%$Id: ocean_version.tex 1080 2012-12-13 13:39:39Z maronga $ \input{header_tmp.tex} %\input{../header_lectures.tex} %\documentclass{beamer} \usepackage[utf8]{inputenc} \usepackage{ngerman} \usepackage{pgf} \usetheme{Dresden} \usepackage{subfigure} \usepackage{units} \usepackage{amsmath} \usepackage{multimedia} \newcommand{\event}[1]{\newcommand{\eventname}{#1}} \usepackage{xmpmulti} \usepackage{tikz} \usepackage{pdfcomment} \usetikzlibrary{shapes,arrows,positioning} \def\Tiny{\fontsize{4pt}{4pt}\selectfont} \usepackage{listings} \lstset{language=[90]Fortran, basicstyle=\ttfamily \tiny, keywordstyle=\color{black}, commentstyle=\color{black}, morecomment=[l]{!\ }% Comment only with space after ! } \institute{Institut für Meteorologie und Klimatologie, Leibniz Universität Hannover} \date{last update: \today} \event{PALM Seminar} \setbeamertemplate{navigation symbols}{} \setbeamertemplate{footline} {% \begin{beamercolorbox}[rightskip=-0.1cm]& {\includegraphics[height=0.65cm]{imuk_logo.pdf}\hfill \includegraphics[height=0.65cm]{luh_logo.pdf}} \end{beamercolorbox} \begin{beamercolorbox}[ht=2.5ex,dp=1.125ex,% leftskip=.3cm,rightskip=0.3cm plus1fil]{title in head/foot}% {\leavevmode{\usebeamerfont{author in head/foot}\insertshortauthor} \hfill \eventname \hfill \insertframenumber \; / \inserttotalframenumber}% \end{beamercolorbox}% % \begin{beamercolorbox}[colsep=1.5pt]{lower separation line foot}% % \end{beamercolorbox} } %\logo{\includegraphics[width=0.3\textwidth]{luhimuk_logo.png}} \title[PALM Ocean Version]{PALM Ocean Version} \author{Siegfried Raasch} % Notes: % jede subsection bekommt einen punkt im menu (vertikal ausgerichtet. % jeder frame in einer subsection bekommt einen punkt (horizontal ausgerichtet) \begin{document} \begin{frame} \titlepage \end{frame} \section{PALM Ocean Version} \subsection{PALM Ocean Version} %Folie 01 \begin{frame} \frametitle{PALM - Ocean Version - General Features} \begin{itemize} \item<2->{Ocean and atmosphere version are sharing the same code.} \item<3->{The ocean version is switched on by setting the +inipar - parameter:\\\quad{\tiny \texttt{ocean = .TRUE.}}} \item<4->{There are only few parts in the code which differ between both versions. In the ocean version:} \begin{itemize} \item<5->{an additional prognostic equation for salinity is solved,} \item<6->{in the buoyancy term (w-equation) and the stability-related terms (SGS-TKE-equation), potential temperature is replaced by potential density,} \item<7->{density is calculated from the nonlinear equation of state for seawater. So far, only the initial hydrostatic pressure is entered into this equation.} \end{itemize} \end{itemize} \end{frame} %Folie 02 \begin{frame} \frametitle{PALM - Ocean Version - Equations} \vspace{15pt} \tikzstyle{white} = [rectangle, text width=0.9\textwidth, font=\normalsize] \tikzstyle{space} = [rectangle, text width=0.01\textwidth, font=\normalsize] \tikzstyle{clear} = [rectangle, draw, text width=0.55\textwidth, minimum size=15pt, font=\small] \tikzstyle{clear2} = [rectangle, draw, text width=0.18\textwidth, minimum size=40pt, font=\normalsize] \tikzstyle{line} = [draw, -] \tikzstyle{red} = [rectangle, draw, color=red, text width=0.28\textwidth, minimum size=40pt, font=\normalsize] \begin{tikzpicture}[auto, node distance=0] \uncover<1->{\node [white] (first) { Momentum: \begin{align*} \frac{\partial \bar{u}_i}{\partial t} =& - \frac{\partial \bar{u}_k \bar{u}_i}{\partial x_k} - \frac{1}{\rho_0} \frac{\partial \bar{p}^*}{\partial x_i} - \varepsilon_{ijk} f_{j} (\bar{u}_k-\bar{u}_{k_g}) - \delta_{i3} g \frac{\bar{\rho}- \tilde{\bar{\rho}}}{\rho_{ref}} - \frac{\partial \overline{u'_k u'_i}}{\partial x_k}\\ \intertext{Potential Temperature:} \frac{\partial \bar{\theta}}{\partial t} =& - \frac{\partial \bar{u}_k \bar{\theta}}{\partial x_k} - \frac{\partial \overline{u'_k \theta'}}{\partial x_k}\\ \intertext{Salinity:} \frac{\partial \bar{S}}{\partial t} =& - \frac{\partial \bar{u}_k \bar{S}}{\partial x_k} - \frac{\partial \overline{u'_k S'}}{\partial x_k} \end{align*} };} \uncover<1->{\node [white, right=-7.3cm of first] (second) {};} \uncover<1->{\node [clear, below=-1.2cm of second] (density) { Density r = r(S,q,ph) is calculated from the equation of state for seawater using the algorithm from Jackett et al. (2006) };} \uncover<1->{\node [space, below=1.0cm of density] (space) {};} \uncover<1->{\node [space, left=2.35cm of space] (kontis) {\begin{align*}\frac{\partial \bar{u}_k}{\partial x_k} = 0\end{align*}};} \uncover<1->{\node [space, right=-0.28cm of space] (reds) {\begin{align*}\frac{\partial^2 \bar{p}^*}{\partial x_{k}^{2}} = \frac{\rho_0}{\Delta t}\frac{\partial \hat{\bar{u}}_k}{\partial x_k}\end{align*}};} \uncover<1->{\node [space, below=1.2cm of density] (space2) {};} \uncover<1->{\node [clear2, left=0.7cm of space2] (konti) {};} \uncover<1->{\node [red, right=-0.38cm of space2] (red) {};} \end{tikzpicture} \end{frame} %Folie 03 \begin{frame} \frametitle{PALM - Ocean Version - Grid Structure and Conventions} \tikzstyle{grid} = [rectangle, minimum size=4pt] \tikzstyle{w} = [rectangle, draw, color=green, fill=green!50, minimum size=4pt] \tikzstyle{u} = [circle, draw, color=gray, fill=gray!50, minimum size=4pt] \tikzstyle{scalar} = [diamond, draw, color=red, fill=red!50, minimum size=4pt] \tikzstyle{line} = [draw, -] \tikzstyle{label} = [rectangle, font=\tiny] \tikzstyle{labelred} = [rectangle, color=red, font=\tiny] \tikzstyle{2dtextbox} = [rectangle, align=center, fill=white!100, text width=0.42\textwidth, minimum size=35pt, font=\tiny] \begin{tikzpicture}[auto, node distance=0,inner sep=0mm,>=latex', edge from parent path= {(\tikzparentnode.west) .. controls +(-0.15,0) and +(0.15,0) .. (\tikzchildnode.east)}] %grid \uncover<1->{\node [grid] (grid11) {};} \uncover<1->{\node [grid, right=0.6cm of grid11] (grid12) {};} \uncover<1->{\node [grid, right=0.6cm of grid12] (grid13) {};} \uncover<1->{\node [grid, right=0.6cm of grid13] (grid14) {};} \uncover<1->{\node [grid, right=0.6cm of grid14] (grid15) {};} \uncover<1->{\node [grid, below=0.6cm of grid11] (grid21) {};} \uncover<1->{\node [grid, right=0.6cm of grid21] (grid22) {};} \uncover<1->{\node [grid, right=0.6cm of grid22] (grid23) {};} \uncover<1->{\node [grid, right=0.6cm of grid23] (grid24) {};} \uncover<1->{\node [grid, right=0.6cm of grid24] (grid25) {};} \uncover<1->{\node [grid, below=0.6cm of grid21] (grid31) {};} \uncover<1->{\node [grid, right=0.6cm of grid31] (grid32) {};} \uncover<1->{\node [grid, right=0.6cm of grid32] (grid33) {};} \uncover<1->{\node [grid, right=0.6cm of grid33] (grid34) {};} \uncover<1->{\node [grid, right=0.6cm of grid34] (grid35) {};} \uncover<1->{\node [grid, below=0.6cm of grid31] (grid41) {};} \uncover<1->{\node [grid, right=0.6cm of grid41] (grid42) {};} \uncover<1->{\node [grid, right=0.6cm of grid42] (grid43) {};} \uncover<1->{\node [grid, right=0.6cm of grid43] (grid44) {};} \uncover<1->{\node [grid, right=0.6cm of grid44] (grid45) {};} \uncover<1->{\node [grid, below=0.6cm of grid41] (grid51) {};} \uncover<1->{\node [grid, right=0.6cm of grid51] (grid52) {};} \uncover<1->{\node [grid, right=0.6cm of grid52] (grid53) {};} \uncover<1->{\node [grid, right=0.6cm of grid53] (grid54) {};} \uncover<1->{\node [grid, right=0.6cm of grid54] (grid55) {};} \uncover<1->{\node [grid, below=0.6cm of grid51] (grid61) {};} \uncover<1->{\node [grid, right=0.6cm of grid61] (grid62) {};} \uncover<1->{\node [grid, right=0.6cm of grid62] (grid63) {};} \uncover<1->{\node [grid, right=0.6cm of grid63] (grid64) {};} \uncover<1->{\node [grid, right=0.6cm of grid64] (grid65) {};} \uncover<1->{\node [grid, below=0.6cm of grid61] (grid71) {};} \uncover<1->{\node [grid, right=0.6cm of grid71] (grid72) {};} \uncover<1->{\node [grid, right=0.6cm of grid72] (grid73) {};} \uncover<1->{\node [grid, right=0.6cm of grid73] (grid74) {};} \uncover<1->{\node [grid, right=0.6cm of grid74] (grid75) {};} %horzontal lines \path<1-> [line] (grid11.west) -- (grid12.east); \path<1-> [line] (grid12.west) -- (grid13.east); \path<1-> [line] (grid13.west) -- (grid14.east); \path<1-> [line] (grid14.west) -- (grid15.east); \path<1-> [line] (grid21.west) -- (grid22.east); \path<1-> [line] (grid22.west) -- (grid23.east); \path<1-> [line] (grid23.west) -- (grid24.east); \path<1-> [line] (grid24.west) -- (grid25.east); \path<1-> [line] (grid31.west) -- (grid32.east); \path<1-> [line] (grid32.west) -- (grid33.east); \path<1-> [line] (grid33.west) -- (grid34.east); \path<1-> [line] (grid34.west) -- (grid35.east); \path<1-> [line] (grid41.west) -- (grid42.east); \path<1-> [line] (grid42.west) -- (grid43.east); \path<1-> [line] (grid43.west) -- (grid44.east); \path<1-> [line] (grid44.west) -- (grid45.east); %vertical lines \path<1-> [line] (grid11.north) -- (grid21.south); \path<1-> [line] (grid12.north) -- (grid22.south); \path<1-> [line] (grid13.north) -- (grid23.south); \path<1-> [line] (grid14.north) -- (grid24.south); \path<1-> [line] (grid15.north) -- (grid25.south); \path<1-> [line] (grid21.north) -- (grid31.south); \path<1-> [line] (grid22.north) -- (grid32.south); \path<1-> [line] (grid23.north) -- (grid33.south); \path<1-> [line] (grid24.north) -- (grid34.south); \path<1-> [line] (grid25.north) -- (grid35.south); \path<1-> [line] (grid31.north) -- (grid41.south); \path<1-> [line] (grid32.north) -- (grid42.south); \path<1-> [line] (grid33.north) -- (grid43.south); \path<1-> [line] (grid34.north) -- (grid44.south); \path<1-> [line] (grid35.north) -- (grid45.south); \uncover<1->{\draw [->] (grid41.south) -- (grid51.north);} \uncover<1->{\draw [->] (grid42.south) -- (grid52.north);} \uncover<1->{\draw [->] (grid43.south) -- (grid53.north);} \uncover<1->{\draw [->] (grid44.south) -- (grid54.north);} \uncover<1->{\draw [->] (grid45.south) -- (grid55.north);} %gridmarks %drawing the w \uncover<1->{\node [w, right=0.22cm of grid11] (w11) {};} \uncover<1->{\node [w, right=0.6cm of w11] (w12) {};} \uncover<1->{\node [w, right=0.6cm of w12] (w13) {};} \uncover<1->{\node [w, right=0.6cm of w13] (w14) {};} \uncover<1->{\node [w, below=0.6cm of w11] (w21) {};} \uncover<1->{\node [w, right=0.6cm of w21] (w22) {};} \uncover<1->{\node [w, right=0.6cm of w22] (w23) {};} \uncover<1->{\node [w, right=0.6cm of w23] (w24) {};} \uncover<1->{\node [w, below=0.6cm of w21] (w31) {};} \uncover<1->{\node [w, right=0.6cm of w31] (w32) {};} \uncover<1->{\node [w, right=0.6cm of w32] (w33) {};} \uncover<1->{\node [w, right=0.6cm of w33] (w34) {};} \uncover<1->{\node [w, below=0.6cm of w31] (w41) {};} \uncover<1->{\node [w, right=0.6cm of w41] (w42) {};} \uncover<1->{\node [w, right=0.6cm of w42] (w43) {};} \uncover<1->{\node [w, right=0.6cm of w43] (w44) {};} \uncover<1->{\node [grid, below=0.6cm of w41] (w51) {};} \uncover<1->{\node [grid, right=0.6cm of w51] (w52) {};} \uncover<1->{\node [grid, right=0.6cm of w52] (w53) {};} \uncover<1->{\node [grid, right=0.6cm of w53] (w54) {};} \uncover<1->{\node [grid, below=0.6cm of w51] (w61) {};} \uncover<1->{\node [grid, right=0.6cm of w61] (w62) {};} \uncover<1->{\node [grid, right=0.6cm of w62] (w63) {};} \uncover<1->{\node [grid, right=0.6cm of w63] (w64) {};} %drawing the u \uncover<1->{\node [u, below=0.22cm of grid11] (u11) {};} \uncover<1->{\node [u, right=0.6cm of u11] (u12) {};} \uncover<1->{\node [u, right=0.6cm of u12] (u13) {};} \uncover<1->{\node [u, right=0.6cm of u13] (u14) {};} \uncover<1->{\node [u, right=0.6cm of u14] (u15) {};} \uncover<1->{\node [u, below=0.6cm of u11] (u21) {};} \uncover<1->{\node [u, right=0.6cm of u21] (u22) {};} \uncover<1->{\node [u, right=0.6cm of u22] (u23) {};} \uncover<1->{\node [u, right=0.6cm of u23] (u24) {};} \uncover<1->{\node [u, right=0.6cm of u24] (u25) {};} \uncover<1->{\node [u, below=0.6cm of u21] (u31) {};} \uncover<1->{\node [u, right=0.6cm of u31] (u32) {};} \uncover<1->{\node [u, right=0.6cm of u32] (u33) {};} \uncover<1->{\node [u, right=0.6cm of u33] (u34) {};} \uncover<1->{\node [u, right=0.6cm of u34] (u35) {};} \uncover<1->{\node [u, below=0.6cm of u31] (u41) {};} \uncover<1->{\node [u, right=0.6cm of u41] (u42) {};} \uncover<1->{\node [u, right=0.6cm of u42] (u43) {};} \uncover<1->{\node [u, right=0.6cm of u43] (u44) {};} \uncover<1->{\node [u, right=0.6cm of u44] (u45) {};} \uncover<1->{\node [grid, below=0.6cm of u41] (u51) {};} \uncover<1->{\node [grid, right=0.6cm of u51] (u52) {};} \uncover<1->{\node [grid, right=0.6cm of u52] (u53) {};} \uncover<1->{\node [grid, right=0.6cm of u53] (u54) {};} \uncover<1->{\node [grid, right=0.6cm of u54] (u55) {};} \uncover<1->{\node [grid, below=0.6cm of u51] (u61) {};} \uncover<1->{\node [grid, right=0.6cm of u61] (u62) {};} \uncover<1->{\node [grid, right=0.6cm of u62] (u63) {};} \uncover<1->{\node [grid, right=0.6cm of u63] (u64) {};} \uncover<1->{\node [grid, right=0.6cm of u64] (u65) {};} \uncover<1->{\node [u, below=0.6cm of u61] (u71) {};} \uncover<1->{\node [u, right=0.6cm of u71] (u72) {};} \uncover<1->{\node [u, right=0.6cm of u72] (u73) {};} \uncover<1->{\node [u, right=0.6cm of u73] (u74) {};} \uncover<1->{\node [u, right=0.6cm of u74] (u75) {};} %horzontal line,dotteds \path<1-> [line,dotted] (u11.east) -- (u12.west); \path<1-> [line,dotted] (u12.east) -- (u13.west); \path<1-> [line,dotted] (u13.east) -- (u14.west); \path<1-> [line,dotted] (u14.east) -- (u15.west); \path<1-> [line,dotted] (u21.east) -- (u22.west); \path<1-> [line,dotted] (u22.east) -- (u23.west); \path<1-> [line,dotted] (u23.east) -- (u24.west); \path<1-> [line,dotted] (u24.east) -- (u25.west); \path<1-> [line,dotted] (u31.east) -- (u32.west); \path<1-> [line,dotted] (u32.east) -- (u33.west); \path<1-> [line,dotted] (u33.east) -- (u34.west); \path<1-> [line,dotted] (u34.east) -- (u35.west); \path<1-> [line,dotted] (u41.east) -- (u42.west); \path<1-> [line,dotted] (u42.east) -- (u43.west); \path<1-> [line,dotted] (u43.east) -- (u44.west); \path<1-> [line,dotted] (u44.east) -- (u45.west); %vertical line,dotted \path<1-> [line,dotted] (w11.south) -- (w21.north); \path<1-> [line,dotted] (w12.south) -- (w22.north); \path<1-> [line,dotted] (w13.south) -- (w23.north); \path<1-> [line,dotted] (w14.south) -- (w24.north); \path<1-> [line,dotted] (w21.south) -- (w31.north); \path<1-> [line,dotted] (w22.south) -- (w32.north); \path<1-> [line,dotted] (w23.south) -- (w33.north); \path<1-> [line,dotted] (w24.south) -- (w34.north); \path<1-> [line,dotted] (w31.south) -- (w41.north); \path<1-> [line,dotted] (w32.south) -- (w42.north); \path<1-> [line,dotted] (w33.south) -- (w43.north); \path<1-> [line,dotted] (w34.south) -- (w44.north); %drawing the scalar \uncover<1->{\node [scalar, below=0.22cm of w11] (scalar11) {};} \uncover<1->{\node [scalar, right=0.6cm of scalar11] (scalar12) {};} \uncover<1->{\node [scalar, right=0.6cm of scalar12] (scalar13) {};} \uncover<1->{\node [scalar, right=0.6cm of scalar13] (scalar14) {};} \uncover<1->{\node [scalar, below=0.6cm of scalar11] (scalar21) {};} \uncover<1->{\node [scalar, right=0.6cm of scalar21] (scalar22) {};} \uncover<1->{\node [scalar, right=0.6cm of scalar22] (scalar23) {};} \uncover<1->{\node [scalar, right=0.6cm of scalar23] (scalar24) {};} \uncover<1->{\node [scalar, below=0.6cm of scalar21] (scalar31) {};} \uncover<1->{\node [scalar, right=0.6cm of scalar31] (scalar32) {};} \uncover<1->{\node [scalar, right=0.6cm of scalar32] (scalar33) {};} \uncover<1->{\node [scalar, right=0.6cm of scalar33] (scalar34) {};} \uncover<1->{\node [scalar, below=0.6cm of scalar31] (scalar41) {};} \uncover<1->{\node [scalar, right=0.6cm of scalar41] (scalar42) {};} \uncover<1->{\node [scalar, right=0.6cm of scalar42] (scalar43) {};} \uncover<1->{\node [scalar, right=0.6cm of scalar43] (scalar44) {};} \uncover<1->{\node [grid, below=0.6cm of scalar41] (scalar51) {};} \uncover<1->{\node [grid, right=0.6cm of scalar51] (scalar52) {};} \uncover<1->{\node [grid, right=0.6cm of scalar52] (scalar53) {};} \uncover<1->{\node [grid, right=0.6cm of scalar53] (scalar54) {};} \uncover<1->{\node [grid, below=0.6cm of scalar51] (scalar61) {};} \uncover<1->{\node [grid, right=0.6cm of scalar61] (scalar62) {};} \uncover<1->{\node [grid, right=0.6cm of scalar62] (scalar63) {};} \uncover<1->{\node [grid, right=0.6cm of scalar63] (scalar64) {};} \path<1-> [line,dotted] (w41.south) -- (scalar41.north); \path<1-> [line,dotted] (w42.south) -- (scalar42.north); \path<1-> [line,dotted] (w43.south) -- (scalar43.north); \path<1-> [line,dotted] (w44.south) -- (scalar44.north); %continue the grid at the bottom \path<1-> [line,dotted] (u51.south) -- (grid61.north); \path<1-> [line,dotted] (u52.south) -- (grid62.north); \path<1-> [line,dotted] (u53.south) -- (grid63.north); \path<1-> [line,dotted] (u54.south) -- (grid64.north); \path<1-> [line,dotted] (u55.south) -- (grid65.north); \path<1-> [line] (grid71.west) -- (grid72.east); \path<1-> [line] (grid72.west) -- (grid73.east); \path<1-> [line] (grid73.west) -- (grid74.east); \path<1-> [line] (grid74.west) -- (grid75.east); \path<1-> [line] (u61.south) -- (u71.north); \path<1-> [line] (u62.south) -- (u72.north); \path<1-> [line] (u63.south) -- (u73.north); \path<1-> [line] (u64.south) -- (u74.north); \path<1-> [line] (u65.south) -- (u75.north); \uncover<1->{\node [w, below=0.6cm of w61] (w71) {};} \uncover<1->{\node [w, right=0.6cm of w71] (w72) {};} \uncover<1->{\node [w, right=0.6cm of w72] (w73) {};} \uncover<1->{\node [w, right=0.6cm of w73] (w74) {};} \path<1-> [line,dotted] (u71.east) -- (u72.west); \path<1-> [line,dotted] (u72.east) -- (u73.west); \path<1-> [line,dotted] (u73.east) -- (u74.west); \path<1-> [line,dotted] (u74.east) -- (u75.west); \uncover<1->{\node [scalar, below=0.6cm of scalar61] (scalar71) {};} \uncover<1->{\node [scalar, right=0.6cm of scalar71] (scalar72) {};} \uncover<1->{\node [scalar, right=0.6cm of scalar72] (scalar73) {};} \uncover<1->{\node [scalar, right=0.6cm of scalar73] (scalar74) {};} \path<1-> [line,dotted] (w71.south) -- (scalar71.north); \path<1-> [line,dotted] (w72.south) -- (scalar72.north); \path<1-> [line,dotted] (w73.south) -- (scalar73.north); \path<1-> [line,dotted] (w74.south) -- (scalar74.north); %legende 2D \uncover<1->{\node [grid, above=0.6cm of grid11] (2Dlegend00) {};} \uncover<1->{\node [grid, right=0.6cm of 2Dlegend00] (2Dlegend10) {};} \uncover<1->{\node [grid, above=0.6cm of 2Dlegend00] (2Dlegend01) {};} \uncover<1->{\draw [->, color=red] (2Dlegend00.center) -- (2Dlegend10.east);} \uncover<1->{\draw [->, color=black] (2Dlegend00.center) -- (2Dlegend01.north);} \uncover<1->{\node [label, above=0.8cm of 2Dlegend00] (2Dlegend01label) {w,z,k};} \uncover<1->{\node [label, right=0.8cm of 2Dlegend00] (2Dlegend10label) {u,x,i};} \uncover<1->{\node [scalar, above=0.6cm of grid14] (2Dlegendscalar) {};} \uncover<1->{\node [label, right=0.1cm of 2Dlegendscalar] (2Dlegendscalarlabel) {: scalar (e.g. pt)};} \uncover<1->{\node [u, above=0.22cm of 2Dlegendscalar] (2Dlegendu) {};} \uncover<1->{\node [label, right=0.1cm of 2Dlegendu] (2Dlegendulabel) {: u};} \uncover<1->{\node [w, above=0.22cm of 2Dlegendu] (2Dlegendw) {};} \uncover<1->{\node [label, right=0.1cm of 2Dlegendw] (2Dlegendwlabel) {: w};} \uncover<1->{\node [grid, above=0.22cm of 2Dlegendw] (2Dlegendspacing) {};} %2D Grid Label right \uncover<1->{\node [grid, below=0.035cm of grid15] (rightlabelgrid1) {};} \uncover<1->{\node [grid, below=0.6cm of rightlabelgrid1] (rightlabelgrid2) {};} \uncover<1->{\node [grid, below=0.6cm of rightlabelgrid2] (rightlabelgrid3) {};} \uncover<1->{\node [grid, below=0.6cm of rightlabelgrid3] (rightlabelgrid4) {};} \uncover<1->{\node [grid, below=0.6cm of rightlabelgrid4] (rightlabelgrid5) {};} \uncover<1->{\node [grid, below=0.6cm of rightlabelgrid5] (rightlabelgrid6) {};} \uncover<1->{\node [grid, below=0.6cm of rightlabelgrid6] (rightlabelgrid7) {};} \uncover<1->{\node[label, right=0.30cm of rightlabelgrid1] (2Dgridlabelnzt1) {\: k = nzt + 1} child {node [grid, right=0cm of grid15] {}} child {node [grid, right=0cm of u15] {}};} \uncover<1->{\node[label, right=0.30cm of rightlabelgrid2] (2Dgridlabelnzt2) {\: k = nzt} child {node [grid, right=0cm of grid25] {}} child {node [grid, right=0cm of u25] {}};} \uncover<1->{\node[label, right=0.30cm of rightlabelgrid7] (2Dgridlabelnzt7) {\: k = nzb ($\sim0$)} child {node [grid, right=0cm of grid75] {}} child {node [grid, right=0cm of u75] {}};} \uncover<1->{\node [grid, right=0.62cm of u25] (rightlabelarrowtop) {};} \uncover<1->{\node [grid, right=0.62cm of grid75] (rightlabelarrowbottom) {};} \uncover<1->{\draw [->, dotted] (rightlabelarrowtop.south) -- (rightlabelarrowbottom.north);} \uncover<1->{\node [grid, right=0.2cm of grid25] (grid26) {};} \uncover<1->{\node [grid, right=0.6cm of grid26] (grid27) {};} \uncover<1->{\node [grid, right=0.3cm of grid27] (grid28) {};} \uncover<1->{\draw [->, dashed, color=red] (grid28.center) -- (grid26.center);} \uncover<1->{\node [labelred, above=-0.05cm of grid27] (grid27) {(sea sfc)};} %2D Grid Label left \uncover<1->{\node [grid, left=1.4cm of grid11] (leftlabelgrid1) {};} \uncover<1->{\node [grid, below=0.6cm of leftlabelgrid1] (leftlabelgrid3) {};} \uncover<1->{\node [grid, below=0.6cm of leftlabelgrid3] (leftlabelgrid5) {};} \uncover<1->{\node [grid, below=0.6cm of leftlabelgrid5] (leftlabelgrid7) {};} \uncover<1->{\node [grid, below=0.22cm of leftlabelgrid1] (leftlabelgrid2) {};} \uncover<1->{\node [grid, below=0.6cm of leftlabelgrid2] (leftlabelgrid4) {};} \uncover<1->{\node [grid, below=0.6cm of leftlabelgrid4] (leftlabelgrid6) {};} \uncover<1->{\node[label, right=0cm of leftlabelgrid2] {$\text{z}=+\frac{\Delta \text{z}}{2}$};} \uncover<1->{\node[label, right=0cm of leftlabelgrid3] {$\text{z}=0$};} \uncover<1->{\node[label, right=0cm of leftlabelgrid4] {$\text{z}=-\frac{\Delta \text{z}}{2}$};} \uncover<1->{\node[label, right=0cm of leftlabelgrid5] {$\text{z}=-\Delta \text{z}$};} \uncover<1->{\node[label, right=0cm of leftlabelgrid7] {$\text{z}=-2\Delta \text{z}$};} \uncover<1->{\node [grid, left=0.22cm of grid11] (leftarrowgrid1) {};} \uncover<1->{\node [grid, below=0.6cm of leftarrowgrid1] (leftarrowgrid3) {};} \uncover<1->{\node [grid, below=0.6cm of leftarrowgrid3] (leftarrowgrid5) {};} \uncover<1->{\node [grid, below=0.6cm of leftarrowgrid5] (leftarrowgrid7) {};} \uncover<1->{\node [grid, below=0.22cm of leftarrowgrid1] (leftarrowgrid2) {};} \uncover<1->{\node [grid, below=0.6cm of leftarrowgrid2] (leftarrowgrid4) {};} \uncover<1->{\node [grid, below=0.6cm of leftarrowgrid4] (leftarrowgrid6) {};} \uncover<1->{\draw [->, dotted] (u11.west) -- (leftarrowgrid2.east);} \uncover<1->{\draw [->, dotted] (grid21.west) -- (leftarrowgrid3.east);} \uncover<1->{\draw [->, dotted] (u21.west) -- (leftarrowgrid4.east);} \uncover<1->{\draw [->, dotted] (grid31.west) -- (leftarrowgrid5.east);} \uncover<1->{\draw [->, dotted] (grid41.west) -- (leftarrowgrid7.east);} \uncover<1->{\node [grid, below=0.035cm of grid41] (leftlabelarrowtopbase) {};} \uncover<1->{\node [grid, left=1.058cm of leftlabelarrowtopbase] (leftlabelarrowtop) {};} \uncover<1->{\node [grid, left=1.058cm of grid71] (leftlabelarrowbottom) {};} \uncover<1->{\draw [->, dotted] (leftlabelarrowtop.south) -- (leftlabelarrowbottom.north);} %2D textbox \uncover<2->{\node [2dtextbox, below=0.25cm of u43] (2dtextbox) { z=0 (sea surface) is assumed at the \textbf{model top}\\ (vertical grid index k=nzt on the w-grid),\\ with negative values of z indicating the depth. };} %------------------------------------3D-------------------------- %grid \uncover<1->{\node [grid, right=5.0cm of grid11] (2grid11) {};} \uncover<1->{\node [grid, right=0.9cm of 2grid11] (2grid12) {};} \uncover<1->{\node [grid, right=0.9cm of 2grid12] (2grid13) {};} \uncover<1->{\node [grid, right=0.9cm of 2grid13] (2grid14) {};} \uncover<1->{\node [grid, right=0.9cm of 2grid14] (2grid15) {};} \uncover<1->{\node [grid, below=0.9cm of 2grid11] (2grid21) {};} \uncover<1->{\node [grid, right=0.9cm of 2grid21] (2grid22) {};} \uncover<1->{\node [grid, right=0.9cm of 2grid22] (2grid23) {};} \uncover<1->{\node [grid, right=0.9cm of 2grid23] (2grid24) {};} \uncover<1->{\node [grid, right=0.9cm of 2grid24] (2grid25) {};} \uncover<1->{\node [grid, below=0.9cm of 2grid21] (2grid31) {};} \uncover<1->{\node [grid, right=0.9cm of 2grid31] (2grid32) {};} \uncover<1->{\node [grid, right=0.9cm of 2grid32] (2grid33) {};} \uncover<1->{\node [grid, right=0.9cm of 2grid33] (2grid34) {};} \uncover<1->{\node [grid, right=0.9cm of 2grid34] (2grid35) {};} \uncover<1->{\node [grid, below=0.9cm of 2grid31] (2grid41) {};} \uncover<1->{\node [grid, right=0.9cm of 2grid41] (2grid42) {};} \uncover<1->{\node [grid, right=0.9cm of 2grid42] (2grid43) {};} \uncover<1->{\node [grid, right=0.9cm of 2grid43] (2grid44) {};} \uncover<1->{\node [grid, right=0.9cm of 2grid44] (2grid45) {};} \uncover<1->{\node [grid, below=0.9cm of 2grid41] (2grid51) {};} \uncover<1->{\node [grid, right=0.9cm of 2grid51] (2grid52) {};} \uncover<1->{\node [grid, right=0.9cm of 2grid52] (2grid53) {};} \uncover<1->{\node [grid, right=0.9cm of 2grid53] (2grid54) {};} \uncover<1->{\node [grid, right=0.9cm of 2grid54] (2grid55) {};} \fill [fill=blue!20] (2grid12.center) -- (2grid21.center) -- (2grid51.center) -- (2grid54.center) -- (2grid24.center) -- (2grid15.center); \fill [fill=blue!50] (2grid15.center) -- (2grid24.center) -- (2grid54.center) -- (2grid45.center) -- (2grid15.center); \path<1-> [line] (2grid21.center) -- (2grid51.center); \path<1-> [line] (2grid51.center) -- (2grid54.center); \path<1-> [line] (2grid54.center) -- (2grid24.center); \path<1-> [line] (2grid24.center) -- (2grid21.center); \path<1-> [line,dashed] (2grid42.center) -- (2grid12.center); \path<1-> [line,dashed] (2grid42.center) -- (2grid45.center); \path<1-> [line] (2grid45.center) -- (2grid15.center); \path<1-> [line] (2grid15.center) -- (2grid12.center); \path<1-> [line] (2grid21.center) -- (2grid12.center); \path<1-> [line] (2grid24.center) -- (2grid15.center); \path<1-> [line] (2grid54.center) -- (2grid45.center); \path<1-> [line,dashed] (2grid42.center) -- (2grid51.center); %legende 3D \uncover<1->{\node [grid, above=0.6cm of 2grid12] (3Dlegend00) {};} \uncover<1->{\node [grid, right=0.6cm of 3Dlegend00] (3Dlegend10) {};} \uncover<1->{\node [grid, above=0.6cm of 3Dlegend00] (3Dlegend01) {};} \uncover<1->{\draw [->, color=red] (3Dlegend00.center) -- (3Dlegend10.east);} \uncover<1->{\draw [->, color=black] (3Dlegend00.center) -- (3Dlegend01.north);} \uncover<1->{\node [grid, right=0.2cm of 3Dlegend00] (3Dlegend010base) {};} \uncover<1->{\node [grid, above=0.2cm of 3Dlegend010base] (3Dlegend010) {};} \uncover<1->{\draw [->, color=blue] (3Dlegend00.center) -- (3Dlegend010.center);} \uncover<1->{\node [label, above=0.8cm of 3Dlegend00] (3Dlegend001label) {w,z,k};} \uncover<1->{\node [label, right=0.8cm of 3Dlegend00] (3Dlegend100label) {u,x,i};} \uncover<1->{\node [label, right=0cm of 3Dlegend010] (3Dlegend010label) {v,y,j};} %mini koordinaten 3D \uncover<1->{\node [grid, right=0.375cm of 2grid11] (3Dkoordgrid11base) {};} \uncover<1->{\node [grid, below=0.375cm of 3Dkoordgrid11base] (3Dkoordgrid11) {};} \uncover<1->{\node [grid, below=0.375cm of 2grid13] (3Dkoord1base) {};} \uncover<1->{\node [grid, right=0.375cm of 2grid31] (3Dkoord2base) {};} \uncover<1->{\node [grid, right=0.375cm of 2grid42] (3Dkoord3basebase) {};} \uncover<1->{\node [grid, above=0.375cm of 3Dkoord3basebase] (3Dkoord3base) {};} \uncover<1->{\node [grid, left=0.375cm of 2grid24] (3Dkoord4basebase) {};} \uncover<1->{\node [grid, below=0.375cm of 3Dkoord4basebase] (3Dkoord4base) {};} \uncover<1->{\node [grid, left=0.375cm of 2grid35] (3Dkoord5base) {};} \uncover<1->{\node [grid, above=0.375cm of 2grid53] (3Dkoord6base) {};} \uncover<1->{\node [grid, right=0.9cm of 2grid32] (3Dkoord7base) {};} \uncover<1->{\node [grid, left=0.15cm of 3Dkoord1base] (3Dkoord1x1) {};} \uncover<1->{\node [grid, right=0.15cm of 3Dkoord1base] (3Dkoord1x2) {};} \uncover<1->{\node [grid, below=0.15cm of 3Dkoord1base] (3Dkoord1z1) {};} \uncover<1->{\node [grid, above=0.15cm of 3Dkoord1base] (3Dkoord1z2) {};} \uncover<1->{\node [grid, left=0.03cm of 3Dkoord1base] (3Dkoord1y1base) {};} \uncover<1->{\node [grid, below=0.03cm of 3Dkoord1y1base] (3Dkoord1y1) {};} \uncover<1->{\node [grid, right=0.03cm of 3Dkoord1base] (3Dkoord1y2base) {};} \uncover<1->{\node [grid, above=0.03cm of 3Dkoord1y2base] (3Dkoord1y2) {};} \uncover<1->{\draw [<->, color=red] (3Dkoord1x1.center) -- (3Dkoord1x2.center);} \uncover<1->{\draw [<->, color=blue] (3Dkoord1y1.center) -- (3Dkoord1y2.center);} \uncover<1->{\draw [<-, color=black] (3Dkoord1z1.center) -- (3Dkoord1base.center);} \uncover<1->{\node [label, right=0.2cm of 3Dkoord1y1] (3Dkoord1baselabel) {$\text{w}_{\text{i,j,k}}$};} \uncover<1->{\node [grid, left=0.15cm of 3Dkoord2base] (3Dkoord2x1) {};} \uncover<1->{\node [grid, right=0.15cm of 3Dkoord2base] (3Dkoord2x2) {};} \uncover<1->{\node [grid, below=0.15cm of 3Dkoord2base] (3Dkoord2z1) {};} \uncover<1->{\node [grid, above=0.15cm of 3Dkoord2base] (3Dkoord2z2) {};} \uncover<1->{\node [grid, left=0.03cm of 3Dkoord2base] (3Dkoord2y1base) {};} \uncover<1->{\node [grid, below=0.03cm of 3Dkoord2y1base] (3Dkoord2y1) {};} \uncover<1->{\node [grid, right=0.03cm of 3Dkoord2base] (3Dkoord2y2base) {};} \uncover<1->{\node [grid, above=0.03cm of 3Dkoord2y2base] (3Dkoord2y2) {};} \uncover<1->{\draw [->, color=red] (3Dkoord2base.center) -- (3Dkoord2x2.center);} \uncover<1->{\draw [<->, color=blue] (3Dkoord2y1.center) -- (3Dkoord2y2.center);} \uncover<1->{\draw [<->, color=black] (3Dkoord2z1.center) -- (3Dkoord2z2.center);} \uncover<1->{\node [label, below=0cm of 3Dkoord2z1] (3Dkoord2baselabel) {$\text{u}_{\text{i,j,k}}$};} \uncover<1->{\node [grid, left=0.15cm of 3Dkoord3base] (3Dkoord3x1) {};} \uncover<1->{\node [grid, right=0.15cm of 3Dkoord3base] (3Dkoord3x2) {};} \uncover<1->{\node [grid, below=0.15cm of 3Dkoord3base] (3Dkoord3z1) {};} \uncover<1->{\node [grid, above=0.15cm of 3Dkoord3base] (3Dkoord3z2) {};} \uncover<1->{\node [grid, left=0.03cm of 3Dkoord3base] (3Dkoord3y1base) {};} \uncover<1->{\node [grid, below=0.03cm of 3Dkoord3y1base] (3Dkoord3y1) {};} \uncover<1->{\node [grid, right=0.03cm of 3Dkoord3base] (3Dkoord3y2base) {};} \uncover<1->{\node [grid, above=0.03cm of 3Dkoord3y2base] (3Dkoord3y2) {};} \uncover<1->{\draw [<->, color=red] (3Dkoord3x1.center) -- (3Dkoord3x2.center);} \uncover<1->{\draw [->, color=blue] (3Dkoord3base.center) -- (3Dkoord3y2.center);} \uncover<1->{\draw [<->, color=black] (3Dkoord3z1.center) -- (3Dkoord3z2.center);} \uncover<1->{\node [label, right=0.2cm of 3Dkoord3y1] (3Dkoord3baselabel) {$\text{v}_{\text{i,j,k}}$};} \uncover<1->{\node [grid, left=0.15cm of 3Dkoord4base] (3Dkoord4x1) {};} \uncover<1->{\node [grid, right=0.15cm of 3Dkoord4base] (3Dkoord4x2) {};} \uncover<1->{\node [grid, below=0.15cm of 3Dkoord4base] (3Dkoord4z1) {};} \uncover<1->{\node [grid, above=0.15cm of 3Dkoord4base] (3Dkoord4z2) {};} \uncover<1->{\node [grid, left=0.03cm of 3Dkoord4base] (3Dkoord4y1base) {};} \uncover<1->{\node [grid, below=0.03cm of 3Dkoord4y1base] (3Dkoord4y1) {};} \uncover<1->{\node [grid, right=0.03cm of 3Dkoord4base] (3Dkoord4y2base) {};} \uncover<1->{\node [grid, above=0.03cm of 3Dkoord4y2base] (3Dkoord4y2) {};} \uncover<1->{\draw [<->, color=red] (3Dkoord4x1.center) -- (3Dkoord4x2.center);} \uncover<1->{\draw [<-, color=blue] (3Dkoord4y1.center) -- (3Dkoord4base.center);} \uncover<1->{\draw [<->, color=black] (3Dkoord4z1.center) -- (3Dkoord4z2.center);} \uncover<1->{\node [label, left=0.2cm of 3Dkoord4y2] (3Dkoord4baselabel) {$\text{v}_{\text{i,j+1,k}}$};} \uncover<1->{\node [grid, left=0.15cm of 3Dkoord5base] (3Dkoord5x1) {};} \uncover<1->{\node [grid, right=0.15cm of 3Dkoord5base] (3Dkoord5x2) {};} \uncover<1->{\node [grid, below=0.15cm of 3Dkoord5base] (3Dkoord5z1) {};} \uncover<1->{\node [grid, above=0.15cm of 3Dkoord5base] (3Dkoord5z2) {};} \uncover<1->{\node [grid, left=0.03cm of 3Dkoord5base] (3Dkoord5y1base) {};} \uncover<1->{\node [grid, below=0.03cm of 3Dkoord5y1base] (3Dkoord5y1) {};} \uncover<1->{\node [grid, right=0.03cm of 3Dkoord5base] (3Dkoord5y2base) {};} \uncover<1->{\node [grid, above=0.03cm of 3Dkoord5y2base] (3Dkoord5y2) {};} \uncover<1->{\draw [<-, color=red] (3Dkoord5x1.center) -- (3Dkoord5base.center);} \uncover<1->{\draw [<->, color=blue] (3Dkoord5y1.center) -- (3Dkoord5y2.center);} \uncover<1->{\draw [<->, color=black] (3Dkoord5z1.center) -- (3Dkoord5z2.center);} \uncover<1->{\node [label, below=0cm of 3Dkoord5z1] (3Dkoord5baselabel) {$\text{u}_{\text{i+1,j,k}}$};} \uncover<1->{\node [grid, left=0.15cm of 3Dkoord6base] (3Dkoord6x1) {};} \uncover<1->{\node [grid, right=0.15cm of 3Dkoord6base] (3Dkoord6x2) {};} \uncover<1->{\node [grid, below=0.15cm of 3Dkoord6base] (3Dkoord6z1) {};} \uncover<1->{\node [grid, above=0.15cm of 3Dkoord6base] (3Dkoord6z2) {};} \uncover<1->{\node [grid, left=0.03cm of 3Dkoord6base] (3Dkoord6y1base) {};} \uncover<1->{\node [grid, below=0.03cm of 3Dkoord6y1base] (3Dkoord6y1) {};} \uncover<1->{\node [grid, right=0.03cm of 3Dkoord6base] (3Dkoord6y2base) {};} \uncover<1->{\node [grid, above=0.03cm of 3Dkoord6y2base] (3Dkoord6y2) {};} \uncover<1->{\draw [<->, color=red] (3Dkoord6x1.center) -- (3Dkoord6x2.center);} \uncover<1->{\draw [<->, color=blue] (3Dkoord6y1.center) -- (3Dkoord6y2.center);} \uncover<1->{\draw [->, color=black] (3Dkoord6base.center) -- (3Dkoord6z2.center);} \uncover<1->{\node [label, right=0.2cm of 3Dkoord6y1] (3Dkoord6baselabel) {$\text{w}_{\text{i,j,k-1}}$};} \uncover<1->{\node [grid, left=0.15cm of 3Dkoord7base] (3Dkoord7x1) {};} \uncover<1->{\node [grid, right=0.15cm of 3Dkoord7base] (3Dkoord7x2) {};} \uncover<1->{\node [grid, below=0.15cm of 3Dkoord7base] (3Dkoord7z1) {};} \uncover<1->{\node [grid, above=0.15cm of 3Dkoord7base] (3Dkoord7z2) {};} \uncover<1->{\node [grid, left=0.03cm of 3Dkoord7base] (3Dkoord7y1base) {};} \uncover<1->{\node [grid, below=0.03cm of 3Dkoord7y1base] (3Dkoord7y1) {};} \uncover<1->{\node [grid, right=0.03cm of 3Dkoord7base] (3Dkoord7y2base) {};} \uncover<1->{\node [grid, above=0.03cm of 3Dkoord7y2base] (3Dkoord7y2) {};} \uncover<1->{\draw [<->, color=red] (3Dkoord7x1.center) -- (3Dkoord7x2.center);} \uncover<1->{\draw [<->, color=blue] (3Dkoord7y1.center) -- (3Dkoord7y2.center);} \uncover<1->{\draw [<->, color=black] (3Dkoord7z1.center) -- (3Dkoord7z2.center);} \uncover<1->{\node [label, right=0.2cm of 3Dkoord7y1] (3Dkoord7baselabel) {$\text{s}_{\text{i,j,k}}$};} \end{tikzpicture} \end{frame} %Folie 04 \begin{frame} \frametitle{PALM - Ocean Version - Boundary Conditions} The following boundary conditions should be used for the ocean version. Some of them are not set by default, so please set them manually.\\ \begin{itemize} \item<2->{Ocean surface (z=0):} \begin{itemize} \item<2->{Fluxes should be given at the ocean surface for all quantities. This requires parameter\\\quad{\tiny \texttt{top\_momentum\_flux\_u = ..., top\_momentum\_flux\_v = ..., bc\_uv\_t = ‘neumann’}}} \item<3->{Momentum:\\\quad{\tiny \texttt{use\_top\_fluxes = .TRUE.}}} \item<4->{Temperature:\\\quad{\tiny \texttt{top\_heatflux = ..., bc\_pt\_t = ‘neumann’}}} \item<5->{Salinity:\\\quad{\tiny \texttt{top\_salinityflux = ..., bc\_sa\_t = ‘neumann’}}} \end{itemize} \item<6->{Ocean bottom (z=-...)} \begin{itemize} \item<6->{A Prandtl-layer should be used at the bottom:\\\quad{\tiny \texttt{prandtl\_layer = .TRUE.}}} \end{itemize} \end{itemize} \end{frame} %Folie 05 \begin{frame} \frametitle{PALM - Ocean Version - Further Settings} \begin{itemize} \item<2->{Initial profiles:} \begin{itemize} \item<2->{The ocean version can only use:\\\quad{\tiny \texttt{initializing\_actions = ‘set\_constant\_profiles’}}} \item<3->{Profiles are constructed piecewise linear \underline{from the top} (surface), using parameters (e.g.):\\\quad{\tiny \texttt{pt\_surface = ..., pt\_initial\_gradient = ..., pt\_initial\_gradient\_level = ...}}} \end{itemize} \item<4->{Random perturbations:} \begin{itemize} \item<4->{Random perturbations are by default applied to the upper third of the model domain!} \end{itemize} \end{itemize} \end{frame} %Folie 06 \begin{frame} \frametitle{PALM - Ocean Version - Final Remarks} \begin{itemize} \item<2->{The ocean version of PALM has not been tested sufficiently so far! Only some plausibility checks have been done.} \item<3->{Please carefully check the results and please also check the code.} \item<4->{Effects of surface waves (Langmuir circulation, wave breaking) are not included in the standard code.} \end{itemize} \end{frame} \end{document}