[1080] | 1 | %$Id: canopy_model.tex 1205 2013-07-15 10:55:47Z boeske $ |
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| 2 | \input{header_tmp.tex} |
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| 3 | %\input{../header_lectures.tex} |
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| 4 | |
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| 5 | %\documentclass{beamer} |
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| 6 | \usepackage[utf8]{inputenc} |
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| 7 | \usepackage{ngerman} |
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| 8 | \usepackage{pgf} |
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| 9 | \usetheme{Dresden} |
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| 10 | \usepackage{subfigure} |
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| 11 | \usepackage{units} |
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| 12 | \usepackage{amsmath} |
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| 13 | \usepackage{multimedia} |
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| 14 | \newcommand{\event}[1]{\newcommand{\eventname}{#1}} |
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| 15 | \usepackage{xmpmulti} |
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| 16 | \usepackage{tikz} |
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| 17 | \usepackage{pdfcomment} |
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| 18 | \usetikzlibrary{shapes,arrows,positioning,calc,decorations.pathmorphing,decorations.pathreplacing,decorations.markings} |
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| 19 | \def\Tiny{\fontsize{4pt}{4pt}\selectfont} |
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| 20 | \usepackage{listings} |
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| 21 | \lstset{language=[90]Fortran, |
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| 22 | basicstyle=\ttfamily \tiny, |
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| 23 | keywordstyle=\color{black}, |
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| 24 | commentstyle=\color{black}, |
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| 25 | morecomment=[l]{!\ }% Comment only with space after ! |
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| 26 | } |
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| 27 | |
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| 28 | |
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| 29 | \institute{Institut fÌr Meteorologie und Klimatologie, Leibniz UniversitÀt Hannover} |
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| 30 | \date{last update: \today} |
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| 31 | \event{PALM Seminar} |
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| 32 | \setbeamertemplate{navigation symbols}{} |
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| 33 | |
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| 34 | \setbeamertemplate{footline} |
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| 35 | {% |
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| 36 | \begin{beamercolorbox}[rightskip=-0.1cm]& |
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| 37 | {\includegraphics[height=0.65cm]{imuk_logo.pdf}\hfill \includegraphics[height=0.65cm]{luh_logo.pdf}} |
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| 38 | \end{beamercolorbox} |
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| 39 | \begin{beamercolorbox}[ht=2.5ex,dp=1.125ex,% |
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| 40 | leftskip=.3cm,rightskip=0.3cm plus1fil]{title in head/foot}% |
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| 41 | {\leavevmode{\usebeamerfont{author in head/foot}\insertshortauthor} \hfill \eventname \hfill \insertframenumber \; / \inserttotalframenumber}% |
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| 42 | \end{beamercolorbox}% |
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| 43 | % \begin{beamercolorbox}[colsep=1.5pt]{lower separation line foot}% |
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| 44 | % \end{beamercolorbox} |
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| 45 | } |
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| 46 | %\logo{\includegraphics[width=0.3\textwidth]{luhimuk_logo.png}} |
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| 47 | |
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| 48 | \title[PALM's Canopy Model]{PALM's Canopy Model} |
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| 49 | \author{Siegfried Raasch} |
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| 50 | |
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| 51 | |
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| 52 | % Notes: |
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| 53 | % jede subsection bekommt einen punkt im menu (vertikal ausgerichtet. |
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| 54 | % jeder frame in einer subsection bekommt einen punkt (horizontal ausgerichtet) |
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| 55 | \begin{document} |
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| 56 | |
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| 57 | \begin{frame} |
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| 58 | \titlepage |
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| 59 | \end{frame} |
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| 60 | |
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| 61 | \section{PALM's Canopy Model} |
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| 62 | \subsection{The embedded Canopy Model} |
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| 63 | |
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| 64 | %Folie 01 |
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| 65 | \begin{frame} |
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| 66 | \frametitle{Overview} |
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| 67 | \begin{itemize} |
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[1205] | 68 | \item<1->{The canopy model embedded in PALM can be used to study the effect of a plant canopy on e.g.:} |
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[1080] | 69 | \begin{itemize} |
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| 70 | \item<2->{mean flow field,} |
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| 71 | \item<3->{development of coherent turbulence structures,} |
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| 72 | \item<4->{scalar exchange processes between canopy and atmosphere.} |
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| 73 | \end{itemize} |
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[1205] | 74 | \item<5->{Within the canopy model, the plant canopy acts as a sink for momentum and as a source/sink for active (e.g. temperature) and passive (e.g. tracer) scalars.} |
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[1080] | 75 | \item<6->{The canopy model does not account for each plant element, but rather accounts for a volume averaged effect on the flow and scalar concentration, depending on:} |
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| 76 | \begin{itemize} |
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[1205] | 77 | \item<7->{leaf area density,} |
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[1080] | 78 | \item<8->{drag coefficient.} |
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| 79 | \end{itemize} |
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| 80 | \end{itemize} |
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| 81 | \end{frame} |
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| 82 | |
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| 83 | |
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| 84 | |
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| 85 | %Folie 02 |
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| 86 | \begin{frame} |
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| 87 | \frametitle{Theory (I)} |
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| 88 | \begin{footnotesize} |
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| 89 | \begin{itemize} |
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| 90 | \item<1->{A plant canopy affects the flow by acting as a momentum sink due to form and viscous drag forces.} |
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| 91 | \item<2->{The effectiveness of momentum absorption depends on the amount of leaf area per unit volume and the aerodynamic drag.} |
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[1205] | 92 | \item<3->{Due to the aerodynamic drag, the flow is decelerated within the canopy, leading to an inflection point in the vertical profile of the horizontal velocity at the canopy top. |
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[1080] | 93 | \begin{center} |
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| 94 | \includegraphics[width=0.5\textwidth]{canopy_model_figures/abb1.png} |
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| 95 | \end{center} |
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| 96 | } |
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| 97 | \end{itemize} |
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| 98 | \end{footnotesize} |
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| 99 | \end{frame} |
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| 100 | |
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| 101 | |
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| 102 | |
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| 103 | %Folie 03 |
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| 104 | \begin{frame} |
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| 105 | \frametitle{Theory (II)} |
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| 106 | \begin{footnotesize} |
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| 107 | \begin{itemize} |
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[1205] | 108 | \item<1->{The inflection point in the velocity profile introduces instabilities to the flow, leading to the formation of Kelvin-Helmholtz waves near the canopy top (\textcircled{{\tiny 1}}).} |
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| 109 | \item<2->{Wave breaking induces further instabilities, whereby a longitudinal component is added to the developing turbulence structures (\textcircled{{\tiny 2}} \& \textcircled{{\tiny 3}}).} |
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| 110 | \item<3->{Due to the persistent instabilities the turbulence structures develop a distinct three-dimensionality (\textcircled{{\tiny 4}}).} |
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[1080] | 111 | \item<4->{The large turbulence structures developing due to the inflection point instability significantly contribute to the vertical mixing of in-canopy and above-canopy air. |
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| 112 | \begin{center} |
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| 113 | \includegraphics[width=0.5\textwidth]{canopy_model_figures/abb2.png} |
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| 114 | \end{center} |
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| 115 | } |
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| 116 | \end{itemize} |
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| 117 | \end{footnotesize} |
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| 118 | \end{frame} |
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| 119 | |
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| 120 | |
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| 121 | |
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| 122 | %Folie 04 |
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| 123 | \begin{frame} |
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| 124 | \frametitle{Methods (I)} |
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| 125 | \begin{footnotesize} |
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| 126 | \begin{itemize} |
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| 127 | \item<1->{The canopy model in PALM is based on the models used by Shaw and Schumann (1992) and Watanabe (2004).} |
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| 128 | \item<2->{The aerodynamic effect of the canopy on the turbulent flow is accounted for by an additional term in the momentum equations:\\ |
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| 129 | \begin{align*} |
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| 130 | \frac{\partial \bar{u}_{i}}{\partial t} = \text{...} - c_{d} a U \bar{u}_{i} |
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| 131 | \end{align*} |
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| 132 | } |
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| 133 | \begin{itemize} |
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| 134 | \item<3->{ $c_{d}$ : drag coefficient} |
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| 135 | \item<4->{ $a $ : leaf area density $[m^{2}m^{-3}]$} |
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| 136 | \item<5->{ $U$ : $(u^{2} + v^{2} + w^{2})^{1/2}$ $[m s^{-1}]$} |
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| 137 | \item<6->{ $u_{i}$ : velocity component ($u_{1}=u$, $u_{2}=v$, $u_{3}=w$)} |
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| 138 | \end{itemize} |
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| 139 | \end{itemize} |
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| 140 | \uncover<7->{Note: The canopy model does not resolve the effect of single plant elements.} |
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| 141 | \end{footnotesize} |
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| 142 | \end{frame} |
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| 143 | |
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| 144 | |
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| 145 | |
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| 146 | %Folie 05 |
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| 147 | \begin{frame} |
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| 148 | \frametitle{Methods (II)} |
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| 149 | \begin{footnotesize} |
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| 150 | \begin{itemize} |
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| 151 | \item<1->{The effect of the canopy on the subgrid scale turbulence is accounted for by adding a sink term to the prognostic equation for the subgrid scale turbulent kinetic energy:\\ |
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| 152 | \begin{align*} |
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| 153 | \frac{\partial e}{\partial t} = \text{...} - 2 c_{d} a U e |
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| 154 | \end{align*} |
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| 155 | } |
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| 156 | \item<2->{It is assumed that the subgrid scale turbulent kinetic energy is dissipated by the canopy due to the rapid dissipation of wake turbulence in the lee of canopy elements (e.g. Watanabe, 2004).} |
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| 157 | \end{itemize} |
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| 158 | \end{footnotesize} |
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| 159 | \end{frame} |
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| 160 | |
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| 161 | |
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| 162 | |
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| 163 | %Folie 06 |
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| 164 | \begin{frame} |
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| 165 | \frametitle{Methods (III)} |
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| 166 | \begin{footnotesize} |
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| 167 | \begin{itemize} |
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| 168 | \item<1->{If desired, the effect of the canopy on the sensible heat transport can be considered. A source term is added to the prognostic equation for potential temperature:\\ |
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| 169 | \begin{align*} |
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| 170 | \frac{\partial \bar{\theta}}{\partial t} = \text{...} + S_{\theta} |
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| 171 | \end{align*} |
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| 172 | } |
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| 173 | \item<2->{It is assumed that the foliage is warmed by the penetrating solar radiation and, in turn, warms the surrounding air.} |
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[1205] | 174 | \item<3->{The source strength $S_{\theta}$ is defined as the vertical derivative of the upward kinematic vertical heat flux $Q_{\theta}$, given by (Shaw and Schumann, 1992):\\ |
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[1080] | 175 | \begin{align*} |
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| 176 | Q_{\theta}(z) = Q_{\theta}(h) exp(-\alpha F) \text{ , } Q_{\theta}(h) \text{ : Heat flux at canopy top} |
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| 177 | \end{align*} |
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| 178 | } |
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| 179 | \begin{itemize} |
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| 180 | \item<4->{ $\alpha = 0.6$ (extinction coefficient)} |
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| 181 | \item<5->{ $F = \int\limits_{z}^{h} a \: dz$ (downward cumulative leaf area index)} |
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| 182 | \end{itemize} |
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| 183 | \end{itemize} |
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| 184 | \end{footnotesize} |
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| 185 | \end{frame} |
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| 186 | |
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| 187 | |
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| 188 | |
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| 189 | %Folie 07 |
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| 190 | \begin{frame} |
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| 191 | \frametitle{Methods (IV)} |
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| 192 | \begin{footnotesize} |
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| 193 | \begin{itemize} |
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| 194 | \item<1->{The canopy might act as a sink or source for other scalars $q$ (e.g. humidity, passive tracer). Therefore, an additional term is added to the scalar transport equation:\\ |
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| 195 | \begin{align*} |
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| 196 | \frac{\partial \bar{q}}{\partial t} = \text{...} - c_{q} a U (\bar{q} - q_{c}) |
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| 197 | \end{align*} |
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| 198 | } |
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| 199 | \begin{itemize} |
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| 200 | \item<2->{ $c_{q}$ : scalar exchange coefficient} |
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| 201 | \item<3->{ $q_{c}$ : scalar concentration at leaf surface} |
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| 202 | \end{itemize} |
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| 203 | \end{itemize} |
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| 204 | \end{footnotesize} |
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| 205 | \end{frame} |
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| 206 | |
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| 207 | |
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| 208 | |
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| 209 | %Folie 08 |
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| 210 | \begin{frame} |
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| 211 | \frametitle{Basics (I)} |
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| 212 | \begin{itemize} |
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| 213 | \item<1->{The canopy model is switched on by setting the parameter {\small \texttt{plant\_canopy = .TRUE.}} within the \&inipar {\small \texttt{NAMELIST}} in the parameter file ({\small \texttt{PARIN}}).} |
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| 214 | \item<2->{All parameters for steering the canopy model are described in:\\ |
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| 215 | {\scriptsize Documentation $\rightarrow$ Model steering $\rightarrow$ Parameters $\rightarrow$ Initialization $\rightarrow$ Canopy}\\ |
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| 216 | (http://palm.muk.uni-hannover.de) |
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| 217 | } |
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[1205] | 218 | \item<3->{The following slides will describe how to set up a simulation with a simple horizontally homogeneous canopy block covering the entire model domain surface. In this case, {\small \texttt{canopy\_mode = 'block'}} must be set in \&inipar {\small \texttt{NAMELIST}}.} |
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[1080] | 219 | \end{itemize} |
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| 220 | \end{frame} |
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| 221 | |
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| 222 | |
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| 223 | |
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| 224 | %Folie 09 |
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| 225 | \begin{frame} |
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| 226 | \frametitle{Basic canopy parameter (I)} |
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| 227 | The parameters for steering the canopy model have to be added to the \&inipar {\small \texttt{NAMELIST}} in the parameter file ({\small \texttt{PARIN}}).\\ |
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| 228 | \begin{itemize} |
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| 229 | \item<1->{Step I: Define the upper boundary of the plant canopy layer using the parameter {\small \texttt{pch\_index (grid point index, default 0)}}. {\small \texttt{pch\_index}} specifies the number of grid points resolving the canopy layer in the vertical direction.} |
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| 230 | \end{itemize} |
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| 231 | \vspace{10pt} |
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| 232 | |
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| 233 | \tikzstyle{background} = [rectangle, fill=gray!10, text width=1\textwidth, text centered, rounded corners, minimum height=10em] |
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| 234 | \tikzstyle{Key1} = [rectangle, draw, fill=gray!70, text width=0.05, minimum size=0.05, font=\tiny] |
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| 235 | \tikzstyle{Key2} = [rectangle, draw, fill=green!90, text width=0.05, minimum size=0.05, font=\tiny] |
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| 236 | \tikzstyle{Key3} = [rectangle, text width=3.0cm, minimum size=16pt, font=\tiny] |
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| 237 | |
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| 238 | \begin{tikzpicture}[>=latex'] |
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| 239 | %%% Edit the following coordinate to change the shape of your |
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| 240 | %%% cuboid |
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| 241 | |
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| 242 | %% Vanishing points for perspective handling |
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| 243 | \coordinate (P1) at (-4cm,1.5cm); % left vanishing point (To pick) |
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| 244 | \coordinate (P2) at (10cm,1.5cm); % right vanishing point (To pick) |
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| 245 | |
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| 246 | %% (A1) and (A2) defines the 2 central points of the cuboid |
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| 247 | \coordinate (A1) at (0cm,0cm); % central top point (To pick) |
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| 248 | \coordinate (A2) at (0cm,-2cm); % central bottom point (To pick) |
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| 249 | |
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| 250 | %% (A3) to (A8) are computed given a unique parameter (or 2) .8 |
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| 251 | % You can vary .8 from 0 to 1 to change perspective on left side |
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| 252 | \coordinate (A3) at ($(P1)!.8!(A2)$); % To pick for perspective |
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| 253 | \coordinate (A4) at ($(P1)!.8!(A1)$); |
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| 254 | |
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| 255 | % You can vary .8 from 0 to 1 to change perspective on right side |
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| 256 | \coordinate (A7) at ($(P2)!.7!(A2)$); |
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| 257 | \coordinate (A8) at ($(P2)!.7!(A1)$); |
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| 258 | |
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| 259 | %% Automatically compute the last 2 points with intersections |
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| 260 | \coordinate (A5) at |
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| 261 | (intersection cs: first line={(A8) -- (P1)}, |
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| 262 | second line={(A4) -- (P2)}); |
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| 263 | \coordinate (A6) at |
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| 264 | (intersection cs: first line={(A7) -- (P1)}, |
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| 265 | second line={(A3) -- (P2)}); |
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| 266 | |
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| 267 | %% Drawing the canopy layer |
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| 268 | \coordinate (A9) at (0em,-1.7cm); % central bottom point (To pick) |
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| 269 | \coordinate (A10) at ($(P2)!.7!(A9)$); |
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| 270 | \coordinate (A12) at ($(P1)!.8!(A9)$); % To pick for perspective |
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| 271 | \coordinate (A11) at |
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| 272 | (intersection cs: first line={(A10) -- (P1)}, |
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| 273 | second line={(A12) -- (P2)}); |
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| 274 | |
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| 275 | %%% Depending of what you want to display, you can comment/edit |
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| 276 | %%% the following lines |
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| 277 | |
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| 278 | {\node [background, right=-0.8cm of A12] (background) {};} |
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| 279 | |
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| 280 | %% Possibly draw back faces |
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| 281 | |
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| 282 | \fill[gray!70] (A2) -- (A3) -- (A6) -- (A7) -- cycle; % face 6 |
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| 283 | \node at (barycentric cs:A2=1,A3=1,A6=1,A7=1) {\tiny }; |
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| 284 | |
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| 285 | \fill[gray!30] (A3) -- (A4) -- (A5) -- (A6) -- cycle; % face 3 |
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| 286 | \node at (barycentric cs:A3=1,A4=1,A5=1,A6=1) {\tiny }; |
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| 287 | |
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| 288 | \fill[gray!10] (A5) -- (A6) -- (A7) -- (A8) -- cycle; % face 4 |
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| 289 | \node at (barycentric cs:A5=1,A6=1,A7=1,A8=1) {\tiny }; |
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| 290 | |
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| 291 | |
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| 292 | \fill[green!90] (A9) -- (A10) -- (A11) -- (A12) -- cycle; % face 7 |
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| 293 | \node at (barycentric cs:A9=1,A10=1,A11=1,A12=1) {\tiny }; |
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| 294 | |
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| 295 | \fill[green!100] (A9) -- (A12) -- (A3) -- (A2) -- cycle; % face 8 |
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| 296 | \node at (barycentric cs:A9=1,A12=1,A3=1,A2=1) {\tiny }; |
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| 297 | |
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| 298 | \fill[green!100] (A9) -- (A10) -- (A7) -- (A2) -- cycle; % face 9 |
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| 299 | \node at (barycentric cs:A9=1,A10=1,A7=1,A2=1) {\tiny }; |
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| 300 | |
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| 301 | \draw[thin,dashed] (A5) -- (A6); |
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| 302 | \draw[thin,dashed] (A3) -- (A6); |
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| 303 | \draw[thin,dashed] (A7) -- (A6); |
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| 304 | |
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| 305 | \draw[thin,dashed] (A11) -- (A12); |
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| 306 | \draw[thin,dashed] (A10) -- (A11); |
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| 307 | |
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| 308 | %% Possibly draw front faces |
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| 309 | |
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| 310 | % \fill[orange] (A1) -- (A8) -- (A7) -- (A2) -- cycle; % face 1 |
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| 311 | % \node at (barycentric cs:A1=1,A8=1,A7=1,A2=1) {\tiny f1}; |
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| 312 | \fill[gray!50,opacity=0.2] (A1) -- (A2) -- (A3) -- (A4) -- cycle; % f2 |
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| 313 | \node at (barycentric cs:A1=1,A2=1,A3=1,A4=1) {\tiny }; |
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| 314 | \fill[gray!90,opacity=0.2] (A1) -- (A4) -- (A5) -- (A8) -- cycle; % f5 |
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| 315 | \node at (barycentric cs:A1=1,A4=1,A5=1,A8=1) {\tiny }; |
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| 316 | |
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| 317 | %% Possibly draw front lines |
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| 318 | \draw[thin] (A1) -- (A2); |
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| 319 | \draw[thin] (A3) -- (A4); |
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| 320 | \draw[thin] (A7) -- (A8); |
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| 321 | \draw[thin] (A1) -- (A4); |
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| 322 | \draw[thin] (A1) -- (A8); |
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| 323 | \draw[thin] (A2) -- (A3); |
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| 324 | \draw[thin] (A2) -- (A7); |
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| 325 | \draw[thin] (A4) -- (A5); |
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| 326 | \draw[thin] (A8) -- (A5); |
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| 327 | |
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| 328 | \draw[thin] (A9) -- (A10); |
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| 329 | \draw[thin] (A9) -- (A12); |
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| 330 | |
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| 331 | % Possibly draw points |
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| 332 | % (it can help you understand the cuboid structure) |
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| 333 | \foreach \i in {1,2,...,12} |
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| 334 | { |
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| 335 | % \draw[fill=black] (A\i) circle (0.05em) |
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| 336 | % node[above right] {\tiny \i}; |
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| 337 | } |
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| 338 | % \draw[fill=black] (P1) circle (0.1em) node[below] {\tiny p1}; |
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| 339 | % \draw[fill=black] (P2) circle (0.1em) node[below] {\tiny p2}; |
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| 340 | |
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| 341 | %Key |
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| 342 | \coordinate (K1) at (0.5cm,-2.3cm); |
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| 343 | \coordinate (K2) at (0.5cm,-2.7cm); |
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| 344 | |
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| 345 | |
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| 346 | \node [Key1, right=0.0cm of K1] (key1) {}; |
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| 347 | \node [Key2, right=0.0cm of K2] (key2) {}; |
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| 348 | \node [Key3, right=0.4cm of K1] (key11) {Total model domain}; |
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| 349 | \node [Key3, right=0.4cm of K2] (key21) {Plant canopy volume}; |
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| 350 | |
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| 351 | %% frame specific elements |
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| 352 | \node [Key3, right=0.45cm of A10] (label1) {\texttt{zw(pch\_index)} = canopy top}; |
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| 353 | \node [Key3, right=0.05cm of A10] (label0) {}; |
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| 354 | |
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| 355 | \draw[<-] (label0) -- (label1); |
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| 356 | \end{tikzpicture} |
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| 357 | |
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| 358 | |
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| 359 | \end{frame} |
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| 360 | |
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| 361 | |
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| 362 | |
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| 363 | %Folie 10 |
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| 364 | \begin{frame} |
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| 365 | \frametitle{Basic canopy parameter (II)} |
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| 366 | \begin{itemize} |
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| 367 | \item<1->{ Step II: Construct the vertical profile of the leaf area density (lad) to prescribe the distribution of leaf area within the plant canopy volume.\\ |
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| 368 | The canopy top is located between {\small \texttt{zu(pch\_index)}} and {\small \texttt{zu(pch\_index + 1)}} because this is the transition between the in-canopy grid point and the above-canopy grid point. |
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| 369 | } |
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| 370 | \end{itemize} |
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| 371 | \vspace{10pt} |
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| 372 | |
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| 373 | \tikzstyle{background} = [rectangle, fill=gray!10, text width=1\textwidth, text centered, rounded corners, minimum height=10em] |
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| 374 | \tikzstyle{Key1} = [rectangle, draw, fill=gray!70, text width=0.05, minimum size=0.05, font=\tiny] |
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| 375 | \tikzstyle{Key2} = [rectangle, draw, fill=green!90, text width=0.05, minimum size=0.05, font=\tiny] |
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| 376 | \tikzstyle{Key3} = [rectangle, text width=4.5cm, minimum size=16pt, font=\tiny] |
---|
| 377 | \tikzstyle{label} = [rectangle, text width=2.0cm, align=center, minimum size=16pt, font=\tiny] |
---|
| 378 | |
---|
| 379 | \begin{tikzpicture}[>=latex'] |
---|
| 380 | %%% Edit the following coordinate to change the shape of your |
---|
| 381 | %%% cuboid |
---|
| 382 | |
---|
| 383 | %% Vanishing points for perspective handling |
---|
| 384 | \coordinate (P1) at (-4cm,1.5cm); % left vanishing point (To pick) |
---|
| 385 | \coordinate (P2) at (10cm,1.5cm); % right vanishing point (To pick) |
---|
| 386 | |
---|
| 387 | %% (A1) and (A2) defines the 2 central points of the cuboid |
---|
| 388 | \coordinate (A1) at (0cm,0cm); % central top point (To pick) |
---|
| 389 | \coordinate (A2) at (0cm,-2cm); % central bottom point (To pick) |
---|
| 390 | |
---|
| 391 | %% (A3) to (A8) are computed given a unique parameter (or 2) .8 |
---|
| 392 | % You can vary .8 from 0 to 1 to change perspective on left side |
---|
| 393 | \coordinate (A3) at ($(P1)!.8!(A2)$); % To pick for perspective |
---|
| 394 | \coordinate (A4) at ($(P1)!.8!(A1)$); |
---|
| 395 | |
---|
| 396 | % You can vary .8 from 0 to 1 to change perspective on right side |
---|
| 397 | \coordinate (A7) at ($(P2)!.7!(A2)$); |
---|
| 398 | \coordinate (A8) at ($(P2)!.7!(A1)$); |
---|
| 399 | |
---|
| 400 | %% Automatically compute the last 2 points with intersections |
---|
| 401 | \coordinate (A5) at |
---|
| 402 | (intersection cs: first line={(A8) -- (P1)}, |
---|
| 403 | second line={(A4) -- (P2)}); |
---|
| 404 | \coordinate (A6) at |
---|
| 405 | (intersection cs: first line={(A7) -- (P1)}, |
---|
| 406 | second line={(A3) -- (P2)}); |
---|
| 407 | |
---|
| 408 | %% Drawing the canopy layer |
---|
| 409 | \coordinate (A9) at (0em,-1.7cm); % central bottom point (To pick) |
---|
| 410 | \coordinate (A10) at ($(P2)!.7!(A9)$); |
---|
| 411 | \coordinate (A12) at ($(P1)!.8!(A9)$); % To pick for perspective |
---|
| 412 | \coordinate (A11) at |
---|
| 413 | (intersection cs: first line={(A10) -- (P1)}, |
---|
| 414 | second line={(A12) -- (P2)}); |
---|
| 415 | |
---|
| 416 | %%% Depending of what you want to display, you can comment/edit |
---|
| 417 | %%% the following lines |
---|
| 418 | |
---|
| 419 | {\node [background, right=-0.8cm of A12] (background) {};} |
---|
| 420 | |
---|
| 421 | %% Possibly draw back faces |
---|
| 422 | |
---|
| 423 | \fill[gray!70] (A2) -- (A3) -- (A6) -- (A7) -- cycle; % face 6 |
---|
| 424 | \node at (barycentric cs:A2=1,A3=1,A6=1,A7=1) {\tiny }; |
---|
| 425 | |
---|
| 426 | \fill[gray!30] (A3) -- (A4) -- (A5) -- (A6) -- cycle; % face 3 |
---|
| 427 | \node at (barycentric cs:A3=1,A4=1,A5=1,A6=1) {\tiny }; |
---|
| 428 | |
---|
| 429 | \fill[gray!10] (A5) -- (A6) -- (A7) -- (A8) -- cycle; % face 4 |
---|
| 430 | \node at (barycentric cs:A5=1,A6=1,A7=1,A8=1) {\tiny }; |
---|
| 431 | |
---|
| 432 | |
---|
| 433 | \fill[green!90] (A9) -- (A10) -- (A11) -- (A12) -- cycle; % face 7 |
---|
| 434 | \node at (barycentric cs:A9=1,A10=1,A11=1,A12=1) {\tiny }; |
---|
| 435 | |
---|
| 436 | \fill[green!100] (A9) -- (A12) -- (A3) -- (A2) -- cycle; % face 8 |
---|
| 437 | \node at (barycentric cs:A9=1,A12=1,A3=1,A2=1) {\tiny }; |
---|
| 438 | |
---|
| 439 | \fill[green!100] (A9) -- (A10) -- (A7) -- (A2) -- cycle; % face 9 |
---|
| 440 | \node at (barycentric cs:A9=1,A10=1,A7=1,A2=1) {\tiny }; |
---|
| 441 | |
---|
| 442 | \draw[thin,dashed] (A5) -- (A6); |
---|
| 443 | \draw[thin,dashed] (A3) -- (A6); |
---|
| 444 | \draw[thin,dashed] (A7) -- (A6); |
---|
| 445 | |
---|
| 446 | \draw[thin,dashed] (A11) -- (A12); |
---|
| 447 | \draw[thin,dashed] (A10) -- (A11); |
---|
| 448 | |
---|
| 449 | %% Possibly draw front faces |
---|
| 450 | |
---|
| 451 | % \fill[orange] (A1) -- (A8) -- (A7) -- (A2) -- cycle; % face 1 |
---|
| 452 | % \node at (barycentric cs:A1=1,A8=1,A7=1,A2=1) {\tiny f1}; |
---|
| 453 | \fill[gray!50,opacity=0.2] (A1) -- (A2) -- (A3) -- (A4) -- cycle; % f2 |
---|
| 454 | \node at (barycentric cs:A1=1,A2=1,A3=1,A4=1) {\tiny }; |
---|
| 455 | \fill[gray!90,opacity=0.2] (A1) -- (A4) -- (A5) -- (A8) -- cycle; % f5 |
---|
| 456 | \node at (barycentric cs:A1=1,A4=1,A5=1,A8=1) {\tiny }; |
---|
| 457 | |
---|
| 458 | %% Possibly draw front lines |
---|
| 459 | \draw[thin] (A1) -- (A2); |
---|
| 460 | \draw[thin] (A3) -- (A4); |
---|
| 461 | \draw[thin] (A7) -- (A8); |
---|
| 462 | \draw[thin] (A1) -- (A4); |
---|
| 463 | \draw[thin] (A1) -- (A8); |
---|
| 464 | \draw[thin] (A2) -- (A3); |
---|
| 465 | \draw[thin] (A2) -- (A7); |
---|
| 466 | \draw[thin] (A4) -- (A5); |
---|
| 467 | \draw[thin] (A8) -- (A5); |
---|
| 468 | |
---|
| 469 | \draw[thin] (A9) -- (A10); |
---|
| 470 | \draw[thin] (A9) -- (A12); |
---|
| 471 | |
---|
| 472 | % Possibly draw points |
---|
| 473 | % (it can help you understand the cuboid structure) |
---|
| 474 | \foreach \i in {1,2,...,12} |
---|
| 475 | { |
---|
| 476 | % \draw[fill=black] (A\i) circle (0.05em) |
---|
| 477 | % node[above right] {\tiny \i}; |
---|
| 478 | } |
---|
| 479 | % \draw[fill=black] (P1) circle (0.1em) node[below] {\tiny p1}; |
---|
| 480 | % \draw[fill=black] (P2) circle (0.1em) node[below] {\tiny p2}; |
---|
| 481 | |
---|
| 482 | %Key |
---|
| 483 | \coordinate (K1) at (0.5cm,-2.3cm); |
---|
| 484 | \coordinate (K2) at (0.5cm,-2.7cm); |
---|
| 485 | |
---|
| 486 | |
---|
| 487 | \node [Key1, right=0.0cm of K1] (key1) {}; |
---|
| 488 | \node [Key2, right=0.0cm of K2] (key2) {}; |
---|
| 489 | \node [Key3, right=0.4cm of K1] (key11) {Total model domain}; |
---|
| 490 | \node [Key3, right=0.4cm of K2] (key21) {Plant canopy volume}; |
---|
| 491 | |
---|
| 492 | %% frame specific elements |
---|
| 493 | |
---|
| 494 | %% boundary layer profile 2D |
---|
| 495 | \coordinate (B1) at (4.0cm,0.3cm); |
---|
| 496 | \coordinate (B2) at (4.0cm,-2.5cm); |
---|
| 497 | |
---|
| 498 | \coordinate (B3) at (4.0cm,0.6cm); |
---|
| 499 | \coordinate (B4) at (6.6cm,-2.5cm); |
---|
| 500 | |
---|
| 501 | \draw[thin, dotted] (A10) -- (B1); |
---|
| 502 | \draw[thin, dotted] (A7) -- (B2); |
---|
| 503 | \draw[<-] (B3) -- (B2); |
---|
| 504 | \draw[<-] (B4) -- (B2); |
---|
| 505 | |
---|
| 506 | \coordinate (xlab) at (5.3cm,-2.5cm); |
---|
| 507 | \coordinate (ylab) at (4.0cm,-1.1cm); |
---|
| 508 | \node [label, below=0.0cm of xlab] (xlabel) {lad $[m^{2}m^{-3}]$}; |
---|
| 509 | \node [label, rotate=90, above=0.0cm of ylab] (ylabel) {z$[m]$}; |
---|
| 510 | |
---|
| 511 | |
---|
| 512 | \coordinate (B5) at (4.5cm,-2.5cm); |
---|
| 513 | % \draw [-,color=red] (B1) to [out=-10,in=90,looseness=2.0, relative=false] .. controls (4,0) and (5,0) .. (B5); |
---|
| 514 | \draw {(B1) .. controls (8.0,-0.2) and (4.5,-1.0) .. (B5)}; |
---|
| 515 | |
---|
| 516 | \draw [decorate, decoration={markings, |
---|
| 517 | mark=at position 00mm with{\draw[fill=black] (0,0) circle (0.1em);}, |
---|
| 518 | mark=at position 04mm with{\draw[fill=black] (0,0) circle (0.1em);}, |
---|
| 519 | mark=at position 08mm with{\draw[fill=black] (0,0) circle (0.1em);}, |
---|
| 520 | mark=at position 12mm with{\draw[fill=black] (0,0) circle (0.1em);}, |
---|
| 521 | mark=at position 16mm with{\draw[fill=black] (0,0) circle (0.1em);}, |
---|
| 522 | mark=at position 20mm with{\draw[fill=black] (0,0) circle (0.1em);}, |
---|
| 523 | mark=at position 24mm with{\draw[fill=black] (0,0) circle (0.1em);}, |
---|
| 524 | mark=at position 28mm with{\draw[fill=black] (0,0) circle (0.1em);}, |
---|
| 525 | mark=at position 32mm with{\draw[fill=black] (0,0) circle (0.1em);}, |
---|
| 526 | mark=at position 36mm with{\draw[fill=black] (0,0) circle (0.1em);}, |
---|
| 527 | mark=at position 40mm with{\draw[fill=black] (0,0) circle (0.1em);}, |
---|
| 528 | mark=at position 44mm with{\draw[fill=black] (0,0) circle (0.1em);}, |
---|
| 529 | }] |
---|
| 530 | {(B5) .. controls (4.5,-1.0) and (8.0,-0.2) .. (B1)}; |
---|
| 531 | |
---|
| 532 | \node [Key3, right=1.1cm of B1] (label1) {\texttt{zu(pch\_index + 1)}: lad = 0.0 (default)}; |
---|
| 533 | \node [Key3, left=0.1cm of B1] (label0) {}; |
---|
| 534 | \draw[-, dashed] (label0) -- (label1); |
---|
| 535 | |
---|
| 536 | \coordinate (curvelabel00) at (4.65cm,-2.45cm); |
---|
| 537 | \coordinate (curvelabel01) at (5.0cm,-2.25cm); |
---|
| 538 | \draw[<-] (curvelabel00) -- (curvelabel01); |
---|
| 539 | \node [Key3, right=0.0cm of curvelabel01] (curvelabel02) {\texttt{lad\_surface} (default 0.0)}; |
---|
| 540 | |
---|
| 541 | \coordinate (curvelabel10) at (5.4cm,-1.3cm); |
---|
| 542 | \coordinate (curvelabel11) at (5.6cm,-1.6cm); |
---|
| 543 | \draw[<-] (curvelabel10) -- (curvelabel11); |
---|
| 544 | \node [Key3, right=0.0cm of curvelabel11] (curvelabel12) {\texttt{lad\_vertical\_gradient\_level} (5)}; |
---|
| 545 | |
---|
| 546 | \coordinate (curvelabel10) at (5.47cm,-1.05cm); |
---|
| 547 | \coordinate (curvelabel11) at (5.8cm,-1.3cm); |
---|
| 548 | \draw[<-] (curvelabel10) -- (curvelabel11); |
---|
| 549 | \node [Key3, right=0.0cm of curvelabel11] (curvelabel12) {\texttt{lad\_vertical\_gradient} (5)}; |
---|
| 550 | |
---|
| 551 | \coordinate (curvelabel10) at (5.7cm,-0.93cm); |
---|
| 552 | \coordinate (curvelabel11) at (5.9cm,-1.0cm); |
---|
| 553 | \draw[<-] (curvelabel10) -- (curvelabel11); |
---|
| 554 | \node [Key3, right=0.0cm of curvelabel11] (curvelabel12) {\texttt{lad\_vertical\_gradient\_level} (6)}; |
---|
| 555 | \end{tikzpicture} |
---|
| 556 | |
---|
| 557 | |
---|
| 558 | \end{frame} |
---|
| 559 | |
---|
| 560 | |
---|
| 561 | |
---|
| 562 | %Folie 11 |
---|
| 563 | \begin{frame} |
---|
| 564 | \frametitle{Basic canopy parameter (III)} |
---|
| 565 | \begin{footnotesize} |
---|
| 566 | \begin{itemize} |
---|
| 567 | \item<1->{Step III: Prescribe a value for the parameter {\small \texttt{drag\_coefficient (default 0.0)}}. The drag coefficient is a dimensionless factor describing the magnitude of the form drag by the canopy working against the flow. A larger form drag results in a greater momentum reduction.} |
---|
| 568 | \end{itemize} |
---|
| 569 | |
---|
| 570 | |
---|
| 571 | \begin{minipage}{0.47\textwidth} |
---|
| 572 | \begin{center} |
---|
| 573 | \includegraphics[width=1\textwidth]{canopy_model_figures/large.png}\\ |
---|
| 574 | \end{center} |
---|
| 575 | \end{minipage} |
---|
| 576 | \hfill |
---|
| 577 | \begin{minipage}{0.47\textwidth} |
---|
| 578 | \begin{center} |
---|
| 579 | \includegraphics[width=1\textwidth]{canopy_model_figures/small.png}\\ |
---|
| 580 | \end{center} |
---|
| 581 | \end{minipage} |
---|
| 582 | |
---|
| 583 | \begin{minipage}{0.47\textwidth} |
---|
| 584 | \begin{center} |
---|
| 585 | Strong trees offer a larger form drag to the flow. |
---|
| 586 | \end{center} |
---|
| 587 | \end{minipage} |
---|
| 588 | \hfill |
---|
| 589 | \begin{minipage}{0.47\textwidth} |
---|
| 590 | \begin{center} |
---|
| 591 | Young / small trees offer a smaller form drag to the flow because they are more flexible. |
---|
| 592 | \end{center} |
---|
| 593 | \end{minipage} |
---|
| 594 | |
---|
| 595 | \end{footnotesize} |
---|
| 596 | |
---|
| 597 | \end{frame} |
---|
| 598 | |
---|
| 599 | |
---|
| 600 | |
---|
| 601 | %Folie 12 |
---|
| 602 | \begin{frame} |
---|
| 603 | \frametitle{Basic canopy parameter (IV)} |
---|
| 604 | \begin{itemize} |
---|
| 605 | \item<1->{For steering the effect of the canopy sensible heat transfer, prescribe a value for the sensible heat flux at the canopy top, using the parameter \texttt{cthf} (see Methods (III)).} |
---|
| 606 | \item<2->{The sink/source effect of the canopy on other scalar quantities, such as humidity or a passive tracer can be steered by the parameters \texttt{leaf\_surface\_concentration} and \texttt{scalar\_exchange\_coefficient} (see Methods (IV)).} |
---|
| 607 | \end{itemize} |
---|
| 608 | \end{frame} |
---|
| 609 | |
---|
| 610 | |
---|
| 611 | |
---|
| 612 | %Folie 13 |
---|
| 613 | \begin{frame} |
---|
| 614 | \frametitle{User-defined canopy} |
---|
| 615 | \begin{footnotesize} |
---|
| 616 | Do you want to simulate a more customized canopy, which e.g. covers only half the model surface?\\ |
---|
| 617 | \begin{itemize} |
---|
[1205] | 618 | \item<2->{Step I: Copy the file \texttt{user\_init\_plant\_canopy.f90} from {\small \texttt{trunk/SOURCE}} to the directory {\small \texttt{\$Home/palm/current\_version/USER\_CODE/<enter job name>}} and make the desired changes for {\small \texttt{CASE ('user\_defined\_canopy\_1')}}.} |
---|
[1080] | 619 | \item<3->{Step II: In your parameter file set: {\scriptsize \texttt{canopy\_mode = 'user\_defined\_canopy\_1'}}} |
---|
| 620 | \end{itemize} |
---|
| 621 | \end{footnotesize} |
---|
| 622 | \vspace{7pt} |
---|
[1205] | 623 | |
---|
[1080] | 624 | \tikzstyle{background} = [rectangle, fill=gray!10, text width=1\textwidth, text centered, rounded corners, minimum height=10em] |
---|
| 625 | \tikzstyle{Key1} = [rectangle, draw, fill=gray!70, text width=0.05, minimum size=0.05, font=\tiny] |
---|
| 626 | \tikzstyle{Key2} = [rectangle, draw, fill=green!90, text width=0.05, minimum size=0.05, font=\tiny] |
---|
| 627 | \tikzstyle{Key3} = [rectangle, text width=2.0cm, minimum size=4pt, font=\tiny] |
---|
| 628 | \tikzstyle{text1} = [rectangle, text width=0.4\textwidth, minimum height=10em] |
---|
| 629 | \begin{tikzpicture}[>=latex'] |
---|
| 630 | %%% Edit the following coordinate to change the shape of your |
---|
| 631 | %%% cuboid |
---|
| 632 | |
---|
| 633 | %% Vanishing points for perspective handling |
---|
| 634 | \coordinate (P1) at (-4cm,1.5cm); % left vanishing point (To pick) |
---|
| 635 | \coordinate (P2) at (10cm,1.5cm); % right vanishing point (To pick) |
---|
| 636 | |
---|
| 637 | %% (A1) and (A2) defines the 2 central points of the cuboid |
---|
| 638 | \coordinate (A1) at (0cm,0cm); % central top point (To pick) |
---|
| 639 | \coordinate (A2) at (0cm,-2cm); % central bottom point (To pick) |
---|
| 640 | |
---|
| 641 | %% (A3) to (A8) are computed given a unique parameter (or 2) .8 |
---|
| 642 | % You can vary .8 from 0 to 1 to change perspective on left side |
---|
| 643 | \coordinate (A3) at ($(P1)!.8!(A2)$); % To pick for perspective |
---|
| 644 | \coordinate (A4) at ($(P1)!.8!(A1)$); |
---|
| 645 | |
---|
| 646 | % You can vary .8 from 0 to 1 to change perspective on right side |
---|
| 647 | \coordinate (A7) at ($(P2)!.7!(A2)$); |
---|
| 648 | \coordinate (A8) at ($(P2)!.7!(A1)$); |
---|
| 649 | |
---|
| 650 | %% Automatically compute the last 2 points with intersections |
---|
| 651 | \coordinate (A5) at |
---|
| 652 | (intersection cs: first line={(A8) -- (P1)}, |
---|
| 653 | second line={(A4) -- (P2)}); |
---|
| 654 | \coordinate (A6) at |
---|
| 655 | (intersection cs: first line={(A7) -- (P1)}, |
---|
| 656 | second line={(A3) -- (P2)}); |
---|
| 657 | |
---|
| 658 | %% Drawing the canopy layer |
---|
| 659 | \coordinate (A9) at (0em,-1.7cm); % central bottom point (To pick) |
---|
| 660 | \coordinate (A10) at ($(P2)!.7!(A9)$); |
---|
| 661 | \coordinate (A12) at ($(P1)!.8!(A9)$); % To pick for perspective |
---|
| 662 | \coordinate (A11) at |
---|
| 663 | (intersection cs: first line={(A10) -- (P1)}, |
---|
| 664 | second line={(A12) -- (P2)}); |
---|
| 665 | |
---|
| 666 | \coordinate (A13) at ($(A9)!.54!(A10)$); |
---|
| 667 | \coordinate (A14) at ($(A2)!.54!(A7)$); |
---|
| 668 | |
---|
| 669 | \coordinate (A15) at |
---|
| 670 | (intersection cs: first line={(A13) -- (P1)}, |
---|
| 671 | second line={(A12) -- (P2)}); |
---|
| 672 | \coordinate (A16) at |
---|
| 673 | (intersection cs: first line={(A14) -- (P1)}, |
---|
| 674 | second line={(A3) -- (P2)}); |
---|
| 675 | %%% Depending of what you want to display, you can comment/edit |
---|
| 676 | %%% the following lines |
---|
| 677 | |
---|
| 678 | {\node [background, right=-0.8cm of A12] (background) {};} |
---|
| 679 | |
---|
| 680 | %% Possibly draw back faces |
---|
| 681 | |
---|
| 682 | \fill[gray!70] (A2) -- (A3) -- (A6) -- (A7) -- cycle; % face 6 |
---|
| 683 | \node at (barycentric cs:A2=1,A3=1,A6=1,A7=1) {\tiny }; |
---|
| 684 | |
---|
| 685 | \fill[gray!30] (A3) -- (A4) -- (A5) -- (A6) -- cycle; % face 3 |
---|
| 686 | \node at (barycentric cs:A3=1,A4=1,A5=1,A6=1) {\tiny }; |
---|
| 687 | |
---|
| 688 | \fill[gray!10] (A5) -- (A6) -- (A7) -- (A8) -- cycle; % face 4 |
---|
| 689 | \node at (barycentric cs:A5=1,A6=1,A7=1,A8=1) {\tiny }; |
---|
| 690 | |
---|
| 691 | |
---|
| 692 | \fill[green!90] (A13) -- (A10) -- (A11) -- (A15) -- cycle; % face 4 |
---|
| 693 | \node at (barycentric cs:A9=1,A10=1,A11=1,A12=1) {\tiny }; |
---|
| 694 | |
---|
| 695 | \fill[green!100] (A13) -- (A15) -- (A16) -- (A14) -- cycle; % face 4 |
---|
| 696 | \node at (barycentric cs:A9=1,A12=1,A3=1,A2=1) {\tiny }; |
---|
| 697 | |
---|
| 698 | \fill[green!100] (A13) -- (A10) -- (A7) -- (A14) -- cycle; % face 4 |
---|
| 699 | \node at (barycentric cs:A9=1,A10=1,A7=1,A2=1) {\tiny }; |
---|
| 700 | |
---|
| 701 | \draw[thin,dashed] (A5) -- (A6); |
---|
| 702 | \draw[thin,dashed] (A3) -- (A6); |
---|
| 703 | \draw[thin,dashed] (A7) -- (A6); |
---|
| 704 | |
---|
| 705 | \draw[thin,dashed] (A11) -- (A15); |
---|
| 706 | \draw[thin,dashed] (A10) -- (A11); |
---|
| 707 | |
---|
| 708 | %% Possibly draw front faces |
---|
| 709 | |
---|
| 710 | % \fill[orange] (A1) -- (A8) -- (A7) -- (A2) -- cycle; % face 1 |
---|
| 711 | % \node at (barycentric cs:A1=1,A8=1,A7=1,A2=1) {\tiny f1}; |
---|
| 712 | \fill[gray!50,opacity=0.2] (A1) -- (A2) -- (A3) -- (A4) -- cycle; % f2 |
---|
| 713 | \node at (barycentric cs:A1=1,A2=1,A3=1,A4=1) {\tiny }; |
---|
| 714 | \fill[gray!90,opacity=0.2] (A1) -- (A4) -- (A5) -- (A8) -- cycle; % f5 |
---|
| 715 | \node at (barycentric cs:A1=1,A4=1,A5=1,A8=1) {\tiny }; |
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| 716 | |
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| 717 | %% Possibly draw front lines |
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| 718 | \draw[thin] (A1) -- (A2); |
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| 719 | \draw[thin] (A3) -- (A4); |
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| 720 | \draw[thin] (A7) -- (A8); |
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| 721 | \draw[thin] (A1) -- (A4); |
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| 722 | \draw[thin] (A1) -- (A8); |
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| 723 | \draw[thin] (A2) -- (A3); |
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| 724 | \draw[thin] (A2) -- (A7); |
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| 725 | \draw[thin] (A4) -- (A5); |
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| 726 | \draw[thin] (A8) -- (A5); |
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| 727 | |
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| 728 | \draw[thin] (A13) -- (A10); |
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| 729 | \draw[thin] (A13) -- (A15); |
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| 730 | \draw[thin] (A14) -- (A16); |
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| 731 | \draw[thin] (A13) -- (A14); |
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| 732 | \draw[thin] (A15) -- (A16); |
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| 733 | |
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| 734 | % Possibly draw points |
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| 735 | % (it can help you understand the cuboid structure) |
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| 736 | \foreach \i in {1,2,...,16} |
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| 737 | { |
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| 738 | % \draw[fill=black] (A\i) circle (0.05em) |
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| 739 | % node[above right] {\tiny \i}; |
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| 740 | } |
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| 741 | % \draw[fill=black] (P1) circle (0.1em) node[below] {\tiny p1}; |
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| 742 | % \draw[fill=black] (P2) circle (0.1em) node[below] {\tiny p2}; |
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| 743 | |
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| 744 | %Key |
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| 745 | \coordinate (K1) at (0.5cm,-2.3cm); |
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| 746 | \coordinate (K2) at (0.5cm,-2.7cm); |
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| 747 | |
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| 748 | |
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| 749 | \node [Key1, right=0.0cm of K1] (key1) {}; |
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| 750 | \node [Key2, right=0.0cm of K2] (key2) {}; |
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| 751 | \node [Key3, right=0.4cm of K1] (key11) {Total model domain}; |
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| 752 | \node [Key3, right=0.4cm of K2] (key21) {Plant canopy volume}; |
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| 753 | |
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| 754 | % % Text |
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| 755 | \uncover<4->{\node [text1, right=0.7cm of A7] (text1) {{\footnotesize Note: You might have to make changes in other parts of your {\small \texttt{USER\_CODE}} according to the changes / used parameters in: \texttt{user\_init\_plant\_canopy.f90}}};} |
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| 756 | \end{tikzpicture} |
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| 757 | |
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| 758 | |
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| 759 | \end{frame} |
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| 760 | |
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| 761 | \end{document} |
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