iarc_07_2016.tex

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% title page
\title[] % (optional, use only with long paper titles)
{Disappearing Ice Sheets}



\author[Aschwanden] % (optional, use only with lots of authors)
{Andy Aschwanden}
% - Give the names in the same order as the appear in the paper.
% - Use the \inst{?} command only if the authors have different
%   affiliation.

\institute[Geophysical Institute] % (optional, but mostly needed)
{Geophysical Institute}
% - Use the \inst command only if there are several affiliations.
% - Keep it simple, no one is interested in your street address.

\titlegraphic{\vskip-0.5cm\shadowimage[width=\textwidth]{gris-nw-speed-exp-600m}}

\date{}

\begin{document}

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    \frametitle{Outline}
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  \titlepage
  \note[item]{Today I'd like to present some of the work the ``modeling corner'' of the glacier's group is doing}
\end{frame}


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\begin{frame}[plain]
    \begin{itemize}
      \item Combustion of available fossil fuel resources sufficient to eliminate the Antarctic Ice Sheet (Winkelmann \emph{et al.}, 2015)
      \item this would raise sea level by 58\,m (plus another 7\,m from the Greenland Ice Sheet)
    \end{itemize}
\end{frame}


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\begin{frame}{How an ice sheet loses mass}
  \begin{figure}
    \includegraphics[width=\textwidth]{ice-sheet-cartoon}
  \end{figure}
  \note[item]{explain surface melt, ice discharge/calving, and basal melt}
  \note[item]{snow accumulates in the colder, higher altitude areas in the interior}
  \note[item]{turns into ice}
  \note[item]{and starts to flow downhill towards the coast}
  \note[item]{near the coast, surface melting can occur in the summer}
  \note[item]{but also some ice is dumped directly into the ocean}
  \note[item]{before the mid-90s mass loss was dominated by surface mass balance (80-90\%)}
  \note[item]{contribution of ice discharge was modest (10--20\%)}
  \note[item]{explaining in more detail in the next slide}
\end{frame}


\begin{frame}{Why we expect strong mass loss}
  \begin{block}{Positive feedbacks}
    (at least) two positive feedbacks accelerate mass loss
    \begin{itemize}
    \item with the climate (Bodvardsson effect)
    \item geometrical instability (marine ice sheet hypothesis)
    \end{itemize}
  \end{block}
\end{frame}

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\begin{frame}{Bodvardsson effect: mountain Glacier}
 \begin{figure}
    \includegraphics[width=\textwidth]{bodvardsson-effect_mountain_glacier}
  \end{figure}
\end{frame}

\begin{frame}{Bodvardsson effect: ice Sheet}
 \begin{figure}
    \includegraphics[width=\textwidth]{bodvardsson-effect_ice_sheet}
  \end{figure}
\end{frame}

\begin{frame}[label=misi]{Marine Ice Sheet Instability Hypothesis}
 \begin{figure}
    \includegraphics[height=8cm]{vaughan-misi}
  \end{figure}
\end{frame}

\begin{frame}{Marine Ice Sheet Instability Hypothesis}
 \begin{figure}
    \includegraphics[width=\textwidth]{mercer_1978}
  \end{figure}
\end{frame}

\begin{frame}{Marine Ice Sheet Instability Hypothesis}
  \begin{columns}[c]
    \begin{column}{.65\linewidth}
      \begin{figure}
        \includegraphics<1>[height=8cm]{ant-marine}
        \includegraphics<2>[height=8cm]{ant-shelves}
      \end{figure}
    \end{column}
    \begin{column}{.38\linewidth}
      \begin{itemize}
      \item large areas are below sea level
      \item up to 1\,m SLR by 2100 (DeConto \& Pollard, 2016)
      \item up to 15\,m SLR by 2500 (DeConto \& Pollard, 2016)
      \end{itemize}
    \end{column}
  \end{columns}
\end{frame}



\begin{frame}{Focus on Greenland}
  \begin{columns}[c]
    \begin{column}{.60\linewidth}
      \begin{figure}
        \includegraphics[height=8cm]{gris-marine}
      \end{figure}
    \end{column}
    \begin{column}{.40\linewidth}
      \begin{itemize}
        \item interior is below sea level
        \item but few ``gates'' exist
      \end{itemize}
    \end{column}
  \end{columns}
\end{frame}


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\begin{frame}[plain]
    \begin{itemize}
    \item extent of $1200\,\text{km}\,\times 2400\,\text{km}$ \dots it's a ``dwarf continent''
    \item total area: 2.1 million km$^2$
    \item ice covered area:  1.7 million km$^2$
    \item \alert{for comparison: that's the total area of Alaska}
    \item has ice equivalent to 7 m of sea-level rise
    \item big enough to create its own weather
    \item over past 2 decades: losing mass at an accelerating rate
    \end{itemize}
    \note[item]{Explain why Greenland is of interest}
\end{frame}


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\begin{frame}[plain]
    \begin{figure}
      \movie[showcontrols=true,loop,width=12cm]{\includegraphics[width=12cm]{grace_greenland_2004_2012_still_print}}{grace_greenland_2004_2013_1080p.mov}
  \end{figure}
  \begin{itemize}
  \item<2> 280\,Gt is about half of Lake Eerie or a 15\,cm high layer of water covering Alaska
  \end{itemize}
  \note[item]{show NASA GRACE mass loss animation}
  \note[item]{greatest losses occur on the west coast and SE coast} 
  \note[item]{explain how much 280 Gt really are}
\end{frame}


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\begin{frame}[plain]
  \textbf{The increase in mass loss is roughly equally split between changes in}
  \begin{columns}[c]
    \begin{column}{.3\linewidth}
      \begin{figure}
        \includegraphics[width=\linewidth]{gris-melt-ponds}
      \end{figure}
    \end{column}
    \begin{column}{.3\linewidth}
      \textbf{surface mass balance}
    \end{column}
  \end{columns}
  \begin{columns}[c]
    \begin{column}{.3\linewidth}
      \begin{figure}
        \includegraphics<1>[width=\linewidth]{storeglacier}
      \end{figure}
    \end{column}
    \begin{column}{.3\linewidth}
      \textbf{ice discharge}
    \end{column}
  \end{columns}
  \bigskip
  \textbf{What does that mean?}
  \note[item]{}
\end{frame}


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\begin{frame}[plain]
  \textbf{In Greenland}
    \begin{itemize}
    \item surface mass balance: Regine talked about this
    \item here we focus on ice dynamics
    \item ice discharge to the ocean occurs through 200+ ``outlet glaciers''
    \item outlet glaciers are flowing fast ($>$200\,m/yr), are controlled by bedrock geometry, and terminate in narrow fjords ($\sim <$10\,km wide)
    \end{itemize}
    \note[item]{outlet glaciers look pretty spectacular}
\end{frame}
 
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\begin{frame}{Focus on Greenland}
      \begin{figure}
        \includegraphics[height=8cm]{gris-marine-4outlet}
      \end{figure}
\end{frame}


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\begin{frame}[plain]
  \note[item]{some very passionate glaciologists get really close to the terminus in their sailing boats}
\end{frame}


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\begin{frame}[plain]
  \note[item]{some very passionate glaciologists get really close to the terminus in their sailing boats}
\end{frame}



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\begin{frame}{Jakobshavn Isbr{\ae}, west Greenland}
 \begin{figure}
    \includegraphics[height=.8\textheight]{MODISGreenlandJakobshavn} \\
    \scriptsize{based on MODIS data from M. Fahnestock}
  \end{figure}
  \note[item]{in this talk I will focus on Jakobshavn}
  \note[item]{Greenland's biggest and fastest flowing outlet glacier}
  \note[item]{drains about 7\% of the entire ice sheet}
\end{frame}


\begin{frame}{A short history}
 \begin{figure}
    \includegraphics[width=\textwidth]{Jakobshavn_groundline_retreat} \\
  \end{figure}
  \note[item]{Will Harrison and late Keith Echelmeyer investigated Jakobshavn in the mid-80s}
  \note[item]{at that time JIB had a $\sim$10\,km long floating tongue}
  \note[item]{they found high flow speeds}
  \note[item]{relatively steady behavior}
  \note[item]{in 1997, the glacier suddenly switched from slow thickening to rapid thinning}
  \note[item]{caused by an increase in subsurface ocean temperature from 1.7degC in 1995 to 3.3degC in 1998, leading to increased melting}
  \note[item]{In summer 1998 the first major increase in surface velocity was seen}
  \note[item]{first departure from the normal pattern of frontal positions 1998}
  \note[item]{retreat of the ice front started around 2002}
\end{frame}


\begin{frame}{Frontal retreat 1990--2005}
 \begin{figure}
    \includegraphics<1>[width=\textwidth]{jib-front-1990}
    \includegraphics<2>[width=\textwidth]{jib-front-1990-floating}
    \includegraphics<3>[width=\textwidth]{jib-front-2005}
    \includegraphics<4>[width=\textwidth]{jib-front-1990-2005-change}
    \includegraphics<5>[width=\textwidth]{jib-front-1990-2005-plug}
  \end{figure}
  \note[item]{the loss of the floating tongue is what I'm calling pulling the plug}
  \note[item]{exact timing of the break-up remains elusive due to poor satellite coverage at that time}
\end{frame}


\begin{frame}{When you pull the plug: speed-up 1992-2000}
  \begin{itemize}
    \item almost doubled its flow speed between the 1992 and 2000
    \item slow but steady increase since then
  \end{itemize}
  \begin{figure}
    \includegraphics[width=\textwidth]{Joughin2004Fig2} \\
    \footnotesize{Joughin et al. (2004)}
  \end{figure}
  \note[item]{illustration of the speed up}
\end{frame}

\againframe{misi}

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\begin{frame}{When you pull the plug: changes in ice discharge 2000-2010}
  \begin{itemize}
  \item increase in discharge from 40\,Gt/yr in 2000 to $\sim$60\,Gt/yr in 2010
  \item compared to $\sim$75\,Gt/yr total mass loss from all Alaskan glaciers
  \item fresh water flux into Artic ocean affects ocean circulation
  \end{itemize}
  \note[item]{illustration of the speed up}
\end{frame}


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\begin{frame}{When you pull the plug: surface elevation changes 1985-2007}

  \begin{figure}
    \includegraphics[width=.8\textwidth]{jib-obs-surface-diff-motyka} \\
    \footnotesize{Motyka, Fahnestock, Truffer (2010)}
  \end{figure}
  \note[item]{as a consequence of the increased discharge, the ice surface is drawing down near the glacier terminus}
\end{frame}


\begin{frame}{How can we reconcile/understand these changes?}
 \begin{figure}
    \includegraphics[height=4.15cm]{Joughin2004Fig2} \\
    \includegraphics[height=3.20cm]{jib-front-1990-2005-change}
    \includegraphics[height=3.20cm]{jib-obs-surface-diff-motyka}
  \end{figure}
\end{frame}


\begin{frame}{Answer: use an ice sheet model}
  \begin{figure}
    \includegraphics[width=8cm]{grn_system_eqns}
  \end{figure}
  \begin{columns}[c]
    \begin{column}{.40\linewidth}
      \begin{itemize}
      \item ice dynamics
      \item thermodynamics
      \item surface processes
      \end{itemize}
    \end{column}
    \begin{column}{.55\linewidth}
      \begin{itemize}
      \item boundary conditions
      \item hydrology
      \item ice-ocean interaction (e.g. calving)
      \end{itemize}
    \end{column}
  \end{columns}
  \note[item]{An ice sheet model solves numerical approximations to the balance equations of mass, momentum}
  \note[item]{Ice flow is governed by Stokes equations with a power-law rheology}
  \note[item]{Because the viscosity of ice strongly depends on the thermal state, we also need to solve an energy balance equation}
  \note[item]{This makes the problem thermomechanically-coupled.}
\end{frame}


\begin{frame}{Why ice sheet modeling is easy}
  \begin{columns}[c]
    \begin{column}{.28\linewidth}
      \begin{figure}
        \includegraphics[width=\linewidth]{ggstokes}
        \\ \scriptsize{G.~G.~Stokes}
      \end{figure}
    \end{column}
    \begin{column}{.67\linewidth}
      \begin{itemize}[<+- | alert@+>]
      \item composed of a single, largely homogeneous material
      \item flow governed by the Stokes equations known since the mid-19th century
      \item flows slowly: we can ignore turbulence, Coriolis and other inertial effects
      \item no density/salinity stratification
      \item most of what makes atmosphere and ocean flow interesting is missing
      \item so what makes the flow of slow, cold, laminar ice interesting?
      \end{itemize}
    \end{column}
  \end{columns}
\end{frame}


\begin{frame}{Why ice sheet modeling is so hard}
    \begin{columns}[c]<1-2>
      \begin{column}{.3\linewidth}
        \begin{figure}
          \includegraphics[width=\linewidth]{bw_front_sm}
        \end{figure}
      \end{column}
      \begin{column}{.67\linewidth}
        \begin{block}{Computational costs}
        \begin{itemize}
        \item solving the Stokes equations is computationally very expensive
        \end{itemize}
      \end{block}
      \end{column}
    \end{columns}
    \begin{columns}[c]<1>
      \begin{column}{.28\linewidth}
        \begin{figure}
          \includegraphics[width=\linewidth]{canale_grande_V05}
        \end{figure}
      \end{column}
      \begin{column}{.67\linewidth}
        \begin{block}{Initial conditions}
        \begin{itemize}
        \item ice has a long memory
        \item ice thickness / subglacial topography is a first order constraint on ice flow
        \end{itemize}
      \end{block}
      \end{column}
    \end{columns}
    \begin{columns}[c]<1>
      \begin{column}{.28\linewidth}
        \begin{figure}
          \includegraphics[width=\linewidth]{storeglacier}
        \end{figure}
      \end{column}
      \begin{column}{.67\linewidth}
        \begin{block}{Boundary conditions}
        \begin{itemize}
        \item seaward margin boundary condition
        \item basal boundary condition
        \end{itemize}
      \end{block}
      \end{column}
    \end{columns}
\end{frame}


\begin{frame}
  \frametitle{From Navier-Stokes to Stokes}
  \begin{block}{Momentum Balance}
    \begin{equation}
        \underbrace{\rho \frac{\text{d} \mathbf{v}}{\text{d} t}}_{\text{acceleration}} = - \underbrace{\nabla \cdot \mathbf{T'}}_{\text{deviatoric}} + \underbrace{\nabla p}_{\text{isotropic}} + \underbrace{\rho\mathbf{g}}_{\text{gravity}} - \underbrace{2\rho\boldsymbol{\Omega} \times \mathbf{v}}_{\text{Coriolis force}} 
   \end{equation}
   This is the \alert{Navier-Stokes} equation for incompressible flow
   \vskip.5em
   \begin{itemize}
     \item rather complicated
     \item do we really need all these terms?
     \item \alert{Scale Analysis} is a power- and useful concept to assess the relative importance of terms
     \end{itemize}
  \end{block}
\end{frame}
 
\begin{frame}{From Navier-Stokes to Stokes}
  \begin{block}{Ice sheets are shallow}
    \begin{itemize}
    \item below in red is a no-vertical-exaggeration cross section of Greenland at $71^\circ$
      \small
    \item green and blue: standard vertically-exaggerated cross section
    \end{itemize}
    \begin{center}
      \includegraphics[width=0.4\textwidth]{green_transect} \\
      \footnotesize{Figure by E. Bueler}
    \end{center}
  \end{block}
\end{frame}


\begin{frame}
  \frametitle{Scale Analysis}
  \begin{block}{Some typical values for an ice sheet}
  \begin{equation*}
  \begin{array}{rccl}
    \text{horizontal extend} &  [L] & = & \unit{1000}\kilo\meter\\
    \text{vertical extend} & [H] & = & \unit{1}\kilo\meter \\
    \text{horizontal velocity} & [U] & = & \unit{100}\meter\power{a}{-1}\\
    \text{vertical velocity} & [W] & = & \unit{0.1}\meter\power{a}{-1}\\
    \text{pressure} & [P] & = & \rho g[H] = \unit{10}\mega\pascal\\
    \text{time-scale} & [T] & = &[L]/[U] = 10^{4}\usk\power{a}{1}\\
  \end{array}
  \end{equation*}
  \end{block}
  The aspect ratio $\epsilon$ is defined as
  \begin{equation*}
    \epsilon = \frac{[H]}{[L]} = \frac{[W]}{[L]} = 10^{-3} \text{ for an ice sheet}
  \end{equation*}
  \begin{itemize}
    \item The scaling argument for valley glaciers is almost the same
  \end{itemize}
\end{frame}


\begin{frame}
  \frametitle{Scale Analysis}
  \begin{block}{Froude number}
    The \alert{Froude number $Fr$} is the ratio of acceleration and pressure gradient. In the horizontal we have
  \begin{equation*}
    Fr = \frac{\rho[U]/[t]}{[P]/[L]} = \frac{\rho[U]^{2}/[L]}{\rho g [H]/[L]} = \frac{[U]^{2}}{g[H]} \approx 10^{-15}
  \end{equation*}
  and in the vertical
  \begin{equation*}
    Fr = \frac{\rho[W]/[t]}{[P]/[L]} = \frac{\rho[W]^{2}/[L]}{\rho g [H]/[L]} = \frac{[\epsilon U]^{2}}{g[H]} \approx 10^{-21}
  \end{equation*}
  $\Rightarrow$ The \alert{acceleration term} is \alert{negligible}
  \end{block}
\end{frame}


\begin{frame}
  \frametitle{Scale Analysis}
  \begin{block}{Rossby number}
    The \alert{Rossby number $Ro$} is the ratio of acceleration and Coriolis force
  \begin{equation*}
    Ro = \frac{\rho[U]/[t]}{2\rho\Omega[U]} = \frac{\rho[U]^{2}/[L]}{2\rho\Omega[U]} = \frac{[U]}{2 \Omega [L]} \approx 2\times10^{-8}
  \end{equation*}
  and thus the Coriolis to pressure gradient is
  \begin{equation*}
   \frac{2\rho\Omega[U]}{[P]/[L]} = \frac{Fr}{Ro}\approx 5 \times 10^{-8}
  \end{equation*}
  $\Rightarrow$ The \alert{Coriolis term} is also \alert{negligible}
  \end{block}
\end{frame}


\begin{frame}
  \frametitle{Stokes Equation}
  By neglecting both the
  \begin{itemize}
  \item acceleration term
  \item Coriolis term
  \end{itemize}
  the Navier-Stokes equation simplifies to
  \begin{eqnarray}
     \nabla \cdot \left(\eta\left(\nabla \mathbf{v} + \nabla \mathbf{v}^{\text{T}}\right)\right) - \nabla p & = & - \rho \mathbf{g}
  \end{eqnarray}
  \begin{itemize}
  \item gravitational force exerted on the ice is balanced by stress within the ice
  \end{itemize}
\end{frame}

\begin{frame}{Constitutive equation: ice viscosity $\eta$}
  \begin{columns}
    \column[c]{2.25cm}
    \begin{figure}
      \includegraphics[width=2cm]{figures/fig_4_04}
    \end{figure}
    \column[c]{9cm}
    Numerous lab experiments and field measurements suggest
    \begin{equation}
      \frac{1}{\eta\left(T,p,\sigma_{\text{e}}\right)} =2A\left(T,\omega,p\right)f\left(\sigma_{\text{e}}\right)
    \end{equation}
    \begin{equation*}
      \begin{array}{rcll}
        A(T,\omega,p) & = & A_{0} e^{-(Q+pV)/T} + f(\omega) &\quad \text{Arrhenius law-ish}\\[.25em]
        f\left(\sigma_{\text{e}}\right) & = &\sigma_{\text{e}}^{n-1} &\quad \text{power law}
      \end{array}
    \end{equation*}
  \end{columns}
  \begin{itemize}
  \item $A$ is called \alert{rate factor}, $T$ is temperature, $\omega$ is water content
  \item $n$ is the exponent of the flow law, usually taken as $n=3$
  \end{itemize}
  \vskip1em
  This is known as \alert{Glen's flow law} but similar to Norton's flow law for the flow of steel at high temperatures
\end{frame}


\begin{frame}{Viscosity}
\begin{itemize}
  \item Because viscosity depends on temperature and water content, we have a thermodynamically-coupled problem
  \item[$\Rightarrow$] need to solve an energy balance equation
  \item if ice is at the pressure melting point, it becomes a two-phase flow problem and a Stefan problem
  \end{itemize}
\end{frame}


\begin{frame}{High Performance Computing (HPC)}
  \begin{block}{Exploit modern HPC through parallelism}
    \begin{figure}
      \includegraphics[width=5.5cm]{jason-parallel}
      \hfill
      \includegraphics[width=5.5cm]{bw_front_sm}
    \end{figure}
  \end{block}
\end{frame}


\begin{frame}{Parallel Ice Sheet Model (PISM)}
  \includegraphics[width=4cm]{pism-logo}
  \begin{itemize}
  \item open-source, fully-parallel from start in 2006
  \item primary development at UAF, with global user base
  \item $>$100k lines of code; mostly C++
  \item sustained NASA support \tiny (NAG5-11371, NNX09AJ38C, NNX13AM16G, NNX13AK27G), PI's Bueler, Aschwanden
  \end{itemize}
  \begin{columns}
    \column[c]{4.75cm}
    \begin{figure}
      \includegraphics[width=\textwidth]{pism-uaf-publications}
    \end{figure}
    \column[c]{6.25cm}
    \includegraphics<1>[width=\textwidth]{pism-users}
  \end{columns}
\end{frame}


\begin{frame}{Why ice sheet modeling is so hard}
    \begin{columns}[c]<1>
      \begin{column}{.3\linewidth}
        \begin{figure}
          \includegraphics[width=\linewidth]{bw_front_sm}
        \end{figure}
      \end{column}
      \begin{column}{.67\linewidth}
        \begin{block}{Computational costs}
        \begin{itemize}
        \item solving the Stokes equations is computationally very expensive
        \end{itemize}
      \end{block}
      \end{column}
    \end{columns}
    \begin{columns}[c]<1-2>
      \begin{column}{.28\linewidth}
        \begin{figure}
          \includegraphics[width=\linewidth]{canale_grande_V05}
        \end{figure}
      \end{column}
      \begin{column}{.67\linewidth}
        \begin{block}{Initial conditions}
        \begin{itemize}
        \item ice has a long memory
        \item<1> ice thickness / subglacial topography is a first order constraint on ice flow
        \end{itemize}
      \end{block}
      \end{column}
    \end{columns}
    \begin{columns}[c]<1>
      \begin{column}{.28\linewidth}
        \begin{figure}
          \includegraphics[width=\linewidth]{storeglacier}
        \end{figure}
      \end{column}
      \begin{column}{.67\linewidth}
        \begin{block}{Boundary conditions}
        \begin{itemize}
        \item seaward margin boundary condition
        \item basal boundary condition
        \end{itemize}
      \end{block}
      \end{column}
    \end{columns}
\end{frame}


\begin{frame}{Initialization}
  \begin{figure} \footnotesize
    \begin{tikzpicture}[node distance = 3cm, auto]
      % Place nodes
      \node [initialization] (initialization) {initialization};
      \node [hindcast faded, right of=initialization] (hindcast) {hindcast};
      \node [forecast faded, right of=hindcast] (forecast) {forecast};      
      \path [arrow line] (initialization) -- (hindcast);
      \path [arrow line] (hindcast) -- (forecast);
    \end{tikzpicture}
  \end{figure}
  \begin{itemize}
  \item ice sheet model simulations require an initialized ice sheet
  \end{itemize}
  \begin{columns}[c]
    \begin{column}{.5\textwidth}
      \begin{figure}
        \includegraphics[width=0.25\textwidth]{sr-greenland_topg} \vspace{.1em}
        \includegraphics[width=0.25\textwidth]{sr-greenland_thk} \vspace{.1em}
        \includegraphics[width=0.25\textwidth]{sr-greenland_temp}
      \end{figure}
    \end{column}
    \begin{column}{.5\textwidth}
      distribution of
      \begin{itemize}
      \item mass (ice thickness)
      \item momentum (basal friction)
      \item energy (temperature)
      \end{itemize}
      within the ice sheet
    \end{column}
  \end{columns}   
  \vspace{1em}
  \begin{columns}[t]
    \begin{column}{.5\textwidth}
      \begin{block}{Problem}
        \begin{itemize}
        \item full set of initial conditions not readily available through observations alone
        \end{itemize}
      \end{block}  
    \end{column}
    \begin{column}{.5\textwidth}
      \begin{block}{Solution}
        \begin{itemize}
        \item use of assimilation techniques
          \begin{itemize}
          \item inverse methods
          \item past climate initialization (``spin-up'')
          \end{itemize}
        \end{itemize}
      \end{block}
    \end{column}
  \end{columns}   
\end{frame}


\begin{frame}{Initialization}
  \begin{figure} \footnotesize
    \begin{tikzpicture}[node distance = 3cm, auto]
      % Place nodes
      \node [initialization] (initialization) {initialization};
      \node [hindcast faded, right of=initialization] (hindcast) {hindcast};
      \node [forecast faded, right of=hindcast] (forecast) {forecast};      
      \path [arrow line] (initialization) -- (hindcast);
      \path [arrow line] (hindcast) -- (forecast);
    \end{tikzpicture}
  \end{figure}

  \begin{transbox}[0.75]
    Two general types of methods
    \begin{block}{Inverse methods}
      \begin{itemize}
      \item assimilate present-day data
      \item obtain missing data using inverse theory
      \end{itemize}
    \end{block}
    \begin{block}{Past climate initialization}
      \begin{itemize}
      \item start simulation far back in the past with initial guess
      \item forward simulation using information about past climate
      \end{itemize}
    \end{block}
  \end{transbox}
\end{frame}


\begin{frame}{Initialization: inverse methods}
  data assimilation using adjont methods
  \begin{columns}[c]
    \begin{column}{.46\textwidth}
      \begin{figure}
        \alert{surface velocities} \\
        \includegraphics[height=6cm]{greenland-sar}
      \end{figure}
    \end{column}
    \begin{column}{.04\textwidth}
      \alert{\Large $\Rightarrow$}
    \end{column}
    \begin{column}{.46\textwidth}
      \begin{figure}
        \alert{basal yield stress} \\ 
        \includegraphics[height=6cm]{tauc}
      \end{figure}
    \end{column}
  \end{columns}
\end{frame}


\begin{frame}{Initialization: glacial cycle}
  \begin{figure} \footnotesize
    \begin{tikzpicture}[node distance = 3cm, auto]
      % Place nodes
      \node [initialization] (initialization) {initialization};
      \node [hindcast faded, right of=initialization] (hindcast) {hindcast};
      \node [forecast faded, right of=hindcast] (forecast) {forecast};      
      \path [arrow line] (initialization) -- (hindcast);
      \path [arrow line] (hindcast) -- (forecast);
    \end{tikzpicture}
  \end{figure}
  \begin{itemize}
  \item use low-dimensional time series data from physical surrogates (e.g. $\delta ^{18}O$ record from ice core) for paleo-climate record
  \item run through glacial cycle(s)
  \end{itemize}
  \begin{figure}
    \includegraphics[height=2.5cm]{gripDeltaT}
    \includegraphics[height=2.25cm]{t2m_racmo_clrun_baseline}
    \includegraphics[height=2.25cm]{cmb_racmo_clrun_baseline}
      \end{figure}
\end{frame}


\begin{frame}{Hindcast}
  \begin{figure} \footnotesize
    \begin{tikzpicture}[node distance = 3cm, auto]
      % Place nodes
      \node [initialization faded] (initialization) {initialization};
      \node [hindcast, right of=initialization] (hindcast) {hindcast};
      \node [forecast faded, right of=hindcast] (forecast) {forecast};      
      \path [arrow line] (initialization) -- (hindcast);
      \path [arrow line] (hindcast) -- (forecast);
    \end{tikzpicture}
  \end{figure}
  \begin{itemize}
  \item RACMO2/GR driven by
    \begin{itemize}
      \item ERA-reanalysis from 1961-2004
      \item HadGEM2 from 1971-2004
    \end{itemize}
    \item PISM driven by \alert{monthly time-series} of:
 \end{itemize}
 \begin{columns}[c]
    \begin{column}{.5\linewidth}
      \vspace{-.5cm}
      \begin{figure}
        \scriptsize{2\,m air temperature}\\
        \includegraphics[width=0.6\linewidth]{t2m_racmo_clrun_baseline}
     \end{figure}
    \end{column}
    \begin{column}{.5\linewidth}
      \vspace{-.5cm}
      \begin{figure}
        \scriptsize{climatic mass balance}\\
        \includegraphics[width=0.6\linewidth]{cmb_racmo_clrun_baseline}
     \end{figure}
    \end{column}
  \end{columns}
  \note[item]{Well, ERA-initialization refers to a model initialization using a climate data reanalysis product fed into RACMO,}
  \note[item]{whereas in HadGEM2 initialization, RACMO was driven by the global circulation model HadGEM2}
\end{frame}

\begin{frame}{Forecast}
     \begin{figure} \footnotesize
      \begin{tikzpicture}[node distance = 3cm, auto]
        % Place nodes
        \node [initialization faded] (initialization) {initialization};
        \node [hindcast faded, right of=initialization] (hindcast) {hindcast};
        \node [forecast, right of=hindcast] (forecast) {forecast};      
        \path [arrow line] (initialization) -- (hindcast);
        \path [arrow line] (hindcast) -- (forecast);
      \end{tikzpicture}
    \end{figure}
  \begin{itemize}
  \item RACMO2/GR driven by HadGEM2 RCP 4.5 forcing
  \item PISM driven by RACMO climate:
    \begin{itemize}
      \item RACMO - HadGEM2 directly
      \item RACMO - ERA/HadGEM2 anomalies
    \end{itemize}
  \end{itemize}
      \begin{figure}
       \includegraphics[width=7cm]{ts_HadGEM2_RCP45}
     \end{figure}
\end{frame}

\begin{frame}{Validation: comparison with observations}
  Hindcasts cover an era where we have a variety of in-situ and remotely-sensed observations such as:
  \begin{columns}[c]
    \begin{column}{.4\linewidth}
    \begin{figure}
      \includegraphics[height=1.5cm]{sar-validation}
    \end{figure}
  \end{column}
    \begin{column}{.6\linewidth}
      \begin{itemize}
      \item time series of surface velocities from SAR
  \end{itemize}
\end{column}
 \end{columns}   
  \vspace{-.5em}
  \begin{columns}[c]
    \begin{column}{.4\linewidth}
      \begin{figure}
        \includegraphics[height=1.5cm]{grace-validation} 
      \end{figure}
    \end{column}
    \begin{column}{.6\linewidth}
      \begin{itemize}
      \item cumulative mass change from GRACE
    \end{itemize}
  \end{column}
 \end{columns}   
 \vspace{-1em}
 \begin{columns}[c]
   \begin{column}{.4\linewidth}
     \begin{figure}
       \includegraphics[height=1.5cm]{icesat-validation}
     \end{figure}
   \end{column}
   \begin{column}{.6\linewidth}
     \begin{itemize}     
     \item elevation change from 2003--2009 (ICESat)
     \end{itemize}
 \end{column}
 \end{columns}   
 \begin{columns}[c]
   \begin{column}{.4\linewidth}
   \end{column}
   \begin{column}{.6\linewidth}
     \begin{itemize}     
     \item more data products are becoming available every month
     \end{itemize}
 \end{column}
 \end{columns}   

\end{frame}


\begin{frame}{Why ice sheet modeling is so hard}
    \begin{columns}[c]<1>
      \begin{column}{.3\linewidth}
        \begin{figure}
          \includegraphics[width=\linewidth]{bw_front_sm}
        \end{figure}
      \end{column}
      \begin{column}{.67\linewidth}
        \begin{block}{Computational costs}
        \begin{itemize}
        \item solving the Stokes equations is computationally very expensive
        \end{itemize}
      \end{block}
      \end{column}
    \end{columns}
    \begin{columns}[c]<1-2>
      \begin{column}{.28\linewidth}
        \begin{figure}
          \includegraphics[width=\linewidth]{canale_grande_V05}
        \end{figure}
      \end{column}
      \begin{column}{.67\linewidth}
        \begin{block}{Initial conditions}
        \begin{itemize}
        \item<1> ice has a long memory
        \item ice thickness / subglacial topography is a first order constraint on ice flow
        \end{itemize}
      \end{block}
      \end{column}
    \end{columns}
    \begin{columns}[c]<1>
      \begin{column}{.28\linewidth}
        \begin{figure}
          \includegraphics[width=\linewidth]{storeglacier}
        \end{figure}
      \end{column}
      \begin{column}{.67\linewidth}
        \begin{block}{Boundary conditions}
        \begin{itemize}
        \item seaward margin boundary condition
        \item basal boundary condition
        \end{itemize}
      \end{block}
      \end{column}
    \end{columns}
\end{frame}

\begin{frame}{Challenge: ice thickness}
  \begin{columns}
    \column[c]{1.25cm}
    \includegraphics[width=\textwidth]{nasa-logo} \\
    \includegraphics[width=\textwidth]{oib}
    \column[c]{10cm}
    \begin{itemize}
    \item ice thickness is a leading order constraint on ice flow
    \item but expensive to measure
    \item NASA realized that collecting a lot more ice thickness measurements is crucial to make ice sheet models better
    \item ice thickness measurements using the CReSIS radar became an important part of their Operation IceBridge mission (2009--today)
    \end{itemize}
  \end{columns}
  \begin{figure}
    \includegraphics[width=6cm]{canale_grande_V05}
  \end{figure}
\note[item]{ice thickness is the difference between ice upper surface and the subglacial topography}
\end{frame}


\begin{frame}{NASA Operation IceBridge}
  \vspace{-0.74em}
  \begin{columns}
    \column[c]{4cm}
    \begin{itemize}
    \item additional flight lines since 2009
    \end{itemize}
    \column[c]{6cm}
    \begin{figure}
      \includegraphics[height=8cm]{greenland-bed-old-oib}
    \end{figure}
  \end{columns}
\end{frame}

\begin{frame}{Zoom in to Jakobshavn Isbr{\ae}}
  \begin{figure}
    \small{old (2001) \hspace{5em} new (2014)}
    \includegraphics[width=12cm]{jako_bed}
 \end{figure}
\end{frame}


\begin{frame}{NASA Operation IceBridge}
  \begin{columns}
    \column[c]{8cm}
    \begin{figure}
      \small{old (2001) \hspace{4em} new (2014)}
      \includegraphics[height=7.5cm]{greenland_bed}
    \end{figure}
    \column[c]{4cm}
    \begin{itemize}
    \item from 5\,km to 150\,m horizontal grid resolution
    \end{itemize}
  \end{columns}
\end{frame}



\begin{frame}{Observed flow speeds}
\vspace{-0.74em}
  \begin{columns}
    \column[c]{5cm}
    \begin{figure}
      \includegraphics[width=\textwidth]{greenland-obs-overview}
    \end{figure}
    \column[c]{5cm}
    \only<1>{Jakobshavn Isbr{\ae}}
    \includegraphics<1>[width=\textwidth]{jakobshavn-obs-nogate}
    \only<1>{\\ {} }
  \end{columns}
  \note[item]{let's look at JIB again}
  \note[item]{observations show strongly channelized flow}
  \note[item]{with high flow speeds in the center}
\end{frame}


\begin{frame}{Ice thickness and simulated flow speeds}
\vspace{-0.74em}
  \begin{columns}
    \column[c]{5cm}
    \begin{figure}
      \includegraphics<1-2>[width=\textwidth]{greenland-obs-basal-overview}
      \includegraphics<3-4>[width=\textwidth]{greenland-obs-basal-overview-mo14}
    \end{figure}
    \column[c]{5cm}
    \only<1,3>{Jakobshavn Isbr{\ae}}
    \only<2>{no fast flow}
    \only<4>{fast flow appears}
    \includegraphics<1>[width=\textwidth]{jakobshavn-bed-5000m-ba01}
    \includegraphics<2>[width=\textwidth]{jakobshavn-speed-exp-4500m-ba01}
    \includegraphics<3>[width=\textwidth]{jakobshavn-bed-mo14}
    \includegraphics<4>[width=\textwidth]{jakobshavn-speed-exp-600-v1.2-no-scale-no-gate}
    \only<1>{\\ 5\,km, old data set (2001)}
    \only<2,4>{\\ simulated surface speed}
    \only<3>{\\ 600\,m, new data set (2014)}
  \end{columns}
  \note<1>[item]{now let's do a simualulation with the old ice thickness data}
  \note<2>[item]{there isn't really any fast flow}
  \note<3>[item]{now use the new ice thickness}
  \note<4>[item]{and we get fast flow}
\end{frame}


\begin{frame}{Can we capture the present-day flow field?}
  \begin{figure}
    \includegraphics[height=7cm]{greenland-overview-3}
    \\ \scriptsize{Aschwanden, Fahnestock, Truffer (2016) \textit{Nature Communications}}
  \end{figure}
  \note[item]{first time capturing the flow field for the right reason}
  \note[item]{this is quite a break through in ice sheet modeling}
  \note[item]{though not a surprising one}
  \note[item]{it just confirms what students learn in glaciology 100:}
  \note[item]{ice flows downhill}
\end{frame}



\begin{frame}{Why ice sheet modeling is so hard}
    \begin{columns}[c]<1>
      \begin{column}{.3\linewidth}
        \begin{figure}
          \includegraphics[width=\linewidth]{bw_front_sm}
        \end{figure}
      \end{column}
      \begin{column}{.67\linewidth}
        \begin{block}{Computational costs}
        \begin{itemize}
        \item solving the Stokes equations is computationally very expensive
        \end{itemize}
      \end{block}
      \end{column}
    \end{columns}
    \begin{columns}[c]<1>
      \begin{column}{.28\linewidth}
        \begin{figure}
          \includegraphics[width=\linewidth]{canale_grande_V05}
        \end{figure}
      \end{column}
      \begin{column}{.67\linewidth}
        \begin{block}{Initial conditions}
        \begin{itemize}
        \item ice has a long memory
        \item ice thickness / subglacial topography is a first order constraint on ice flow
        \end{itemize}
      \end{block}
      \end{column}
    \end{columns}
    \begin{columns}[c]<1-2>
      \begin{column}{.28\linewidth}
        \begin{figure}
          \includegraphics[width=\linewidth]{storeglacier}
        \end{figure}
      \end{column}
      \begin{column}{.67\linewidth}
        \begin{block}{Boundary conditions}
        \begin{itemize}
        \item seaward margin boundary condition
        \item basal boundary condition
        \end{itemize}
      \end{block}
      \end{column}
    \end{columns}
\end{frame}



\begin{frame}{Challenge: basal boundary condition}
  \begin{columns}[c]
    \begin{column}{.45\linewidth}
      \begin{figure}
        \scriptsize{basal resistance} \\
        \includegraphics[width=\textwidth]{tauc}
      \end{figure}
    \end{column}
    \begin{column}{.54\linewidth}
      \begin{itemize}
      \item stresses vary by orders of magnitude
      \item basal hydrology, the glacier's ``plumbing system'' runs on a faster ime scale than ice flow
      \item despite more than 5 decades of research, we only have crude parametrizations
      \end{itemize}
    \end{column}
  \end{columns}
  \note[item]{First, stresses at the base vary by several orders of magnitude}
  \note[item]{depend on many factors, most importantly on the presence or absence of water}
  \note[item]{basal hydrology (the glacier's plumbing system) runs on a faster time scale than the ice flow itself}
  \note[item]{but the sub-glacial environment is not easy accessible}
  \note[item]{at the basal boundary, interactions between water flow, friction, heat flow, and sediment deformation is so complex that a deriving a theory from first principles is real challenge}
\end{frame}


\begin{frame}{Challenge: seaward margin boundary condition}
      \begin{figure}
        \includegraphics[width=.75\textwidth]{ice-shelf}
      \end{figure}
      \begin{itemize}
      \item ocean circulation $\Rightarrow$ basal melt rates
      \item calving mechanism
      \end{itemize}
      \note[item]{a big challenge is to understand how changing ocean currents and ocean temperatures affects sub-shelf basal melt rates}
      \note[item]{how this can weaken a shelf, and potentially lead to break up}
\end{frame}


\begin{frame}{What has the future in stock?}
    \begin{figure}
      \movie[showcontrols=true,autostart,loop,width=12cm]{\includegraphics[width=12cm]{jak_collapse_frame000}}{jak_collapse.mov}
  \end{figure}
\end{frame}


\begin{frame}{Ice sheets in Earth System Models}
\begin{itemize}
\item groups are working on integrating ice sheet models as the land ice component in GCMs
\item 2005: first interactive land ice model in a GCM
\item today: a few Earth System Models have interactive ice sheets
\item technical challenges remain, land ice models have to be run at much higher resolution than the atmosphere component
\end{itemize}
\end{frame}



% \begin{frame}{Acknowledgments}
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%   \begin{columns}[c]
%     \begin{column}{2cm}
%       \shadowimage[height=1.75cm]{mark}    
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%     \begin{column}{3cm}
%       Mark Fahnestock
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%     \begin{column}{3.5cm}
%       Martin Truffer
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%       Ed Bueler
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%     \begin{column}{3.5cm}
%       Constantine Khroulev
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%   \bigskip
%   \begin{itemize}
%     \item \ldots and the glacier's group
%   \end{itemize}
% \end{frame}


\end{document}