 1.7 m) throughout the ablation season. At all stations, ten- second measurements of air temperature (Tg), relative humidity (RHg), wind speed (ug), and wind direction (Θg) were recorded as 10 minute means using a Campbell Scientific CR10X datalogger, and instrument specifications are given in Table 2.3. Hourly means were calculated from the 10-minute data. Reflected solar radiation (K↑) was measured at most glacier AWS dur- ing the periods of record indicated in Table 2.2. Kipp&Zonen pyranometers were inverted and suspended using custom-made Gimbel joints (Figure 2.5) mounted 1.7 m above the ground surface. Gimbel joints were used to main- tain the (K ↑) sensor in an approximately horizontal position despite the shifting of the AWS due to surface melt. Net radiation (Q∗) was measured at PM2 in 2007 with a Kipp&Zonen NR-lite net radiometer.
Table 2.1: Location and instrumentation of glacier AWS used in this study. T = temperature, RH = relative humidity, u = wind speed, Θ = wind direction, K ↑ = reflected shortwave radiation, L↓ = incoming longwave radiation, Q∗ = net radiation. Incoming longwave radiation was measured at off-glacier stations. Site Easting Northing Z (m) Instrumentation PM1 528297 5586081 1960 T , RH, u, Θ, K↑ PM2 528523 5585611 2012 T , RH, u, Θ, K↑, Q∗, L↓ PM3 528404 5584819 2100 T , RH, u, Θ, K↑ PM4 527297 5584624 2313 T , RH, u, Θ, K↑ PM1.08 528523 5585611 2047 T , RH, u, Θ, K↑ PM3.08 528166 5585534 2043 T , RH, u, Θ, K↑ WM1 517126 5555997 2168 T , RH, u, Θ, K↑, Q∗ WM2 516062 5554090 2290 T , RH, u,Θ BM1 457788 5629116 1745 T , RH, u, Θ, K↑
10 2.1. Meteorological Data
Figure 2.1: Location of glacier mass balance sites and ambient automatic weather stations (AWS; triangles), Environment Canada AWS (circles), and snow course sites (diamonds). All map coordinates are given in UTM Zone 10N.
11 2.1. Meteorological Data
Figure 2.2: Place Glacier AWS locations.
12 2.1. Meteorological Data
Figure 2.3: Weart Glacier AWS locations.
13 2.1. Meteorological Data
Figure 2.4: Bridge Glacier AWS locations.
14 2.1. Meteorological Data
(a) Glacier AWS station (b) Measuring reflected radiation with in- verted pyranometer
Figure 2.5: Example of the on-ice meteorological stations (a) and a close- up view of the Gimbel joint used to mount pyranometers horizontal to the surface (b).
15 2.1. Meteorological Data
Table 2.2: Summary of on-glacier AWS periods of operation. Variations in station operation are due to deployment dates, collection dates, and battery life. Year Site Period of operation 2006 PM1 Aug - Sep (50 d) PM2 Aug - Sep (49 d) PM3 Aug - Sep (39 d) PM4 Aug - Sep (50 d) 2007 PM1 May - Sep (50 d) PM2 May - Sep (49 d) PM3 May - Sep (39 d) PM4 May - Sep (50 d) WM1 Jul - Sep (58 d) WM2 Jul - Sep (58 d) 2008 PM1.08 May - Aug (98 d) PM2 May - Sep (132 d) PM3.08 May - Sep (117 d) PM4 May - Aug (111 d) WM1 Jun - Sep (115 d) BM1 May - Aug (77 d)
Table 2.3: Meteorological instrumentation specifications. Parameter Sensor Range Accuracy T Rotronic HC-S3 -30 to +60 ◦C ±0.2◦C RH Rotronic HC-S3 0-100% ±1.5% @ 23◦C Q∗ Kipp & Zonen NR-lite 0.2 - 100 µm −1%/m s−1 -30 to +70 ◦C 0.12%/K u RM Young 01503a 0 - 100 m s−1 ±0.3 m s−1 MetOne 014ab 0 - 45 m s−1 ±0.11 m s−1 Θ RM Young 01503 0 - 360◦ ±3◦ Met One 024a 0 - 360◦ ±5◦ K Kipp & Zonen CMP6 0 - 2000 W · m−2 ±5% (daily) L↓ Kipp & Zonen CGR3 Not listed < 5% a: stall speed: 1.0 m s−1 b: stall speed: 0.45 m s−1
16 2.1. Meteorological Data
2.1.2 Ambient Meteorological Stations
Hourly T and RH were also obtained from six stations located at off-glacier sites (Figure 2.1), and are referred to as the ambient climate data (Ta and
RHa). Pemberton (204 m asl), Whistler Low (922 m asl), and Whistler High (1620 m asl) are long-term climate monitoring sites operated by En- vironment Canada [Environment Canada, 2010]. Ridge stations at Weart Glacier (2220 m asl), Helm Glacier (2192 m asl), and Bridge Glacier (1619 m asl) were installed as part of this study, and maintained year-round from 2006 to 2008. A seventh ambient site located on a ridge above Place Glacier (Figure 2.2) was in operation intermittently, and is used for independent model testing.
Table 2.4: Ambient AWS locations and data source Site Easting (m) Northing (m) Elevation (m) Pembertona 518517 5572019 204 Whistler Low Levela 501430 5548637 933 Whistler High Levela 503577 5548004 1640 Helm Ridgeb 501490 5534354 2192 Weart Ridgeb 518349 5556981 2220 Bridge Ridgeb 463200 5632482 1640 Place Ridgeb 526534 5586943 2075 a: Environment Canada[2010] b: This study
2.1.3 Meteorological Data Post-Processing
Incoming longwave radiation (L ↓) measured with Kipp & Zonen CGR3 pyrgeometers required post-processing to separate the longwave radiation emitted by the sensor body from the net incoming longwave radiation (Lnet) recorded by the sensor. Following the CGR3 manual [Kipp & Zonen, 2009],
Steinhart-Hart equations were used to calculate the sensor temperature Tsens (C) from the voltage (v) returned by the sensor: