Start description of Kangerd demo

dual-problems.bib

@@ -371,3 +371,63 @@ @book{attouch2014variational
   year={2014},
   publisher={SIAM}
 }
+
+
+@article{enderlin2014improved,
+  title={An improved mass budget for the {Greenland} ice sheet},
+  author={Enderlin, Ellyn M and Howat, Ian M and Jeong, Seongsu and Noh, Myoung-Jong and Van Angelen, Jan H and Van Den Broeke, Michiel R},
+  journal={Geophysical Research Letters},
+  volume={41},
+  number={3},
+  pages={866--872},
+  year={2014},
+  publisher={Wiley Online Library}
+}
+
+
+@article{mouginot2019forty,
+  title={Forty-six years of {Greenland Ice Sheet} mass balance from 1972 to 2018},
+  author={Mouginot, J{\'e}r{\'e}mie and Rignot, Eric and Bj{\o}rk, Anders A and Van den Broeke, Michiel and Millan, Romain and Morlighem, Mathieu and No{\"e}l, Brice and Scheuchl, Bernd and Wood, Michael},
+  journal={Proceedings of the national academy of sciences},
+  volume={116},
+  number={19},
+  pages={9239--9244},
+  year={2019},
+  publisher={National Acad Sciences}
+}
+
+
+@article{fettweis2020grsmbmip,
+  title={GrSMBMIP: intercomparison of the modelled 1980--2012 surface mass balance over the Greenland Ice Sheet},
+  author={Fettweis, Xavier and Hofer, Stefan and Krebs-Kanzow, Uta and Amory, Charles and Aoki, Teruo and Berends, Constantijn J and Born, Andreas and Box, Jason E and Delhasse, Alison and Fujita, Koji and others},
+  journal={The Cryosphere},
+  volume={14},
+  number={11},
+  pages={3935--3958},
+  year={2020},
+  publisher={Copernicus GmbH}
+}
+
+
+@article{joughin2010greenland,
+  title={Greenland flow variability from ice-sheet-wide velocity mapping},
+  author={Joughin, Ian and Smith, Ben E and Howat, Ian M and Scambos, Ted and Moon, Twila},
+  journal={Journal of Glaciology},
+  volume={56},
+  number={197},
+  pages={415--430},
+  year={2010},
+  publisher={Cambridge University Press}
+}
+
+
+@article{morlighem2017bedmachine,
+  title={{BedMachine v3: Complete bed topography and ocean bathymetry mapping of Greenland from multibeam echo sounding combined with mass conservation}},
+  author={Morlighem, Mathieu and Williams, Chris N and Rignot, Eric and An, Lu and Arndt, Jan Erik and Bamber, Jonathan L and Catania, Ginny and Chauch{\'e}, Nolwenn and Dowdeswell, Julian A and Dorschel, Boris and others},
+  journal={Geophysical research letters},
+  volume={44},
+  number={21},
+  pages={11--051},
+  year={2017},
+  publisher={Wiley Online Library}
+}

dual-problems.tex

@@ -525,6 +525,33 @@ \subsection{Larsen C Ice Shelf}
 To solve the dual momentum balance equation, we used a linearly implicit scheme (see Appendix \ref{subsec:linearly-implicit-schemes}) with a hand-tuned choice of 10 Newton steps per iteration.
 This approach does not exactly solve the discretized dual momentum balance equation with finite timesteps but the approximation error converges to zero in the limit as the stepsize is reduced.
 
+
+\subsection{Kangerdlugssuaq Glacier}
+
+As our final test case, we studied Kangerdlugssuaq Glacier, a grounded outlet glacier on the east coast of Greenland.
+Kangerdlugssuaq is one of the top three contributors to the total discharge from Greenland \citep{enderlin2014improved, mouginot2019forty}.
+The purpose of this exercise is to demonstrate that we can simulate the evolution of a marine-terminating glacier, including the seasonal advance and retreat of the terminus in response to ocean-induced frontal ablation in summer, using the dual form of the momentum balance equation.
+We do not aim to reproduce the exact calving history.
+
+\textcolor{red}{Description of initialization and experiment}
+
+We used the BedMachine Greenland data set for ice thickness and surface elevation \citep{morlighem2017bedmachine} and the MEaSUREs annual velocity mosaic from 2015-2016 \citep{joughin2010greenland}.
+
+To force the mass conservation equation, we need to provide a surface mass balance field.
+We used version 3.12 of the Mod\`ele Atmosph\'erique R\'egional (MAR), which has been tested extensively for Greenland \citep{fettweis2020grsmbmip}.
+We used a surface mass balance field that varies linearly with elevation:
+\begin{equation}
+    \dot a \approx a_0 + \frac{\delta a}{\delta s}\cdot s
+\end{equation}
+where $a_0$ is the surface mass balance at sea level and $\delta a/\delta s$ is the SMB lapse rate.
+We fit $a_0$ and $\delta a/\delta s$ using yearly-averaged outputs from MAR from 2006-2021.
+The fit had $r^2 = 0.91$, so a substantial fraction of the variance is explainable by surface elevation alone.
+
+\textcolor{red}{How did we do the summer ablation?}
+
+\textcolor{red}{Description of results}
+
+
 \section{Discussion}
 
 \textcolor{red}{Finish this...}