Index: /issm/trunk/doc/validation/Makefile =================================================================== --- /issm/trunk/doc/validation/Makefile (revision 811) +++ /issm/trunk/doc/validation/Makefile (revision 811) @@ -0,0 +1,12 @@ +#Makefile for thesis + +all: pdf + + +pdf: + pdflatex validation + pdflatex validation + pdflatex validation + +clean: + rm -rf *.dvi *.ps *.pdf *.toc *.log *.aux *.out *.mtc* *.idx *.maf *.lof *.lot *.bbl *.blg Index: /issm/trunk/doc/validation/validation.tex =================================================================== --- /issm/trunk/doc/validation/validation.tex (revision 811) +++ /issm/trunk/doc/validation/validation.tex (revision 811) @@ -0,0 +1,997 @@ + +%Paper, font, general info %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\documentclass[letterpaper,12pt,oneside,openright]{book}% Classe du document +%article|report|book|letter|slides, 10pt|11pt|12pt, letterpaper|legalpaper|executivepaper|a4paper|a5paper|b5paper, oneside|twoside, openright|openany, onecolumn|twocolumn +%\usepackage[francais]{babel} % Francisation de LaTeX +\usepackage[T1]{fontenc} % Encodage de sortie (l'encodage T1 convient mieux aux langues autres que l'Anglais) +\usepackage{aeguill,aecompl} % Fontes virtuelles (nuit aux recherches et aux copies de texte dans le document PDF) pour PDF: + % ameliore la qualite de la visualisation avec Acrobat Reader +\newcounter{myfootertablecounter} + +\title{Ice documentation} +\author{Larour, Morlighem, Seroussi} +\date{2009} + +%Packages %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\usepackage{graphicx} % Inclusion d'images +\usepackage{array, multirow} % Tableaux +\usepackage{amsmath} % Mode mathematique +\usepackage{amsfonts} % Polices mathematiques +\usepackage{amssymb} % Symboles mathematiques +%\usepackage{makeidx} +\makeindex +\usepackage{longtable} % long tables +\usepackage{float} % Pour faire [H] sur les float +\usepackage[scale=0.9]{geometry} % margins +\usepackage{fancyhdr} % headings +\usepackage{subfig} +\usepackage{bm} % maths letters, real = IR +\usepackage{cancel} +\setcounter{tocdepth}{4} %pour afficher la table des matiere au niveau subsection +\setcounter{secnumdepth}{4} + + +%Headings %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\setlength{\headheight}{20pt} %uppermargin +\renewcommand{\sectionmark}[1]{\markright{#1}{}} %print the actual name of the chapter without converting it to uppercase +\fancyhf{} +\fancyhead[LE,RO]{\thepage} +\fancyhead[RE]{\textit{\nouppercase{\leftmark}}} +\fancyhead[LO]{\textit{\nouppercase{\rightmark}}} +\fancyfoot[LE,RO]{\scriptsize{\today}} + +\fancypagestyle{plain}{ % %If style=plain: remove evrything +\fancyhf{} % remove everything +\renewcommand{\headrulewidth}{0pt} % remove lines as well +\renewcommand{\footrulewidth}{0pt}} + +%pdf properties and hypertext links%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\usepackage[plainpages=false,pdfpagelabels]{hyperref} % hypertext links in pdfs +\hypersetup{% Links Options for the document% +colorlinks=true, +linkcolor=blue, +urlcolor=blue, +citecolor=blue, +plainpages=false, +%%PDF Options% +pdftitle={ISSM Validation}, +pdfauthor={Mathieu Morlighem and Helene Seroussi}, +pdfsubject={Numerical modelling of ice sheets}} + +%newcommands %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\graphicspath{{Images/}} +\newcommand{\defi}[1]{ \begin{itemize} \renewcommand{\labelitemi}{$\blacksquare$} \item \begin{large} \textbf{#1} \end{large} \end{itemize} } +\newcommand{\R}[0]{{\mathbb R}} %real set IR +\newcommand{\N}[0]{{\mathbb N}} %natural set IN +\newcommand{\rigid}[1]{\Re_{#1}} %rigid displacements R +\newcommand{\card}[0]{\text{Card}} %cardinal Card E +\newcommand*{\SET}[1]{\ensuremath{\mathcal{#1}}} %Set, Space (italic) +\newcommand*{\MAT}[1]{\ensuremath{\mathbf{#1}}} %Matrice name (Bold) +\newcommand*{\VEC}[1]{\ensuremath{\bm{#1}}} %Vector name (Bold Italic) +\newcommand*{\abs}[1]{\mathopen| #1 \mathclose|} %absolute value |x| +\newcommand*{\norm}[1]{\mathopen\| #1 \mathclose\|} %norm ||x|| +\newcommand*{\rest}[2]{{#1}_{\left. \right|_{#2}}} %restriction of a function on a domain f|omega +\newcommand*{\ent}[1]{\lfloor #1 \rfloor} %floor function [f] +\newcommand*{\grad}[1]{\overrightarrow{\text{grad}}\left( #1\right) }%vectorial nabla +\newcommand*{\eps}[0]{\dot{\varepsilon}} %vectorial nabla +\newcommand*{\BigO}[1]{\mathcal{O}\left( #1\right) } %Big O landau notation +\newcommand*{\sectionintro}[1]{\medskip \noindent \begin{Large}\textbf{#1}\end{Large}\medskip} + +\begin{document} +\thispagestyle{empty} + +\vspace{10cm} +\begin{center} +\bf \LARGE Ice Sheet System Model 2008\\ Code Validation Guide +\end{center} + +\vspace{4cm} + +\begin{center} +Authors:\\ +\vspace{.5cm} +{\bf \large H\'el\`ene Seroussi$^{2,3}$} \\ +\smallskip +{\bf \large Mathieu Morlighem$^{2,3}$} \\ +\smallskip +{\bf \large \'Eric Larour$^{1}$} \\ +\vfill +%\vspace{4.5cm} +$^{1}$Division 35, Thermal and Cryogenics Section, \\ +Mechanical Division, MS 157-316. \\ +Jet Propulsion Laboratory, 4800 Oak Grove Drive, Pasadena, CA 91109.\\ +\vspace{.2cm} +$^{2}$Division 33, Radar Science and Enginnering Section, \\ +Communications, Tracking and Radar Division, MS 157-316. \\ +Jet Propulsion Laboratory, 4800 Oak Grove Drive, Pasadena, CA 91109.\\ +\vspace{.2cm} +$^{3}$Laboratoire de M\'ecanique des sols, Structures et mat\'eriaux (MSSMat)\\ +\'Ecole Centrale Paris, CNRS UMR 8579\\ +Grande Voie des Vignes, 92295 Chtenay-Malabry Cedex, FRANCE\\ + +\vspace{0.5cm} +\today +\end{center} + + +\cleardoublepage +\pagestyle{headings} +\tableofcontents + +\newpage + +\chapter{EISMINT} + +The tests described in this chapters follow the work of Vincent Rommeleare \cite{Rommelaere1996}. + +\section{Test 1: Mass concervation} +\subsection{Setup of the experiment} +We use an idealized geometry of a square ice shelf of length 200km. The velocity is imposed everywhere as $u_0=400$m/yr and the initial thickness is 500m.\\ +\\ +The boundary conditions are free radiation on all sides except on the left boundary where a thickness wave is imposed: + +\begin{equation} +H(t)=H_0 + \dfrac{H_0}{5}\sin\left( \dfrac{2\pi t}{T}\right) +\end{equation} +\\ +We want to check if the conservation scheme is able to propagate the signal along the shelf. The analytical solution is: + +\begin{equation} +H(x,y,t)=H_0 + \dfrac{H_0}{5}\sin\left( \dfrac{2\pi}{T}\left( t-\dfrac{x}{u_0}\right) \right) +\end{equation} + +\subsection{Results and comparisons} +\begin{figure}[H] + \centering + \subfloat[Vincent Rommeleare's results]{\includegraphics[width=6.5cm]{EISMINT/MassConcervation/thickness_th}}\hspace*{1em} + \subfloat[]{\includegraphics[width=1.5cm]{EISMINT/MassConcervation/legend_th}} + \\ + \subfloat[Thickness with artificial diffusivity]{\includegraphics[width=8cm]{EISMINT/MassConcervation/thickness_art}}\hspace*{1em} + \subfloat[Thickness without artificial diffusivity]{\includegraphics[width=8cm]{EISMINT/MassConcervation/thickness}} + \caption{Comparision of the ISSM results with Vincent Rommeleare's} +\end{figure} + +\newpage +\section{Test 2: Diagnostic 1} +We use a square ice shelf with an imposed velocity everywhere except on the front where a dynamic boundary condition is imposed (water pressure). Here are the results: +\begin{figure}[H] + \centering %\hspace*{-1.5cm} + \subfloat[Vx (m/yr) computed by ISSM]{\includegraphics[width=9cm]{EISMINT/Diagnostic1/vx}} + \subfloat[Vy (m/yr) computed by ISSM]{\includegraphics[width=9cm]{EISMINT/Diagnostic1/vy}}\\ + \subfloat[Vx (m/yr) found by Romelaere]{\includegraphics[width=7.5cm]{EISMINT/Diagnostic1/vx_th}}\hspace*{2em} + \subfloat[Vy (m/yr) found by Romelaere]{\includegraphics[width=7.5cm]{EISMINT/Diagnostic1/vy_th}} + \caption{Comparision of the ISSM results with Vincent Rommeleare's} +\end{figure} + +\newpage +\section{Test 3: Diagnostic 2} +The geometry is exactly the same as the previous one except that the upper boundary condition is change to account for an ice stream entering the ice shelf. The y-velocity becomes: + +\begin{equation} +v(x,(y=L))=400\left( \left[\dfrac{x-100}{25} \right]^2 -1\right)Heav\left( 1-\left[\dfrac{x-100}{25} \right]^2\right) +\end{equation} +\begin{figure}[H] + \centering %\hspace*{-1.5cm} + \subfloat[Vx (m/yr) computed by ISSM]{\includegraphics[width=9cm]{EISMINT/Diagnostic2/vx}} + \subfloat[Vy (m/yr) computed by ISSM]{\includegraphics[width=9cm]{EISMINT/Diagnostic2/vy}}\\ + \subfloat[Vx (m/yr) found by Romelaere]{\includegraphics[width=7.5cm]{EISMINT/Diagnostic2/vx_th}}\hspace*{2em} + \subfloat[Vy (m/yr) found by Romelaere]{\includegraphics[width=7.5cm]{EISMINT/Diagnostic2/vy_th}} + \caption{Comparision of the ISSM results with Vincent Rommeleare's} +\end{figure} +\newpage + +\chapter{ISMIP-HOM} +The tests described in this chapters follow the works of Laura Perichon \cite{Perichon2007} and Frank Pattyn \cite{Pattyn2008}. For a comprehensie description of the experiment, please see \cite{Pattyn2006a}. + +\section{Test A} +\setcounter{subfigure}{0} +\subsection{Geometry} + +This is a 3d ice-sheet flow over a bumpy bed experiment. Periodic boundary conditions are applied. The geometry follows: +\begin{itemize} +\item[--] surface $s(x,y)=-x\tan(0.5^o)$ +\item[--] bed $b(x,y)=s-1000+500\sin\left( \dfrac{2\pi}{L}x\right) \sin\left( \dfrac{2\pi}{L}y\right)$ +\item[--] $5\;km\leqslant L \leqslant 160\;km$ +\end{itemize} +\begin{figure}[H] +\begin{center} +\includegraphics[width=9cm]{ISMIP/TestA/geo.png} +\caption{Test A geometry} +\end{center} +\end{figure} + +\newpage +\subsection{Results} + +\subsubsection{5km} +\setcounter{subfigure}{0} +\begin{figure}[H] + \centering + \subfloat[Vx (m/yr) computed by ISSM (Pattyn) on a cross line]{\includegraphics[width=9.5cm]{ISMIP/TestA/clvx5p}} + \subfloat[Vx (m/yr) comparison]{\includegraphics[width=6.5cm]{ISMIP/TestA/clvx5p_th}} +\end{figure} +\vspace*{-2em} +\begin{figure}[H] + \centering + \subfloat[Vx (m/yr) computed by ISSM (Pattyn)]{\includegraphics[width=9cm]{ISMIP/TestA/vx5p}} + \subfloat[Vy (m/yr) computed by ISSM (Pattyn)]{\includegraphics[width=9cm]{ISMIP/TestA/vy5p}} +\end{figure} +\vspace*{-2em} +\begin{figure}[H] + \centering + \subfloat[Vz (m/yr) computed by ISSM (Pattyn)]{\includegraphics[width=9cm]{ISMIP/TestA/vz5p}} +\end{figure} +\newpage + +\subsubsection{10km} +\setcounter{subfigure}{0} +\begin{figure}[H] + \centering + \subfloat[Vx (m/yr) computed by ISSM (Pattyn) on a cross line]{\includegraphics[width=9.5cm]{ISMIP/TestA/clvx10p}} + \subfloat[Vx (m/yr) comparison]{\includegraphics[width=6.5cm]{ISMIP/TestA/clvx10p_th}} +\end{figure} +\vspace*{-2em} +\begin{figure}[H] + \centering + \subfloat[Vx (m/yr) computed by ISSM (Pattyn)]{\includegraphics[width=9cm]{ISMIP/TestA/vx10p}} + \subfloat[Vy (m/yr) computed by ISSM (Pattyn)]{\includegraphics[width=9cm]{ISMIP/TestA/vy10p}} +\end{figure} +\vspace*{-2em} +\begin{figure}[H] + \centering + \subfloat[Vz (m/yr) computed by ISSM (Pattyn)]{\includegraphics[width=9cm]{ISMIP/TestA/vz10p}} +\end{figure} +\newpage + +\subsubsection{20km} +\begin{figure}[H] + \centering + \subfloat[Vx (m/yr) computed by ISSM (Pattyn) on a cross line]{\includegraphics[width=9.5cm]{ISMIP/TestA/clvx20p}} + \subfloat[Vx (m/yr) comparison]{\includegraphics[width=6.5cm]{ISMIP/TestA/clvx20p_th}} +\end{figure} +\vspace*{-2em} +\begin{figure}[H] + \centering + \subfloat[Vx (m/yr) computed by ISSM (Pattyn)]{\includegraphics[width=9cm]{ISMIP/TestA/vx20p}} + \subfloat[Vy (m/yr) computed by ISSM (Pattyn)]{\includegraphics[width=9cm]{ISMIP/TestA/vy20p}} +\end{figure} +\vspace*{-2em} +\begin{figure}[H] + \centering + \subfloat[Vz (m/yr) computed by ISSM (Pattyn)]{\includegraphics[width=9cm]{ISMIP/TestA/vz20p}} +\end{figure} +\newpage + +\subsubsection{40km} +\setcounter{subfigure}{0} +\begin{figure}[H] + \centering + \subfloat[Vx (m/yr) computed by ISSM (Pattyn) on a cross line]{\includegraphics[width=9.5cm]{ISMIP/TestA/clvx40p}} + \subfloat[Vx (m/yr) comparison]{\includegraphics[width=6.5cm]{ISMIP/TestA/clvx40p_th}} +\end{figure} +\vspace*{-2em} +\begin{figure}[H] + \centering + \subfloat[Vx (m/yr) computed by ISSM (Pattyn)]{\includegraphics[width=9cm]{ISMIP/TestA/vx40p}} + \subfloat[Vy (m/yr) computed by ISSM (Pattyn)]{\includegraphics[width=9cm]{ISMIP/TestA/vy40p}} +\end{figure} +\vspace*{-2em} +\begin{figure}[H] + \centering + \subfloat[Vz (m/yr) computed by ISSM (Pattyn)]{\includegraphics[width=9cm]{ISMIP/TestA/vz40p}} +\end{figure} +\newpage + +\subsubsection{80km} +\setcounter{subfigure}{0} +\begin{figure}[H] + \centering + \subfloat[Vx (m/yr) computed by ISSM (Pattyn) on a cross line]{\includegraphics[width=9.5cm]{ISMIP/TestA/clvx80p}} + \subfloat[Vx (m/yr) comparison]{\includegraphics[width=6.5cm]{ISMIP/TestA/clvx80p_th}} +\end{figure} +\vspace*{-2em} +\begin{figure}[H] + \centering + \subfloat[Vx (m/yr) computed by ISSM (Pattyn)]{\includegraphics[width=9cm]{ISMIP/TestA/vx80p}} + \subfloat[Vy (m/yr) computed by ISSM (Pattyn)]{\includegraphics[width=9cm]{ISMIP/TestA/vy80p}} +\end{figure} +\vspace*{-2em} +\begin{figure}[H] + \centering + \subfloat[Vz (m/yr) computed by ISSM (Pattyn)]{\includegraphics[width=9cm]{ISMIP/TestA/vz80p}} +\end{figure} +\newpage + +\subsubsection{160km} +\setcounter{subfigure}{0} +\begin{figure}[H] + \centering + \subfloat[Vx (m/yr) computed by ISSM (Pattyn) on a cross line]{\includegraphics[width=9.2cm]{ISMIP/TestA/clvx160p}} + \subfloat[Vx (m/yr) comparison]{\includegraphics[width=7cm]{ISMIP/TestA/clvx160p_th}} +\end{figure} +\vspace*{-2em} +\begin{figure}[H] + \centering + \subfloat[Vx (m/yr) computed by ISSM (Pattyn)]{\includegraphics[width=9cm]{ISMIP/TestA/vx160p}} + \subfloat[Vy (m/yr) computed by ISSM (Pattyn)]{\includegraphics[width=9cm]{ISMIP/TestA/vy160p}} +\end{figure} +\vspace*{-2em} +\begin{figure}[H] + \centering + \subfloat[Vz (m/yr) computed by ISSM (Pattyn)]{\includegraphics[width=9cm]{ISMIP/TestA/vz160p}} +\end{figure} +\newpage + +\subsubsection{global (comparison)} +\begin{figure}[H] + \centering + \subfloat[Maximum Vx (m/yr) computed by ISSM (Pattyn)]{\includegraphics[width=9.5cm]{ISMIP/TestA/TestAMaxVx}} + \subfloat[Maximum Vx (m/yr) comparison]{\includegraphics[width=8.5cm]{ISMIP/TestA/TestAMaxVx_th}} +\end{figure} +\vspace*{-2em} +\begin{figure}[H] + \centering + \subfloat[Minimum Vx (m/yr) computed by ISSM (Pattyn)]{\includegraphics[width=9.5cm]{ISMIP/TestA/TestAMinVx}} + \subfloat[Minimum Vx (m/yr) comparison]{\includegraphics[width=8.5cm]{ISMIP/TestA/TestAMinVx_th}} +\end{figure} +\newpage + +\section{Test B} +\setcounter{subfigure}{0} +\subsection{Geometry} +This is a 2d ice-sheet flow over a rippled bed (flowline). Periodic boundary conditions are applied. The geometry follows: +\begin{itemize} +\item[--] surface $s(x,y)=-x\tan(0.5^o)$ +\item[--] bed $b(x,y)=s-1000+500\sin\left( \dfrac{2\pi}{L}x\right) $ +\item[--] $5\;km\leqslant L \leqslant 160\;km$ +\end{itemize} +\begin{figure}[H] +\begin{center} +\includegraphics[width=9cm]{ISMIP/TestB/geo.png} +\caption{Test B geometry} +\end{center} +\end{figure} + +\newpage +\subsection{Results} + + +\subsubsection{5km} +\setcounter{subfigure}{0} +\begin{figure}[H] + \centering + \subfloat[Vx (m/yr) computed by ISSM (Pattyn) on a cross line]{\includegraphics[width=9.5cm]{ISMIP/TestB/clvx5p}} + \subfloat[Vx (m/yr) comparison]{\includegraphics[width=8cm]{ISMIP/TestB/clvx5p_th}} +\end{figure} +\vspace*{-2em} +\begin{figure}[H] + \centering + \subfloat[Vx (m/yr) computed by ISSM (Pattyn)]{\includegraphics[width=9cm]{ISMIP/TestB/vx5p}} + \subfloat[Vz (m/yr) computed by ISSM (Pattyn)]{\includegraphics[width=9cm]{ISMIP/TestB/vz5p}} + \end{figure} +\newpage + +\subsubsection{10km} +\setcounter{subfigure}{0} +\begin{figure}[H] + \centering + \subfloat[Vx (m/yr) computed by ISSM (Pattyn) on a cross line]{\includegraphics[width=9.5cm]{ISMIP/TestB/clvx10p}} + \subfloat[Vx (m/yr) comparison]{\includegraphics[width=8cm]{ISMIP/TestB/clvx10p_th}} +\end{figure} +\vspace*{-2em} +\begin{figure}[H] + \centering + \subfloat[Vx (m/yr) computed by ISSM (Pattyn)]{\includegraphics[width=9cm]{ISMIP/TestB/vx10p}} + \subfloat[Vz (m/yr) computed by ISSM (Pattyn)]{\includegraphics[width=9cm]{ISMIP/TestB/vz10p}} + \end{figure} +\newpage + +\subsubsection{20km} +\setcounter{subfigure}{0} +\begin{figure}[H] + \centering + \subfloat[Vx (m/yr) computed by ISSM (Pattyn) on a cross line]{\includegraphics[width=9.5cm]{ISMIP/TestB/clvx20p}} + \subfloat[Vx (m/yr) comparison]{\includegraphics[width=8cm]{ISMIP/TestB/clvx20p_th}} +\end{figure} +\vspace*{-2em} +\begin{figure}[H] + \centering + \subfloat[Vx (m/yr) computed by ISSM (Pattyn)]{\includegraphics[width=9cm]{ISMIP/TestB/vx20p}} + \subfloat[Vz (m/yr) computed by ISSM (Pattyn)]{\includegraphics[width=9cm]{ISMIP/TestB/vz20p}} +\end{figure} +\newpage + +\subsubsection{40km} +\setcounter{subfigure}{0} +\begin{figure}[H] + \centering + \subfloat[Vx (m/yr) computed by ISSM (Pattyn) on a cross line]{\includegraphics[width=9.5cm]{ISMIP/TestB/clvx40p}} + \subfloat[Vx (m/yr) comparison]{\includegraphics[width=8cm]{ISMIP/TestB/clvx40p_th}} +\end{figure} +\vspace*{-2em} +\begin{figure}[H] + \centering + \subfloat[Vx (m/yr) computed by ISSM (Pattyn)]{\includegraphics[width=9cm]{ISMIP/TestB/vx40p}} + \subfloat[Vz (m/yr) computed by ISSM (Pattyn)]{\includegraphics[width=9cm]{ISMIP/TestB/vz40p}} +\end{figure} +\newpage + +\subsubsection{80km} +\setcounter{subfigure}{0} +\begin{figure}[H] + \centering + \subfloat[Vx (m/yr) computed by ISSM (Pattyn) on a cross line]{\includegraphics[width=9.5cm]{ISMIP/TestB/clvx80p}} + \subfloat[Vx (m/yr) comparison]{\includegraphics[width=6.5cm]{ISMIP/TestB/clvx80p_th}} +\end{figure} +\vspace*{-2em} +\begin{figure}[H] + \centering + \subfloat[Vx (m/yr) computed by ISSM (Pattyn)]{\includegraphics[width=9cm]{ISMIP/TestB/vx80p}} + \subfloat[Vz (m/yr) computed by ISSM (Pattyn)]{\includegraphics[width=9cm]{ISMIP/TestB/vz80p}} +\end{figure} +\newpage + +\subsubsection{160km} +\setcounter{subfigure}{0} +\begin{figure}[H] + \centering + \subfloat[Vx (m/yr) computed by ISSM (Pattyn) on a cross line]{\includegraphics[width=9.5cm]{ISMIP/TestB/clvx160p}} + \subfloat[Vx (m/yr) comparison]{\includegraphics[width=6.5cm]{ISMIP/TestB/clvx160p_th}} +\end{figure} +\vspace*{-2em} +\begin{figure}[H] + \centering + \subfloat[Vx (m/yr) computed by ISSM (Pattyn)]{\includegraphics[width=9cm]{ISMIP/TestB/vx160p}} + \subfloat[Vz (m/yr) computed by ISSM (Pattyn)]{\includegraphics[width=9cm]{ISMIP/TestB/vz160p}} +\end{figure} +\newpage + +\subsubsection{global (comparison)} +\begin{figure}[H] + \centering + \subfloat[Maximum Vx (m/yr) computed by ISSM (Pattyn)]{\includegraphics[width=9.5cm]{ISMIP/TestB/TestBMaxVx}} + \subfloat[Maximum Vx (m/yr) comparison]{\includegraphics[width=8.5cm]{ISMIP/TestB/TestBMaxVx_th}} +\end{figure} +\vspace*{-2em} +\begin{figure}[H] + \centering + \subfloat[Minimum Vx (m/yr) computed by ISSM (Pattyn)]{\includegraphics[width=9.5cm]{ISMIP/TestB/TestBMinVx}}% +% \subfloat[Minimum Vx (m/yr) comparison]{\includegraphics[width=8.5cm]{ISMIP/TestB/TestBMinVx_th}} +\end{figure} +\newpage + +\section{Test C (detailed)} +\setcounter{subfigure}{0} +\subsection{Geometry} + +This is a 3d ice-stream flow over a slippery bed. Periodic boundary conditions are applied. The geometry follows: +\begin{itemize} +\item[--] surface $s(x,y)=-x\tan(0.1^o)$ +\item[--] bed $b(x,y)=s-1000$ +\item[--] sliding $\alpha^2(x,y)=1000+1000\sin\left( \dfrac{2\pi}{L}x\right)\sin\left( \dfrac{2\pi}{L}y\right)$ +\item[--] $5\;km\leqslant L \leqslant 160\;km$ +\end{itemize} +\begin{figure}[H] +\begin{center} +\includegraphics[width=9cm]{ISMIP/TestC/geo.png} +\caption{Test C geometry} +\end{center} +\end{figure} + +\newpage +\subsection{Results} + +\subsubsection{5km} +\setcounter{subfigure}{0} +\begin{figure}[H] + \centering + \subfloat[Vx (m/yr) computed by ISSM (Pattyn) on a cross line]{\includegraphics[width=9.2cm]{ISMIP/TestC/clvx5p}} + \subfloat[Vx (m/yr) comparison]{\includegraphics[width=7cm]{ISMIP/TestC/clvx5p_th}} +\end{figure} +\begin{figure}[H] + \centering + \subfloat[Txz (kPa) computed by ISSM (Pattyn) on a cross line]{\includegraphics[width=9.2cm]{ISMIP/TestC/cltxz5p}} + %\subfloat[Txz (kPa) comparison]{\includegraphics[width=7cm]{ISMIP/TestC/cltxz5p_th}} +\end{figure} +\begin{figure}[H] + \centering + \subfloat[Vx (m/yr) computed by ISSM (Pattyn)]{\includegraphics[width=9cm]{ISMIP/TestC/vx5p}} + \subfloat[Vy (m/yr) computed by ISSM (Pattyn)]{\includegraphics[width=9cm]{ISMIP/TestC/vy5p}} +\end{figure} +\begin{figure}[H] + \centering + \subfloat[Vz (m/yr) computed by ISSM (Pattyn)]{\includegraphics[width=9cm]{ISMIP/TestC/vz5p}} +\end{figure} +\begin{figure}[H] + \centering + \subfloat[Txz (kPa) computed by ISSM (Pattyn)]{\includegraphics[width=9cm]{ISMIP/TestC/txz5p}} + \subfloat[Tyz (kPa) computed by ISSM (Pattyn)]{\includegraphics[width=9cm]{ISMIP/TestC/tyz5p}} +\end{figure} +\newpage + +\subsubsection{10km} +\setcounter{subfigure}{0} +\begin{figure}[H] + \centering + \subfloat[Vx (m/yr) computed by ISSM (Pattyn) on a cross line]{\includegraphics[width=9.2cm]{ISMIP/TestC/clvx10p}} + \subfloat[Vx (m/yr) comparison]{\includegraphics[width=7cm]{ISMIP/TestC/clvx10p_th}} +\end{figure} +\begin{figure}[H] + \centering + \subfloat[Txz (kPa) computed by ISSM (Pattyn) on a cross line]{\includegraphics[width=9.2cm]{ISMIP/TestC/cltxz10p}} + %\subfloat[Txz (kPa) comparison]{\includegraphics[width=7cm]{ISMIP/TestC/cltxz10p_th}} +\end{figure} +\begin{figure}[H] + \centering + \subfloat[Vx (m/yr) computed by ISSM (Pattyn)]{\includegraphics[width=9cm]{ISMIP/TestC/vx10p}} + \subfloat[Vy (m/yr) computed by ISSM (Pattyn)]{\includegraphics[width=9cm]{ISMIP/TestC/vy10p}} +\end{figure} +\begin{figure}[H] + \centering + \subfloat[Vz (m/yr) computed by ISSM (Pattyn)]{\includegraphics[width=9cm]{ISMIP/TestC/vz10p}} +\end{figure} +\begin{figure}[H] + \centering + \subfloat[Txz (kPa) computed by ISSM (Pattyn)]{\includegraphics[width=9cm]{ISMIP/TestC/txz10p}} + \subfloat[Tyz (kPa) computed by ISSM (Pattyn)]{\includegraphics[width=9cm]{ISMIP/TestC/tyz10p}} +\end{figure} +\newpage + +\subsubsection{20km} +\setcounter{subfigure}{0} +\begin{figure}[H] + \centering + \subfloat[Vx (m/yr) computed by ISSM (Pattyn) on a cross line]{\includegraphics[width=9.2cm]{ISMIP/TestC/clvx20p}} + \subfloat[Vx (m/yr) comparison]{\includegraphics[width=7cm]{ISMIP/TestC/clvx20p_th}} +\end{figure} +\begin{figure}[H] + \centering + \subfloat[Txz (kPa) computed by ISSM (Pattyn) on a cross line]{\includegraphics[width=9.2cm]{ISMIP/TestC/cltxz20p}} + %\subfloat[Txz (kPa) comparison]{\includegraphics[width=7cm]{ISMIP/TestC/cltxz20p_th}} +\end{figure} +\begin{figure}[H] + \centering + \subfloat[Vx (m/yr) computed by ISSM (Pattyn)]{\includegraphics[width=9cm]{ISMIP/TestC/vx20p}} + \subfloat[Vy (m/yr) computed by ISSM (Pattyn)]{\includegraphics[width=9cm]{ISMIP/TestC/vy20p}} +\end{figure} +\begin{figure}[H] + \centering + \subfloat[Vz (m/yr) computed by ISSM (Pattyn)]{\includegraphics[width=9cm]{ISMIP/TestC/vz20p}} +\end{figure} +\begin{figure}[H] + \centering + \subfloat[Txz (kPa) computed by ISSM (Pattyn)]{\includegraphics[width=9cm]{ISMIP/TestC/txz20p}} + \subfloat[Tyz (kPa) computed by ISSM (Pattyn)]{\includegraphics[width=9cm]{ISMIP/TestC/tyz20p}} +\end{figure} +\newpage + +\subsubsection{40km} +\setcounter{subfigure}{0} +\begin{figure}[H] + \centering + \subfloat[Vx (m/yr) computed by ISSM (Pattyn) on a cross line]{\includegraphics[width=9.2cm]{ISMIP/TestC/clvx40p}} + \subfloat[Vx (m/yr) comparison]{\includegraphics[width=7cm]{ISMIP/TestC/clvx40p_th}} +\end{figure} +\begin{figure}[H] + \centering + \subfloat[Txz (kPa) computed by ISSM (Pattyn) on a cross line]{\includegraphics[width=9.2cm]{ISMIP/TestC/cltxz40p}} + %\subfloat[Txz (kPa) comparison]{\includegraphics[width=7cm]{ISMIP/TestC/cltxz40p_th}} +\end{figure} +\begin{figure}[H] + \centering + \subfloat[Vx (m/yr) computed by ISSM (Pattyn)]{\includegraphics[width=9cm]{ISMIP/TestC/vx40p}} + \subfloat[Vy (m/yr) computed by ISSM (Pattyn)]{\includegraphics[width=9cm]{ISMIP/TestC/vy40p}} +\end{figure} +\begin{figure}[H] + \centering + \subfloat[Vz (m/yr) computed by ISSM (Pattyn)]{\includegraphics[width=9cm]{ISMIP/TestC/vz40p}} +\end{figure} +\begin{figure}[H] + \centering + \subfloat[Txz (kPa) computed by ISSM (Pattyn)]{\includegraphics[width=9cm]{ISMIP/TestC/txz40p}} + \subfloat[Tyz (kPa) computed by ISSM (Pattyn)]{\includegraphics[width=9cm]{ISMIP/TestC/tyz40p}} +\end{figure} +\newpage + +\subsubsection{80km} +\setcounter{subfigure}{0} +\begin{figure}[H] + \centering %\hspace*{-1.5cm} + \subfloat[Vx (m/yr) computed by ISSM (Pattyn) on a cross line]{\includegraphics[width=9.5cm]{ISMIP/TestC/clvx80p}} + \subfloat[Vx (m/yr) comparison]{\includegraphics[width=6.5cm]{ISMIP/TestC/clvx80p_th}} +\end{figure} +\begin{figure}[H] + \centering + \subfloat[Txz (kPa) computed by ISSM (Pattyn) on a cross line]{\includegraphics[width=9.2cm]{ISMIP/TestC/cltxz80p}} + %\subfloat[Txz (kPa) compatison]{\includegraphics[width=7cm]{ISMIP/TestC/cltxz80p_th}} +\end{figure} +\begin{figure}[H] + \centering + \subfloat[Vx (m/yr) computed by ISSM (Pattyn)]{\includegraphics[width=9.2cm]{ISMIP/TestC/vx80p}} + \subfloat[Vx (m/yr) comparison]{\includegraphics[width=7cm]{ISMIP/TestC/vx80p_th}} + \end{figure} +\begin{figure}[H] + \centering + \subfloat[Vy (m/yr) computed by ISSM (Pattyn)]{\includegraphics[width=9.2cm]{ISMIP/TestC/vy80p}} + \subfloat[Vy (m/yr) comparison]{\includegraphics[width=7cm]{ISMIP/TestC/vy80p_th}} +\end{figure} +\begin{figure}[H] + \centering + \subfloat[Vz (m/yr) computed by ISSM (Pattyn)]{\includegraphics[width=9.2cm]{ISMIP/TestC/vz80p}} + \subfloat[Vz (m/yr) compatison]{\includegraphics[width=7cm]{ISMIP/TestC/vz80p_th}} +\end{figure} +\begin{figure}[H] + \centering + \subfloat[Txz (kPa) computed by ISSM (Pattyn)]{\includegraphics[width=9.2cm]{ISMIP/TestC/txz80p}} + \subfloat[Txz (kPa) compatison]{\includegraphics[width=7cm]{ISMIP/TestC/txz80p_th}} +\end{figure} +\begin{figure}[H] + \centering + \subfloat[Tyz (kPa) computed by ISSM (Pattyn)]{\includegraphics[width=9.2cm]{ISMIP/TestC/tyz80p}} + \subfloat[Tyz (kPa) compatison]{\includegraphics[width=7cm]{ISMIP/TestC/tyz80p_th}} +\end{figure} +\newpage + +\subsubsection{160km} +\setcounter{subfigure}{0} +\begin{figure}[H] + \centering + \subfloat[Vx (m/yr) computed by ISSM (Pattyn) on a cross line]{\includegraphics[width=9.2cm]{ISMIP/TestC/clvx160p}} + \subfloat[Vx (m/yr) comparison]{\includegraphics[width=7cm]{ISMIP/TestC/clvx160p_th}} +\end{figure} +\begin{figure}[H] + \centering + \subfloat[Txz (kPa) computed by ISSM (Pattyn) on a cross line]{\includegraphics[width=9.2cm]{ISMIP/TestC/cltxz160p}} + %\subfloat[Txz (kPa) comparison]{\includegraphics[width=7cm]{ISMIP/TestC/cltxz160p_th}} +\end{figure} +\begin{figure}[H] + \centering + \subfloat[Vx (m/yr) computed by ISSM (Pattyn)]{\includegraphics[width=9cm]{ISMIP/TestC/vx160p}} + \subfloat[Vy (m/yr) computed by ISSM (Pattyn)]{\includegraphics[width=9cm]{ISMIP/TestC/vy160p}} +\end{figure} +\begin{figure}[H] + \centering + \subfloat[Vz (m/yr) computed by ISSM (Pattyn)]{\includegraphics[width=9cm]{ISMIP/TestC/vz160p}} +\end{figure} +\begin{figure}[H] + \centering + \subfloat[Txz (kPa) computed by ISSM (Pattyn)]{\includegraphics[width=9cm]{ISMIP/TestC/txz160p}} + \subfloat[Tyz (kPa) computed by ISSM (Pattyn)]{\includegraphics[width=9cm]{ISMIP/TestC/tyz160p}} +\end{figure} +\newpage + +\subsubsection{global (comparison)} +\begin{figure}[H] + \centering + \subfloat[Maximum Vx (m/yr) computed by ISSM (Pattyn)]{\includegraphics[width=9.5cm]{ISMIP/TestC/TestCMaxVx}} + \subfloat[Maximum Vx (m/yr) comparison]{\includegraphics[width=8.5cm]{ISMIP/TestC/TestCMaxVx_th}} +\end{figure} +\vspace*{-2em} +\begin{figure}[H] + \centering + \subfloat[Minimum Vx (m/yr) computed by ISSM (Pattyn)]{\includegraphics[width=9.5cm]{ISMIP/TestC/TestCMinVx}} + \subfloat[Minimum Vx (m/yr) comparison]{\includegraphics[width=8.5cm]{ISMIP/TestC/TestCMinVx_th}} +\end{figure} +\vspace*{-2em} +\begin{figure}[H] + \centering + \subfloat[Maximum Txz (kPa) computed by ISSM (Pattyn)]{\includegraphics[width=9.5cm]{ISMIP/TestC/TestCMaxTxz}} + \subfloat[Maximum Txz (kPa) comparison]{\includegraphics[width=8.5cm]{ISMIP/TestC/TestCMaxTxz_th}} +\end{figure} +\vspace*{-2em} +\begin{figure}[H] + \centering + \subfloat[Minimum Txz (kPa) computed by ISSM (Pattyn)]{\includegraphics[width=9.5cm]{ISMIP/TestC/TestCMinTxz}} + \subfloat[Minimum Txz (kPa) comparison]{\includegraphics[width=8.5cm]{ISMIP/TestC/TestCMinTxz_th}} +\end{figure} +\newpage + + +\section{Test D} +\setcounter{subfigure}{0} +\subsection{Geometry} +This is a 2d ice-stream flow over a slippery bed (flowline). Periodic boundary conditions are applied. The geometry follows: +\begin{itemize} +\item[--] surface $s(x,y)=-x\tan(0.1^o)$ +\item[--] bed $b(x,y)=s-1000$ +\item[--] sliding $\alpha^2(x,y)=1000+1000\sin\left( \dfrac{2\pi}{L}x\right)$ +\item[--] $5\;km\leqslant L \leqslant 160\;km$ +\end{itemize} +\begin{figure}[H] +\begin{center} +\includegraphics[width=9cm]{ISMIP/TestD/geo.png} +\caption{Test D geometry} +\end{center} +\end{figure} + +\newpage +\subsection{Results} + +\subsubsection{5km} +\setcounter{subfigure}{0} +\begin{figure}[H] + \centering + \subfloat[Vx (m/yr) computed by ISSM (Pattyn) on a cross line]{\includegraphics[width=9.5cm]{ISMIP/TestD/clvx5p}} + \subfloat[Vx (m/yr) comparison]{\includegraphics[width=6.5cm]{ISMIP/TestD/clvx5p_th}} +\end{figure} +\begin{figure}[H] + \centering + \subfloat[Txz (kPa) computed by ISSM (Pattyn) on a cross line]{\includegraphics[width=9.2cm]{ISMIP/TestD/cltxz5p}} + \subfloat[Txz (kPa) comparison]{\includegraphics[width=7cm]{ISMIP/TestD/cltxz5p_th}} +\end{figure} +\begin{figure}[H] + \centering + \subfloat[Vx (m/yr) computed by ISSM (Pattyn)]{\includegraphics[width=9cm]{ISMIP/TestD/vx5p}} + \subfloat[Vz (m/yr) computed by ISSM (Pattyn)]{\includegraphics[width=9cm]{ISMIP/TestD/vz5p}} +\end{figure} +\begin{figure}[H] + \centering + \subfloat[Txz (kPa) computed by ISSM (Pattyn)]{\includegraphics[width=9cm]{ISMIP/TestD/txz5p}} +\end{figure} +\newpage + +\subsubsection{10km} +\setcounter{subfigure}{0} +\begin{figure}[H] + \centering + \subfloat[Vx (m/yr) computed by ISSM (Pattyn) on a cross line]{\includegraphics[width=9.5cm]{ISMIP/TestD/clvx10p}} + \subfloat[Vx (m/yr) comparison]{\includegraphics[width=6.5cm]{ISMIP/TestD/clvx10p_th}} +\end{figure} +\begin{figure}[H] + \centering + \subfloat[Txz (kPa) computed by ISSM (Pattyn) on a cross line]{\includegraphics[width=9.2cm]{ISMIP/TestD/cltxz10p}} + \subfloat[Txz (kPa) comparison]{\includegraphics[width=7cm]{ISMIP/TestD/cltxz10p_th}} +\end{figure} +\begin{figure}[H] + \centering + \subfloat[Vx (m/yr) computed by ISSM (Pattyn)]{\includegraphics[width=9cm]{ISMIP/TestD/vx10p}} + \subfloat[Vz (m/yr) computed by ISSM (Pattyn)]{\includegraphics[width=9cm]{ISMIP/TestD/vz10p}} +\end{figure} +\begin{figure}[H] + \centering + \subfloat[Txz (kPa) computed by ISSM (Pattyn)]{\includegraphics[width=9cm]{ISMIP/TestD/txz10p}} +\end{figure} +\newpage + +\subsubsection{20km} +\setcounter{subfigure}{0} +\begin{figure}[H] + \centering + \subfloat[Vx (m/yr) computed by ISSM (Pattyn) on a cross line]{\includegraphics[width=9.5cm]{ISMIP/TestD/clvx20p}} + \subfloat[Vx (m/yr) comparison]{\includegraphics[width=6.5cm]{ISMIP/TestD/clvx20p_th}} +\end{figure} +\begin{figure}[H] + \centering + \subfloat[Txz (kPa) computed by ISSM (Pattyn) on a cross line]{\includegraphics[width=9.2cm]{ISMIP/TestD/cltxz20p}} + \subfloat[Txz (kPa) comparison]{\includegraphics[width=7cm]{ISMIP/TestD/cltxz20p_th}} +\end{figure} +\begin{figure}[H] + \centering + \subfloat[Vx (m/yr) computed by ISSM (Pattyn)]{\includegraphics[width=9cm]{ISMIP/TestD/vx20p}} + \subfloat[Vz (m/yr) computed by ISSM (Pattyn)]{\includegraphics[width=9cm]{ISMIP/TestD/vz20p}} +\end{figure} +\begin{figure}[H] + \centering + \subfloat[Txz (kPa) computed by ISSM (Pattyn)]{\includegraphics[width=9cm]{ISMIP/TestD/txz20p}} +\end{figure} +\newpage + +\subsubsection{40km} +\setcounter{subfigure}{0} +\begin{figure}[H] + \centering + \subfloat[Vx (m/yr) computed by ISSM (Pattyn) on a cross line]{\includegraphics[width=9.5cm]{ISMIP/TestD/clvx40p}} + \subfloat[Vx (m/yr) comparison]{\includegraphics[width=6.5cm]{ISMIP/TestD/clvx40p_th}} +\end{figure} +\begin{figure}[H] + \centering + \subfloat[Txz (kPa) computed by ISSM (Pattyn) on a cross line]{\includegraphics[width=9.2cm]{ISMIP/TestD/cltxz40p}} + \subfloat[Txz (kPa) comparison]{\includegraphics[width=7cm]{ISMIP/TestD/cltxz40p_th}} +\end{figure} +\begin{figure}[H] + \centering + \subfloat[Vx (m/yr) computed by ISSM (Pattyn)]{\includegraphics[width=9cm]{ISMIP/TestD/vx40p}} + \subfloat[Vz (m/yr) computed by ISSM (Pattyn)]{\includegraphics[width=9cm]{ISMIP/TestD/vz40p}} +\end{figure} +\begin{figure}[H] + \centering + \subfloat[Txz (kPa) computed by ISSM (Pattyn)]{\includegraphics[width=9cm]{ISMIP/TestD/txz40p}} +\end{figure} +\newpage + +\subsubsection{80km} +\setcounter{subfigure}{0} +\begin{figure}[H] + \centering + \subfloat[Vx (m/yr) computed by ISSM (Pattyn) on a cross line]{\includegraphics[width=9.5cm]{ISMIP/TestD/clvx80p}} + \subfloat[Vx (m/yr) comparison]{\includegraphics[width=6.5cm]{ISMIP/TestD/clvx80p_th}} +\end{figure} +\begin{figure}[H] + \centering + \subfloat[Txz (kPa) computed by ISSM (Pattyn) on a cross line]{\includegraphics[width=9.2cm]{ISMIP/TestD/cltxz80p}} + \subfloat[Txz (kPa) comparison]{\includegraphics[width=7cm]{ISMIP/TestD/cltxz80p_th}} +\end{figure} +\begin{figure}[H] + \centering + \subfloat[Vx (m/yr) computed by ISSM (Pattyn)]{\includegraphics[width=9cm]{ISMIP/TestD/vx80p}} + \subfloat[Vz (m/yr) computed by ISSM (Pattyn)]{\includegraphics[width=9cm]{ISMIP/TestD/vz80p}} +\end{figure} +\begin{figure}[H] + \centering + \subfloat[Txz (kPa) computed by ISSM (Pattyn)]{\includegraphics[width=9cm]{ISMIP/TestD/txz80p}} +\end{figure} +\newpage + +\subsubsection{160km} +\setcounter{subfigure}{0} +\begin{figure}[H] + \centering + \subfloat[Vx (m/yr) computed by ISSM (Pattyn) on a cross line]{\includegraphics[width=9.5cm]{ISMIP/TestD/clvx160p}} + \subfloat[Vx (m/yr) comparison]{\includegraphics[width=6.5cm]{ISMIP/TestD/clvx160p_th}} +\end{figure} +\begin{figure}[H] + \centering + \subfloat[Txz (kPa) computed by ISSM (Pattyn) on a cross line]{\includegraphics[width=9.2cm]{ISMIP/TestD/cltxz160p}} + \subfloat[Txz (kPa) comparison]{\includegraphics[width=7cm]{ISMIP/TestD/cltxz160p_th}} +\end{figure} +\begin{figure}[H] + \centering + \subfloat[Vx (m/yr) computed by ISSM (Pattyn)]{\includegraphics[width=9cm]{ISMIP/TestD/vx160p}} + \subfloat[Vz (m/yr) computed by ISSM (Pattyn)]{\includegraphics[width=9cm]{ISMIP/TestD/vz160p}} +\end{figure} +\begin{figure}[H] + \centering + \subfloat[Txz (kPa) computed by ISSM (Pattyn)]{\includegraphics[width=9cm]{ISMIP/TestD/txz160p}} +\end{figure} +\newpage + +\subsubsection{global (comparison)} +\begin{figure}[H] + \centering + \subfloat[Maximum Vx (m/yr) computed by ISSM (Pattyn)]{\includegraphics[width=9.5cm]{ISMIP/TestD/TestDMaxVx}} + \subfloat[Maximum Vx (m/yr) comparison]{\includegraphics[width=8.5cm]{ISMIP/TestD/TestDMaxVx_th}} +\end{figure} +\vspace*{-2em} +\begin{figure}[H] + \centering + \subfloat[Minimum Vx (m/yr) computed by ISSM (Pattyn)]{\includegraphics[width=9.5cm]{ISMIP/TestD/TestDMinVx}} + \subfloat[Minimum Vx (m/yr) comparison]{\includegraphics[width=8.5cm]{ISMIP/TestD/TestDMinVx_th}} +\end{figure} +\vspace*{-2em} +\begin{figure}[H] + \centering + \subfloat[Maximum Txz (kPa) computed by ISSM (Pattyn)]{\includegraphics[width=9.5cm]{ISMIP/TestD/TestDMaxTxz}} + \subfloat[Maximum Txz (kPa) comparison]{\includegraphics[width=8.5cm]{ISMIP/TestD/TestDMaxTxz_th}} +\end{figure} +\vspace*{-2em} +\begin{figure}[H] + \centering + \subfloat[Minimum Txz (kPa) computed by ISSM (Pattyn)]{\includegraphics[width=9.5cm]{ISMIP/TestD/TestDMinTxz}} + \subfloat[Minimum Txz (kPa) comparison]{\includegraphics[width=8.5cm]{ISMIP/TestD/TestDMinTxz_th}} +\end{figure} +\newpage + +\section{Test E} +\setcounter{subfigure}{0} +\subsection{Geometry} +This experiment deals with the cross section of a real glacier: \emph{Haut Glacier d'Arolla}. Two cases are studied: +\begin{itemize} +\item[--] basal velocity = 0 on the bed +\item[--] sliding $\alpha^2(x,y)=0$ for $0.44\leqslant x \leqslant 0.5$ +\end{itemize} +\begin{figure}[H] +\begin{center} +\includegraphics[width=9cm]{ISMIP/TestE/geo.png} +\caption{Test E geometry} +\end{center} +\end{figure} + +\newpage +\subsection{Results} + +\subsubsection{Frozen Bed} +\begin{figure}[H] + \centering + \subfloat[Vx (m/yr) comparison]{\includegraphics[width=6.5cm]{ISMIP/TestE/case1_th}} +\end{figure} +\begin{figure}[H] + \centering + \subfloat[Vx (m/yr) computed by ISSM (Pattyn) on a cross line]{\includegraphics[width=9.5cm]{ISMIP/TestE/velfrp}} + \subfloat[Vx (m/yr) computed by ISSM (Stokes) on a cross line]{\includegraphics[width=9.5cm]{ISMIP/TestE/velfrs}} +\end{figure} + +\newpage + +\subsubsection{Sliding} +\setcounter{subfigure}{0} +\begin{figure}[H] + \centering + \subfloat[Vx (m/yr) comparison]{\includegraphics[width=6.5cm]{ISMIP/TestE/case2_th}} +\end{figure} +\begin{figure}[H] + \centering + \subfloat[Vx (m/yr) computed by ISSM (Pattyn) on a cross line]{\includegraphics[width=9.5cm]{ISMIP/TestE/velslp}} + \subfloat[Vx (m/yr) computed by ISSM (Stokes) on a cross line]{\includegraphics[width=9.5cm]{ISMIP/TestE/velsls}} +\end{figure} +\newpage + +\bibliographystyle{plain} +\begin{thebibliography}{10} +\bibitem{Huybrechts1996} + P.~Huybrechts, A.J. 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