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\begin{document}

\title[Whistler, Horstman, Blackcomb Glaciers, southwest British Columbia, Canada]{Supplementary Material: On the demise of Whistler, Horstman and Blackcomb Glaciers, southwest British Columbia, Canada: historical use, recent change and future prospects within a mountain resort}

\author[Monty et al.]{Chloé MONTY$^1$, Gwenn E. FLOWERS$^1$, 
Jeffrey W. CROMPTON$^2$, Brian MENOUNOS$^{2,3,4}$, \\ Caleb MATHIAS$^3$}

\affiliation{%
$^1$Department of Earth Sciences, Simon Fraser University, Burnaby, British Columbia, Canada \\
$^2$Natural Resources Canada, Geological Survey of Canada -- Pacific, Vancouver, British Columbia, Canada \\
$^3$Department of Geography, Earth, and Environmental Science, University of Northern British Columbia, Prince George, British Columbia, Canada \\
$^4$ Hakai Institute, Campbell River, British Columbia, Canada \\
  Correspondence: Chloé Monty 
  \email{chloe\_monty@sfu.ca}}
  
\begin{frontmatter}

\maketitle

% \tableofcontents

\end{frontmatter}

\renewcommand{\thetable}{S\arabic{table}}
\renewcommand{\thefigure}{S\arabic{figure}}

\subsection{Remote sensing imagery details}

% Aerial photographs
We used high-resolution aerial photographs from the Government of British Columbia from 1973, 1989, 1990 and 2005 to delineate glacier extent \citep{Government_of_british_columbia_digital_2025}. These images were photogrammetrically processed using Agisoft Metashape (version 2.1.0; https://www.agisoftmetashape.com, last access 17 June 2025) to generate orthoimagery with ground sampling distance (GSD) between 0.11--0.19\,m. We also mapped glacier extent from a 2006 aerial orthophoto from the Resort Municipality of Whistler (0.4\,m GSD). \citep{Resort_municipality_of_whistler_aerial_2006}.
% 
% Google Earth (Maxar Technologies): WorldView-3
% 
We mapped glacier extents from spaceborne imagery from three sources of optical satellite imagery, including a 2014 image from Maxar Technologies obtained through Google Earth. This image was captured by the WorldView-3 optical satellite at a resolution of 30\,cm \citep{Maxar_technologies_worldview-3_2025}.
% 
% Sentinel-2
% 
A 2015 image with 10\,m resolution captured by the European Space Agency's Sentinel-2 satellite was also used (ESA, \citeyear{European_space_agency_esa_sentinel-2_2025}), 
% 
% PlanetScope
% 
as were 2016 to 2024 images with 3\,m resolution from Planet Lab's PlanetScope satellite constellation \citep{Planet_developers_planetscope_2025}. The PlanetScope satellites used here were the Dove Classic for 2016--20 and the SuperDove for 2021--24. 
%
See Table \ref{tab:imagery} for the dates of each image used, their resolution and source.

\subsection{Glacier extent}

See Table \ref{tab:extent_all} for glacier area values and associated errors for Whistler, Horstman and Blackcomb Glaciers, including the western section of Whistler Glacier. See Fig. \ref{fig:all_w} and \ref{fig:all_h_b} for all glacier outlines between 1973--2024. See Fig. \ref{fig:piecewise} for unweighted and piecewise linear regressions (2010/11) for glacier area change.

\subsection{Climate datasets}

The climate datasets used in this study include downscaled CMIP6 air-temperature data (Coupled Model Intercomparison Project, Phase 6) from the Pacific Impacts Climate Consortium (PCIC, \citeyear{Pacific_climate_impacts_consortium_statistically_2023}), temperature and snowfall measurements from Environment and Climate Change Canada (ECCC) stations (PCIC, \citeyear{Pacific_climate_impacts_consortium_bc_2025}), snowfall measurements provided by the avalanche forecasters at Whistler Mountain (\citeyear{Whistler_avalanche_forecasters_seasonal_2025}), and snowfall density measurements from \citet{Barton_twenty-seven_2017}.
ERA5-Land geopotential heights \citep{Munoz_sabater_era5-land_2019} were used to assign an elevation to each downscaled CMIP6 gridcell in order to adjust the temperature and accumulation data to the mean elevation of each glacier.

The downscaled CMIP6 data can be accessed from PCIC at https://www.pacificclimate.org/data/statistically-downscaled-climate-scenarios, and the BC weather station data can be accessed at https://www.pacificclimate.org/data/bc-station-data. The ERA5-Land data can be accessed at https://cds.climate.copernicus.eu/datasets/reanalysis-era5-land?tab=overview.

\subsection{Temperature lapse rate}

See Fig. \ref{fig:stations_map} for a map of the weather stations used to calculate the temperature lapse rate, and Fig. \ref{fig:T_lapse} for monthly temperature lapse rates calculated between April and October 2005--21. The temperature data were binned monthly at each station, and the mean monthly temperatures were used to calculate the temperature lapse rate for months where at least two stations had temperature data available.

\subsection{Accumulation lapse rate}

See Fig. \ref{fig:stations_map} for a map of the weather stations used to calculate the accumulation lapse rate, and Fig. \ref{fig:acc_lapse} for seasonal (November to April) accumulation lapse rates calculated between 1984--90. All five weather stations used had winter snowfall measurements available from 1983/84 to 1989/90, so the accumulation lapse rate was calculated for each season across the five weather stations.

\subsection{DDF calculations}

See Table \ref{tab:DDF} for mean elevation and elevation change between LiDAR surveys (27 September 2017, 28 September 2020, 16 September 2024), net balance, accumulation adjusted with an empirical lapse rate, ablation, number of days with positive temperatures between LiDAR survey dates, PDDs and DDFs for Whistler, Horstman and Blackcomb Glaciers.

\subsection{Disappearance dates for all methods}

See Table \ref{tab:extent_disappear} for projected disappearance dates of Whistler, Horstman and Blackcomb Glaciers using different least-squares linear regressions. See Table \ref{tab:vol_disappear} for disappearance dates of Whistler, Horstman and Blackcomb Glaciers for different ice-thickness models (\citet{Farinotti_consensus_2019} and \citet{Millan_ice_2022}), initialisation dates and CMIP6 SSPs. Note that the range of dates reported represents the range calculated for DDFs using ice densities of 790 to 910\,kg\,m\textsuperscript{-3}.

\subsection{Spatially distributed projections of glacier change}

See Fig. \ref{fig:PDD} for spatially distributed glacier loss projected with the mass-balance model for both \citet{Farinotti_consensus_2019} and \citet{Millan_ice_2022} ice-thicknes models initialized in 2000 under CMIP6 SSP2 with an ice density of 850\,kg\,m\textsuperscript{-3}.

\subsection{Sensitivity of mass-balance model}

See Table \ref{tab:sensitivity} for the average DDFs and disappearance dates for cases where the density of snow, annual accumulation, and temperature and accumulation lapse rates are varied by $\pm$20\% from their reference values and the model is initialised with the \citet{Millan_ice_2022} ice-thickness distribution in 2007 under CMIP6 SSP2. See Fig. \ref{fig:sensitivity} for the associated normalised volume curves.

\subsection{Rate of area change comparison for Methods 1 and 2}

See Table \ref{tab:area_comp} for rates of area change calculated from glacier extent measurements (Method 1) and application of the mass-balance model (Method 2). See Fig. \ref{fig:area_comp} for a comparison of linear regressions from Method 1 (unweighted, weighted) and Method 2 applied to both the \citet{Farinotti_consensus_2019} model initialised in 2000 and 2007, and the \citet{Millan_ice_2022} model initialised in 2000 and 2015.

\clearpage

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% 
% \section{Remote sensing imagery details}

\begin{table}
\caption{Airborne and satellite imagery used to map glacier extent between 1973--2024 with associated date, image type, resolution and source.}
\label{tab:imagery}
\begin{minipage}{120mm}
\begin{tabular}{@{}lllrl}
\hline
Year & Date & Image type & Resolution & Source \\
\hline
1973 & 08 Aug & Aerial photograph* & 0.17\,m & BC Lands Service Forest Survey \\
1985 & Unknown & DEM \& optical imagery & 30\,m & TRIM corrected w/ Landsat \citep{Bevington_accelerated_2022} \\
1989 & 22 Jul & Aerial photograph* & 0.11\,m & BC Surveys and Resource Mapping \\
1990 & 16 Jul & Aerial photograph* & 0.16\,m & BC Surveys and Resource Mapping \\
2005 & 24 Sep & Aerial photograph & 0.19\,m & Selkirk Remote Sensing Limited \\
2006 & Unknown & Aerial photograph & 0.40\,m & Resort Municipality of Whistler \\
2014 & 09 Sep & Optical imagery & 0.30\,m & Maxar Technologies: WorldView-3 (accessed via Google Earth) \\
2015 & 04 Oct & Optical imagery & 10\,m & European Space Agency: Sentinel-2 \\
2016 & 16 Aug & Optical imagery & 3\,m & Planet Labs: PlanetScope \\
2017 & 30 Aug & Optical imagery & 3\,m & Planet Labs: PlanetScope \\
2018 & 28 Aug & Optical imagery & 3\,m & Planet Labs: PlanetScope \\
2019 & 27 Aug & Optical imagery & 3\,m & Planet Labs: PlanetScope \\
2020 & 11 Sep & Optical imagery & 3\,m & Planet Labs: PlanetScope \\
2021 & 15 Aug & Optical imagery & 3\,m & Planet Labs: PlanetScope \\
2022 & 31 Aug & Optical imagery & 3\,m & Planet Labs: PlanetScope \\
2023 & 27 Aug & Optical imagery & 3\,m & Planet Labs: PlanetScope \\
2024 & 04 Sep & Optical imagery & 3\,m & Planet Labs: PlanetScope \\
\hline
\end{tabular}
*snow-covered
\end{minipage}
\end{table}

% \section{Glacier extent values}

\begin{table}
\caption{Values of glacier area and associated error for Whistler Glacier (main/eastern and western sections), Horstman and Blackcomb Glaciers. All values in m\textsuperscript{2}.}
\label{tab:extent_all}
\begin{tabular}{@{}lcccccccc}
\hline
Year%
 & Whistler 
 & Error
 & Whistler 
 & Error
 & Horstman 
 & Error
 & Blackcomb 
 & Error \\ 
 & (main/east) & & (west) & & & & \\
\hline
 1973 &  224,310 &   1057 &  74,922 &    322 &  467,433 &   1127 &  724,913 &    1610 \\
 1985 &  148,864 &  57,450 &   --- &     --- &  359,137 &  90,870 &  611,882 &  156,030 \\
 1989 &  197,802 &    755 &  66,815 &    235 &     --- &   --- &      --- &     --- \\
 1990 &     --- &    --- &    --- &    --- &  420,064 &   1203 &  675,066 &    1569 \\
 2005 &   72,732 &    500 &  33,744 &    312 &  283,549 &    594 &  451,345 &    1500 \\
 2006 &   72,405 &    762 &  32,250 &    419 &  260,112 &   1073 &  434,610 &    1920 \\
 2014 &   58,132 &    533 &  25,157 &    331 &  223,803 &    978 &  384,245 &    1875 \\
 2015 &   48,899 &  19,150 &  27,593 &  10,770 &  249,200 &  29,570 &  391,821 &   50,280 \\
 2016 &   56,652 &   6663 &  27,251 &   4158 &  227,006 &  10,953 &  419,272 &   14,412 \\
 2017 &   48,930 &   7605 &  26,449 &   4239 &  220,592 &  12,102 &  406,488 &   15,024 \\
 2018 &   33,762 &   6333 &  22,629 &   3084 &  187,261 &   9519 &  364,965 &   19,533 \\
 2019 &   29,616 &   5571 &  19,961 &   2499 &  174,486 &  10,329 &  362,059 &   19,602 \\
 2020 &   22,289 &   5892 &  16,657 &   2199 &  156,055 &   8244 &  355,404 &   19,701 \\
 2021 &   21,203 &   3894 &  15,771 &   1791 &  150,173 &   9126 &  343,328 &   18,387 \\
 2022 &     --- &    --- &    --- &    --- &  146,721 &   9075 &     --- &     --- \\
 2023 &   13,026 &   2160 &  11,028 &   2115 &  128,623 &   8088 &  323,115 &   17,973 \\
 2024 &   11,687 &   1974 &   9401 &   1860 &  121,245 &   7995 &  306,920 &   19,263 \\
\hline
\end{tabular}
\end{table}

\begin{figure}
\centering
\includegraphics[width=125mm]{Figures/All_outlines_W.pdf}
\caption{1973--2024 Whistler Glacier extents mapped from airborne and satellite imagery. Background image credit: \textcopyright \citeyear{Planet_copyright_2024} Planet Labs PBC.}
\label{fig:all_w}
\end{figure}

\begin{figure}
\centering
\includegraphics[width=165mm]{Figures/All_outlines_H_B.pdf}
\caption{1973--2024 Horstman and Blackcomb Glacier extents mapped from airborne and satellite imagery. Background image credit: \textcopyright \citeyear{Planet_copyright_2024} Planet Labs PBC.}
\label{fig:all_h_b}
\end{figure}

\begin{figure}
\centering
\includegraphics[width=115mm]{Figures/W_2024.png}
\caption{Map of Whistler Glacier without outlines. Background image credit: \textcopyright \citeyear{Planet_copyright_2024} Planet Labs PBC.}
\label{fig:w_2024}
\end{figure}

\begin{figure}
\centering
\includegraphics[width=150mm]{Figures/H_B_2024.png}
\caption{Map of Horstman and Blackcomb glaciers without outlines. Background image credit: \textcopyright \citeyear{Planet_copyright_2024} Planet Labs PBC.}
\label{fig:h_b_2024}
\end{figure}

\begin{figure}
\centering
\includegraphics[width=120mm]{Figures/extent_piecewise_01.pdf}
\caption{Timeseries with unweighted and piecewise least-squares linear regressions. Black dashed line indicates the 0.05\,km\textsuperscript{2} threshold \citep{Bolch_landsat-based_2010,Bevington_accelerated_2022,Pelto_loss_2025} and grey dashed line indicates the 0.01\,km\textsuperscript{2} threshold \citep{Leigh_identifying_2019,Maussion_randolph_2023}. Piecewise regressions split at 2010/11, calculated using data between 1973--2006 and 2014--24. The regressions post-2011 are all steeper than pre-2010, especially for Horstman Glacier. Note asymmetric uncertainties in 1973, 1989, 1990, where snow cover permitted only an upper bound on area.}
\label{fig:piecewise}
\end{figure}

\begin{figure}
\centering
\includegraphics[width=120mm]{Figures/glacier_extent_log_01.pdf}
\caption{Semi-log plot with timeseries of glacier extent. Black dashed line indicates the 0.05\,km\textsuperscript{2} threshold \citep{Bolch_landsat-based_2010,Bevington_accelerated_2022,Pelto_loss_2025} and grey dashed line indicates the 0.01\,km\textsuperscript{2} threshold \citep{Leigh_identifying_2019,Maussion_randolph_2023}. Note asymmetric uncertainties in 1973, 1989, 1990, where snow cover permitted only an upper bound on area.}
\label{fig:semilog}
\end{figure}

% \section{Climate datasets}

% 

% \section{Temperature lapse rate}

\begin{figure}
\centering
\includegraphics[width=178mm]{Figures/WB_stations_final.pdf}
\caption{Overview map showing labelled weather stations. Station names that start with `EC' represent Environment and Climate Change Canada, data obtained via the \citet{Pacific_climate_impacts_consortium_bc_2025}. Pig Alley weather station data were obtained from the avalanche forecasters on Whistler Mountain in \citeyear{Whistler_avalanche_forecasters_seasonal_2025}. Stations shown in magenta were used for temperature (T) lapse rate calculations, stations shown in blue were used for accumulation (acc.) lapse rate calculations, and those represented by white triangles were used for both.}
\label{fig:stations_map}
\end{figure}

\clearpage

\begin{figure}
\centering
\includegraphics[width=178mm]{Figures/temp_lapse_corrected.pdf}
\caption{Monthly temperature lapse rates calculated between April and October 2005--2021. Each point represents a temperature lapse-rate value calculated over a single month where at least two stations had temperature data available.}
\label{fig:T_lapse}
\end{figure}

% \section{Accumulation lapse rate}

\begin{figure}
\centering
\includegraphics[width=178mm]{Figures/acc_lapse_corrected_v2.pdf}
\caption{Seasonal (November to April) accumulation lapse rates calculated between 1984--90. All five stations used had winter snowfall measurements available from 1983/84 to 1989/90.}
\label{fig:acc_lapse}
\end{figure}

% \section{DDF calculations}

\begin{landscape}
\begin{table}
\caption{DDF calculation quantities: mean elevation and elevation change between LiDAR surveys (YYYYMMDD: 20170927, 20200928, 20240916), net balance, accumulation adjusted with empirical lape rate, ablation, number of days with positive temperatures between LiDAR survey dates, PDDs and DDFs for Whistler, Horstman and Blackcomb Glaciers.}
\label{tab:DDF}
\begin{tabular}{@{}lcccccccccc}
\hline
 & & \multicolumn{2}{c}{Elevation change (m)} & \multicolumn{2}{c}{Net balance (m\,w.e.)} & \multicolumn{2}{c}{Adjusted acc. (m\,w.e.)} & \multicolumn{2}{c}{Ablation (m\,w.e.)} \\
\hline
\textbf{Glacier}
 & Mean elevation (m)
 & 2017--20
 & 2020--24
 & 2017--20
 & 2020--24 
 & 2017--20
 & 2020--24
 & 2017--20
 & 2020--24\\
\hline
 Whistler & 2006 & --- & --- & --- & --- & 3.18 & 4.24 & --- & --- \\
 Horstman & 2151 & -3.16 & -5.73 & -2.68 & -4.86 & 3.35 & 4.47 & -6.04 & -9.34 \\
 Blackcomb & 2118 & -2.50 & -5.41 & -2.12 & -4.59 & 3.31 & 4.42 & -5.44 & -9.01 \\
\hline
 & & \multicolumn{2}{c}{\# of days} & \multicolumn{2}{c}{PDD (\textdegree C\,d)} & \multicolumn{3}{c}{DDF (mm\,w.e.\,\textdegree\,C\textsuperscript{-1}\,d\textsuperscript{-1})} \\
\hline
 & & 2017--20 & 2020--24 & 2017--20 & 2020--24 & 2017--20 & 2020--24 & \textbf{2017--24 avg} \\
\hline
 Whistler & & 549 & 785 & 4081 & 5611 & --- & --- & --- \\
 Horstman & & 519 & 732 & 3721 & 5091 & 1.50 & 1.69 & \textbf{1.60} \\
 Blackcomb & & 489 & 679 & 3231 & 4409 & 1.56 & 1.89 & \textbf{1.72} \\
\hline
 & & & & & & & \textbf{Mean used for Whistler} & \textbf{1.66} \\
\hline
\end{tabular}
\end{table} 
\end{landscape}

% \section{Disappearance dates for all methods}

\begin{table}
\centering
\caption{Disappearance dates of Whistler, Horstman and Blackcomb Glaciers estimated by extrapolating various least-squares linear regressions of glacier area as a function of time: unweighted, weighted inversely proportional to uncertainties (1/err) or the logarithm of uncertainties (1/log(err)), and piecewise (post-2011).}
\label{tab:extent_disappear}
\begin{tabular}{@{}lcccc}
\hline
Glacier & Unweighted regression & Weighted (1/err) & Weighted (1/log(err)) & Piecewise (post-2011) \\
\hline
Whistler & 2027 & 2035 & 2027 & 2026 \\
Horstman & 2046 & 2047 & 2049 & 2033 \\
Blackcomb & 2063 & 2070 & 2065 & 2057 \\
\hline
\end{tabular}
\end{table}

\begin{table}
\centering
\caption{Disappearance dates of Whistler, Horstman and Blackcomb Glaciers for the different ice-thickness models (\citet{Farinotti_consensus_2019} and \citet{Millan_ice_2022}), initialisation dates (representative of range of acquisition dates of the surface DEMs used by the ice-thickness models) and CMIP6 SSPs. Note that the range of dates for each scenario represents the range calculated for DDFs using ice densities of 790 to 910\,kg\,m\textsuperscript{-3}.}
\label{tab:vol_disappear}
\begin{tabular}{@{}lllccc}
\hline
Glacier   & Ice model & Initialisation date & SSP1       & SSP2       & SSP5      \\
\hline
Whistler  & Farinotti & 2000         & 2018--21 & 2018--21 & 2018--21 \\
          &           & 2007         & 2023--25 & 2023--25 & 2023--25 \\
          & Millan    & 2000         & 2032--35 & 2032--35 & 2032--35 \\
          &           & 2015         & 2042--44 & 2042--45 & 2040--42 \\
\hline
Horstman  & Farinotti & 2000         & 2038--43 & 2038--43 & 2037--41 \\
          &           & 2007         & 2042--46 & 2042--46 & 2041--44 \\
          & Millan    & 2000         & 2061--67 & 2059--64 & 2055--59 \\
          &           & 2015         & 2068--74 & 2065--70 & 2059--63 \\
\hline
Blackcomb & Farinotti & 2000         & 2046--51 & 2046--50 & 2044--47 \\
          &           & 2007         & 2049--54 & 2049--53 & 2046--49 \\
          & Millan    & 2000         & 2089--2100 & 2080--87 & 2071--76 \\
          &           & 2015         & 2096--(>2100) & 2085--91 & 2074--78 \\
\hline
\end{tabular}
\end{table}

\begin{figure}
\centering
\includegraphics[width=178mm]{Figures/GlacierVolumeWide_final.pdf}
\caption{Spatially distributed projections of ice thicknesses (m) using the mass-balance model initialized in 2000 under CMIP6 SSP2 with an ice density of 850\,kg\,m\textsuperscript{-3}. Distributions shown for 2007, 2020 and 2035 for Whistler (W), Horstman (H) and Blackcomb (B) Glaciers. (a) \citet{Farinotti_consensus_2019} ice-thickness model. (b) \citet{Millan_ice_2022} ice-thickness model. Note the change in colour scale between (a) and (b).}
\label{fig:PDD}
\end{figure}

\clearpage

% \section{Sensitivity of mass-balance model}

\begin{table}
\caption{Whistler (W), Horstman (H) and Blackcomb Glacier (B) DDFs, in units of mm\,w.e.\,\textdegree\,C\textsuperscript{-1}\,d\textsuperscript{-1}, and disappearance dates for scenarios where the density of snow, annual accumulation, temperature and accumulation lapse rates are varied by $\pm$20\% from their reference values (bold). Note that W DDF is the average of H DDF and B DDF. Mass-balance model initialised with the \citet{Millan_ice_2022} ice thicknesses in 2007 under CMIP6 SSP2.}
\label{tab:sensitivity}
\begin{tabular}{@{}lcccccc}
\hline
 & W DDF & H DDF & B DDF & Whistler & Horstman & Blackcomb \\
\hline
 Density of snow (72.4\,kg\,m\textsuperscript{-3}) & 1.48 & 1.43 & 1.54 & 2039 & 2064 & 2088 \\
 \textbf{Density of snow (90.5\,kg\,m\textsuperscript{-3})} & \textbf{1.66} & \textbf{1.60} & \textbf{1.72} & \textbf{2038} & \textbf{2063} & \textbf{2086}  \\
 Density of snow (108.6\,kg\,m\textsuperscript{-3}) & 1.84 & 1.76 & 1.91 & 2037 & 2063 & 2084  \\
\hline
 Annual accumulation (824\,cm\,a\textsuperscript{-1}) & N/A & N/A & N/A & 2034 & 2058 & 2077 \\
 \textbf{Annual accumulation (1030\,cm\,a\textsuperscript{-1})} & N/A & N/A & N/A & \textbf{2038} & \textbf{2063} & \textbf{2086} \\
 Annual accumulation (1236\,cm\,a\textsuperscript{-1}) & N/A & N/A & N/A & 2042 & 2071 & 2094 \\
\hline
 Temp. lapse rate (4.59\,\textdegree C\,km\textsuperscript{-1}) & 1.54 & 1.47 & 1.60 & 2042 & 2070 & 2093 \\
 \textbf{Temp. lapse rate (5.74\,\textdegree C\,km\textsuperscript{-1})} & \textbf{1.66} & \textbf{1.60} & \textbf{1.72} & \textbf{2038} & \textbf{2063} & \textbf{2086} \\
 Temp. lapse rate (6.89\,\textdegree C\,km\textsuperscript{-1}) & 1.80 & 1.73 & 1.86 & 2034 & 2058 & 2078 \\
\hline
 Acc. lapse rate (358\,cm\,a\textsuperscript{-1}\,km\textsuperscript{-1}) & 1.63 & 1.56 & 1.69 & 2038 & 2064 & 2086 \\
 \textbf{Acc. lapse rate (447\,cm\,a\textsuperscript{-1}\,km\textsuperscript{-1})} & \textbf{1.66} & \textbf{1.60} & \textbf{1.72} & \textbf{2038} & \textbf{2063} & \textbf{2086} \\
 Acc. lapse rate (537\,cm\,a\textsuperscript{-1}\,km\textsuperscript{-1}) & 1.69 & 1.63 & 1.76 & 2038 & 2065 & 2085 \\
\hline
\end{tabular}
\end{table} 

\begin{figure}
\centering
\includegraphics[width=178mm]{Figures/sensitivity_corrected_v2.pdf}
\caption{Normalised glacier volume initialised at 1.0 with the \citet{Millan_ice_2022} ice-thickness model in 2007 under CMIP6 SSP2 for cases varying the following parameters by $\pm$20\% from their reference values: density of snow, annual accumulation, temperature (T) and accumulation (acc) lapse rate.}
\label{fig:sensitivity}
\end{figure}

\clearpage

% \section{Rate of area change comparison}

\begin{table}
\caption{Rates of area change in km\textsuperscript{2}\,a\textsuperscript{-1} for Whistler, Horstman and Blackcomb Glaciers. Top section: values determined from least-squares linear regression of glacier area as a function of time; these include regressions that are unweighted, weighted inversely proportional to uncertainties (1/err) or the logarithm of uncertainties (1/log(err)), and piecewise pre-2010 and post-2011. Bottom section: values determined from applying the mass-balance model under the CMIP6 SSP2 scenario with an ice density of 850\,kg\,m\textsuperscript{-3} to the \citet{Farinotti_consensus_2019} and \citet{Millan_ice_2022} ice-thickness models variously initialised in 2000, 2007 and 2015.}
\label{tab:area_comp}
\begin{tabular}{@{}lcccccc}
\hline
Glacier & Unweighted regression & Weighted (1/err) & Weighted (1/log(err)) & Piecewise: Pre-2010 & Post-2011 \\
\hline
Whistler & $-0.0042$ & $-0.0025$ & $-0.0042$ & $-0.0047$ & $-0.0051$ \\
Horstman & $-0.0066$ & $-0.0068$ & $-0.0063$ & $-0.0058$ & $-0.0130$ \\
Blackcomb & $-0.0082$ & $-0.0069$ & $-0.0081$ & $-0.0088$ & $-0.0097$ \\
\hline
 & Farinotti, 2000 & Millan, 2000 & Farinotti, 2007 & Millan, 2015 & \\
\hline
Whistler & $-0.0042$ & $-0.0027$ & $-0.0046$ & $-0.0032$ & \\
Horstman & $-0.0075$ & $-0.0055$ & $-0.0084$ & $-0.0063$ & \\
Blackcomb & $-0.0112$ & $-0.0067$ & $-0.0013$ & $-0.0075$ & \\
\hline
\end{tabular}
\end{table}

\begin{figure}
\centering
\includegraphics[width=178mm]{Figures/area_comparison_final.pdf}
\caption{Glacier area versus time determined using a subset of the methods described in Table \ref{tab:area_comp}, with the exception of the piecewise regression (see legend). (a) Whistler Glacier. (b) Horstman Glacier. (c) Blackcomb Glacier.}
\label{fig:area_comp}
\end{figure}


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