source: palm/trunk/TUTORIAL/SOURCE/canopy_model.tex @ 1205

Last change on this file since 1205 was 1205, checked in by kanani, 8 years ago

added additional hint for palm installation at hlrn and removed some typos

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1%$Id: canopy_model.tex 1205 2013-07-15 10:55:47Z kanani $
2\input{header_tmp.tex}
3%\input{../header_lectures.tex}
4
5%\documentclass{beamer}
6\usepackage[utf8]{inputenc}
7\usepackage{ngerman}
8\usepackage{pgf}
9\usetheme{Dresden}
10\usepackage{subfigure}
11\usepackage{units}
12\usepackage{amsmath}
13\usepackage{multimedia}
14\newcommand{\event}[1]{\newcommand{\eventname}{#1}}
15\usepackage{xmpmulti}
16\usepackage{tikz}
17\usepackage{pdfcomment}
18\usetikzlibrary{shapes,arrows,positioning,calc,decorations.pathmorphing,decorations.pathreplacing,decorations.markings}
19\def\Tiny{\fontsize{4pt}{4pt}\selectfont}
20\usepackage{listings}
21\lstset{language=[90]Fortran,
22  basicstyle=\ttfamily \tiny,
23  keywordstyle=\color{black},
24  commentstyle=\color{black},
25  morecomment=[l]{!\ }% Comment only with space after !
26}
27
28
29\institute{Institut fÌr Meteorologie und Klimatologie, Leibniz UniversitÀt Hannover}
30\date{last update: \today}
31\event{PALM Seminar}
32\setbeamertemplate{navigation symbols}{}
33
34\setbeamertemplate{footline}
35  {%
36    \begin{beamercolorbox}[rightskip=-0.1cm]&
37     {\includegraphics[height=0.65cm]{imuk_logo.pdf}\hfill \includegraphics[height=0.65cm]{luh_logo.pdf}}
38    \end{beamercolorbox}
39    \begin{beamercolorbox}[ht=2.5ex,dp=1.125ex,%
40      leftskip=.3cm,rightskip=0.3cm plus1fil]{title in head/foot}%
41      {\leavevmode{\usebeamerfont{author in head/foot}\insertshortauthor} \hfill \eventname \hfill \insertframenumber \; / \inserttotalframenumber}%
42    \end{beamercolorbox}%
43%    \begin{beamercolorbox}[colsep=1.5pt]{lower separation line foot}%
44%    \end{beamercolorbox}
45  }
46%\logo{\includegraphics[width=0.3\textwidth]{luhimuk_logo.png}}
47
48\title[PALM's Canopy Model]{PALM's Canopy Model}
49\author{Siegfried Raasch}
50
51
52% Notes:
53% jede subsection bekommt einen punkt im menu (vertikal ausgerichtet.
54% jeder frame in einer subsection bekommt einen punkt (horizontal ausgerichtet)
55\begin{document}
56
57\begin{frame}
58\titlepage
59\end{frame}
60
61\section{PALM's Canopy Model}
62\subsection{The embedded Canopy Model}
63
64%Folie 01
65\begin{frame}
66   \frametitle{Overview}
67   \begin{itemize}
68      \item<1->{The canopy model embedded in PALM can be used to study the effect of a plant canopy on e.g.:}
69      \begin{itemize}
70         \item<2->{mean flow field,}
71         \item<3->{development of coherent turbulence structures,}
72         \item<4->{scalar exchange processes between canopy and atmosphere.}
73      \end{itemize}
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.}
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:}
76      \begin{itemize}
77         \item<7->{leaf area density,}
78         \item<8->{drag coefficient.}
79      \end{itemize}
80   \end{itemize}
81\end{frame}
82
83
84
85%Folie 02
86\begin{frame}
87   \frametitle{Theory (I)}
88   \begin{footnotesize}
89   \begin{itemize}
90      \item<1->{A plant canopy affects the flow by acting as a momentum sink due to form and viscous drag forces.}
91      \item<2->{The effectiveness of momentum absorption depends on the amount of leaf area per unit volume and the aerodynamic drag.}
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.
93         \begin{center}
94            \includegraphics[width=0.5\textwidth]{canopy_model_figures/abb1.png}
95         \end{center}
96      }
97   \end{itemize}
98   \end{footnotesize}
99\end{frame}
100
101
102
103%Folie 03
104\begin{frame}
105   \frametitle{Theory (II)}
106   \begin{footnotesize}
107   \begin{itemize}
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}}).}
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}}).}
110      \item<3->{Due to the persistent instabilities the turbulence structures develop a distinct three-dimensionality (\textcircled{{\tiny 4}}).}
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.
112         \begin{center}
113            \includegraphics[width=0.5\textwidth]{canopy_model_figures/abb2.png}
114         \end{center}
115      }
116   \end{itemize}
117   \end{footnotesize}
118\end{frame}
119
120
121
122%Folie 04
123\begin{frame}
124   \frametitle{Methods (I)}
125   \begin{footnotesize}
126   \begin{itemize}
127      \item<1->{The canopy model in PALM is based on the models used by Shaw and Schumann (1992) and Watanabe (2004).}
128      \item<2->{The aerodynamic effect of the canopy on the turbulent flow is accounted for by an additional term in the momentum equations:\\
129         \begin{align*}
130            \frac{\partial \bar{u}_{i}}{\partial t} = \text{...} - c_{d} a U \bar{u}_{i}
131         \end{align*}
132      }
133      \begin{itemize}
134         \item<3->{ $c_{d}$ : drag coefficient}
135         \item<4->{ $a $ : leaf area density $[m^{2}m^{-3}]$}
136         \item<5->{ $U$ : $(u^{2} + v^{2} + w^{2})^{1/2}$ $[m s^{-1}]$}
137         \item<6->{ $u_{i}$ : velocity component ($u_{1}=u$, $u_{2}=v$, $u_{3}=w$)}
138      \end{itemize}
139   \end{itemize}
140   \uncover<7->{Note: The canopy model does not resolve the effect of single plant elements.}
141   \end{footnotesize}
142\end{frame}
143
144
145
146%Folie 05
147\begin{frame}
148   \frametitle{Methods (II)}
149   \begin{footnotesize}
150   \begin{itemize}
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:\\
152         \begin{align*}
153            \frac{\partial e}{\partial t} = \text{...} - 2 c_{d} a U e
154         \end{align*}
155      }
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).}
157   \end{itemize}
158   \end{footnotesize}
159\end{frame}
160
161
162
163%Folie 06
164\begin{frame}
165   \frametitle{Methods (III)}
166   \begin{footnotesize}
167   \begin{itemize}
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:\\
169         \begin{align*}
170            \frac{\partial \bar{\theta}}{\partial t} = \text{...} +  S_{\theta}
171         \end{align*}
172      }
173      \item<2->{It is assumed that the foliage is warmed by the penetrating solar radiation and, in turn, warms the surrounding air.}
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):\\
175         \begin{align*}
176            Q_{\theta}(z) = Q_{\theta}(h) exp(-\alpha F) \text{ , } Q_{\theta}(h) \text{ : Heat flux at canopy top}
177         \end{align*}
178      }
179      \begin{itemize}
180         \item<4->{ $\alpha = 0.6$ (extinction coefficient)}
181         \item<5->{ $F = \int\limits_{z}^{h} a \: dz$ (downward cumulative leaf area index)}
182      \end{itemize}
183   \end{itemize}
184   \end{footnotesize}
185\end{frame}
186
187
188
189%Folie 07
190\begin{frame}
191   \frametitle{Methods (IV)}
192   \begin{footnotesize}
193   \begin{itemize}
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:\\
195         \begin{align*}
196            \frac{\partial \bar{q}}{\partial t} = \text{...} - c_{q} a U (\bar{q} - q_{c})
197         \end{align*}
198      }
199      \begin{itemize}
200         \item<2->{ $c_{q}$ : scalar exchange coefficient}
201         \item<3->{ $q_{c}$ : scalar concentration at leaf surface}
202      \end{itemize}
203   \end{itemize}
204   \end{footnotesize}
205\end{frame}
206
207
208
209%Folie 08
210\begin{frame}
211   \frametitle{Basics (I)}
212   \begin{itemize}
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}}).}
214      \item<2->{All parameters for steering the canopy model are described in:\\
215      {\scriptsize Documentation $\rightarrow$ Model steering $\rightarrow$ Parameters $\rightarrow$ Initialization $\rightarrow$ Canopy}\\
216      (http://palm.muk.uni-hannover.de)
217      }
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}}.}
219   \end{itemize}
220\end{frame}
221
222
223
224%Folie 09
225\begin{frame}
226   \frametitle{Basic canopy parameter (I)}
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}}).\\
228    \begin{itemize}
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.}
230    \end{itemize}
231   \vspace{10pt}
232
233   \tikzstyle{background} = [rectangle, fill=gray!10, text width=1\textwidth, text centered, rounded corners, minimum height=10em]
234   \tikzstyle{Key1} = [rectangle, draw, fill=gray!70, text width=0.05, minimum size=0.05, font=\tiny]
235   \tikzstyle{Key2} = [rectangle, draw, fill=green!90, text width=0.05, minimum size=0.05, font=\tiny]
236   \tikzstyle{Key3} = [rectangle, text width=3.0cm, minimum size=16pt, font=\tiny]
237
238\begin{tikzpicture}[>=latex']
239        %%% Edit the following coordinate to change the shape of your
240        %%% cuboid
241
242        %% Vanishing points for perspective handling
243        \coordinate (P1) at (-4cm,1.5cm); % left vanishing point (To pick)
244        \coordinate (P2) at (10cm,1.5cm); % right vanishing point (To pick)
245
246        %% (A1) and (A2) defines the 2 central points of the cuboid
247        \coordinate (A1) at (0cm,0cm); % central top point (To pick)
248        \coordinate (A2) at (0cm,-2cm); % central bottom point (To pick)
249       
250        %% (A3) to (A8) are computed given a unique parameter (or 2) .8
251        % You can vary .8 from 0 to 1 to change perspective on left side
252        \coordinate (A3) at ($(P1)!.8!(A2)$); % To pick for perspective
253        \coordinate (A4) at ($(P1)!.8!(A1)$);
254
255        % You can vary .8 from 0 to 1 to change perspective on right side
256        \coordinate (A7) at ($(P2)!.7!(A2)$);
257        \coordinate (A8) at ($(P2)!.7!(A1)$);
258
259        %% Automatically compute the last 2 points with intersections
260        \coordinate (A5) at
261          (intersection cs: first line={(A8) -- (P1)},
262                            second line={(A4) -- (P2)});
263        \coordinate (A6) at
264          (intersection cs: first line={(A7) -- (P1)},
265                            second line={(A3) -- (P2)});
266
267        %% Drawing the canopy layer
268        \coordinate (A9) at (0em,-1.7cm); % central bottom point (To pick)
269        \coordinate (A10) at ($(P2)!.7!(A9)$);
270        \coordinate (A12) at ($(P1)!.8!(A9)$); % To pick for perspective
271        \coordinate (A11) at
272          (intersection cs: first line={(A10) -- (P1)},
273                            second line={(A12) -- (P2)});
274
275        %%% Depending of what you want to display, you can comment/edit
276        %%% the following lines
277
278        {\node [background, right=-0.8cm of A12] (background) {};}
279
280        %% Possibly draw back faces
281
282        \fill[gray!70] (A2) -- (A3) -- (A6) -- (A7) -- cycle; % face 6
283        \node at (barycentric cs:A2=1,A3=1,A6=1,A7=1) {\tiny };
284       
285        \fill[gray!30] (A3) -- (A4) -- (A5) -- (A6) -- cycle; % face 3
286        \node at (barycentric cs:A3=1,A4=1,A5=1,A6=1) {\tiny };
287       
288        \fill[gray!10] (A5) -- (A6) -- (A7) -- (A8) -- cycle; % face 4
289        \node at (barycentric cs:A5=1,A6=1,A7=1,A8=1) {\tiny };
290       
291       
292        \fill[green!90] (A9) -- (A10) -- (A11) -- (A12) -- cycle; % face 7
293        \node at (barycentric cs:A9=1,A10=1,A11=1,A12=1) {\tiny };
294       
295        \fill[green!100] (A9) -- (A12) -- (A3) -- (A2) -- cycle; % face 8
296        \node at (barycentric cs:A9=1,A12=1,A3=1,A2=1) {\tiny };
297       
298        \fill[green!100] (A9) -- (A10) -- (A7) -- (A2) -- cycle; % face 9
299        \node at (barycentric cs:A9=1,A10=1,A7=1,A2=1) {\tiny };
300       
301        \draw[thin,dashed] (A5) -- (A6);
302        \draw[thin,dashed] (A3) -- (A6);
303        \draw[thin,dashed] (A7) -- (A6);
304
305        \draw[thin,dashed] (A11) -- (A12);
306        \draw[thin,dashed] (A10) -- (A11);
307       
308        %% Possibly draw front faces
309
310        % \fill[orange] (A1) -- (A8) -- (A7) -- (A2) -- cycle; % face 1
311        % \node at (barycentric cs:A1=1,A8=1,A7=1,A2=1) {\tiny f1};
312        \fill[gray!50,opacity=0.2] (A1) -- (A2) -- (A3) -- (A4) -- cycle; % f2
313        \node at (barycentric cs:A1=1,A2=1,A3=1,A4=1) {\tiny };
314        \fill[gray!90,opacity=0.2] (A1) -- (A4) -- (A5) -- (A8) -- cycle; % f5
315        \node at (barycentric cs:A1=1,A4=1,A5=1,A8=1) {\tiny };
316
317        %% Possibly draw front lines
318        \draw[thin] (A1) -- (A2);
319        \draw[thin] (A3) -- (A4);
320        \draw[thin] (A7) -- (A8);
321        \draw[thin] (A1) -- (A4);
322        \draw[thin] (A1) -- (A8);
323        \draw[thin] (A2) -- (A3);
324        \draw[thin] (A2) -- (A7);
325        \draw[thin] (A4) -- (A5);
326        \draw[thin] (A8) -- (A5);
327       
328        \draw[thin] (A9) -- (A10);
329        \draw[thin] (A9) -- (A12);
330       
331        % Possibly draw points
332        % (it can help you understand the cuboid structure)
333        \foreach \i in {1,2,...,12}
334        {
335        %  \draw[fill=black] (A\i) circle (0.05em)
336        %    node[above right] {\tiny \i};
337        }
338        % \draw[fill=black] (P1) circle (0.1em) node[below] {\tiny p1};
339        % \draw[fill=black] (P2) circle (0.1em) node[below] {\tiny p2};
340       
341        %Key   
342        \coordinate (K1) at (0.5cm,-2.3cm);
343        \coordinate (K2) at (0.5cm,-2.7cm);
344       
345       
346        \node [Key1, right=0.0cm of K1] (key1) {};
347        \node [Key2, right=0.0cm of K2] (key2) {};
348        \node [Key3, right=0.4cm of K1] (key11) {Total model domain};
349        \node [Key3, right=0.4cm of K2] (key21) {Plant canopy volume};
350       
351        %% frame specific elements
352        \node [Key3, right=0.45cm of A10] (label1) {\texttt{zw(pch\_index)} = canopy top};
353        \node [Key3, right=0.05cm of A10] (label0) {};
354       
355        \draw[<-] (label0) -- (label1);
356\end{tikzpicture}
357
358
359\end{frame}
360
361
362
363%Folie 10
364\begin{frame}
365   \frametitle{Basic canopy parameter (II)}
366    \begin{itemize}
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.\\
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.
369       }
370    \end{itemize}
371   \vspace{10pt}
372
373   \tikzstyle{background} = [rectangle, fill=gray!10, text width=1\textwidth, text centered, rounded corners, minimum height=10em]
374   \tikzstyle{Key1} = [rectangle, draw, fill=gray!70, text width=0.05, minimum size=0.05, font=\tiny]
375   \tikzstyle{Key2} = [rectangle, draw, fill=green!90, text width=0.05, minimum size=0.05, font=\tiny]
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}
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')}}.}
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}
623
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 };
716
717        %% Possibly draw front lines
718        \draw[thin] (A1) -- (A2);
719        \draw[thin] (A3) -- (A4);
720        \draw[thin] (A7) -- (A8);
721        \draw[thin] (A1) -- (A4);
722        \draw[thin] (A1) -- (A8);
723        \draw[thin] (A2) -- (A3);
724        \draw[thin] (A2) -- (A7);
725        \draw[thin] (A4) -- (A5);
726        \draw[thin] (A8) -- (A5);
727       
728        \draw[thin] (A13) -- (A10);
729        \draw[thin] (A13) -- (A15);
730        \draw[thin] (A14) -- (A16);
731        \draw[thin] (A13) -- (A14);
732        \draw[thin] (A15) -- (A16);
733       
734        % Possibly draw points
735        % (it can help you understand the cuboid structure)
736        \foreach \i in {1,2,...,16}
737        {
738        %  \draw[fill=black] (A\i) circle (0.05em)
739        %    node[above right] {\tiny \i};
740        }
741        % \draw[fill=black] (P1) circle (0.1em) node[below] {\tiny p1};
742        % \draw[fill=black] (P2) circle (0.1em) node[below] {\tiny p2};
743       
744        %Key   
745        \coordinate (K1) at (0.5cm,-2.3cm);
746        \coordinate (K2) at (0.5cm,-2.7cm);
747       
748       
749        \node [Key1, right=0.0cm of K1] (key1) {};
750        \node [Key2, right=0.0cm of K2] (key2) {};
751        \node [Key3, right=0.4cm of K1] (key11) {Total model domain};
752        \node [Key3, right=0.4cm of K2] (key21) {Plant canopy volume};
753       
754        % % Text
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}}};}
756\end{tikzpicture}
757
758
759\end{frame}
760
761\end{document}
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