source: palm/trunk/TUTORIAL/SOURCE/canopy_model.tex @ 1493

Last change on this file since 1493 was 1493, checked in by kanani, 9 years ago

updates due to new code structure and steering of canopy model

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1%$Id: canopy_model.tex 1493 2014-11-12 15:39:53Z 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\usepackage{tabto}
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
65%Folie 01
66\begin{frame}
67   \frametitle{Overview}
68   \begin{itemize}
69      \item<1->{The canopy model embedded in PALM can be used to study the effect of a plant canopy on e.g.:}
70      \begin{itemize}
71         \item<2->{mean flow field,}
72         \item<3->{development of coherent turbulence structures,}
73         \item<4->{scalar exchange processes between canopy and atmosphere.}
74      \end{itemize}
75      \item<5->{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.}
76      \item<6->{The source/sink strength for momentum and scalars depends on e.g.:}
77      \begin{itemize}
78         \item<7->{leaf area density,}
79         \item<8->{drag coefficient,}
80         \item<9->{wind speed.}
81      \end{itemize}
82   \end{itemize}
83\end{frame}
84
85
86
87%Folie 02
88\begin{frame}
89   \frametitle{Theory (I)}
90   \begin{footnotesize}
91   \begin{itemize}
92      \item<1->{A plant canopy affects the flow by acting as a momentum sink due to form and viscous drag forces.}
93      \item<2->{The effectiveness of momentum absorption depends on the amount of leaf area per unit volume and the aerodynamic drag.}
94      \item<3->{Due to the aerodynamic drag, the flow is decelerated within the canopy, creating an inflection point in the vertical profile of the horizontal velocity at the canopy top.
95         \begin{center}
96            \includegraphics[width=0.5\textwidth]{canopy_model_figures/abb1.png}
97         \end{center}
98      }
99   \end{itemize}
100   \end{footnotesize}
101\end{frame}
102
103
104
105%Folie 03
106\begin{frame}
107   \frametitle{Theory (II)}
108   \begin{footnotesize}
109   \begin{itemize}
110      \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}}).}
111      \item<2->{Wave breaking induces further instabilities, whereby a longitudinal component is added to the developing turbulence structures (\textcircled{{\tiny 2}} \& \textcircled{{\tiny 3}}).}
112      \item<3->{Due to the persistent instabilities the turbulence structures develop a distinct three-dimensionality (\textcircled{{\tiny 4}}).}
113      \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.
114         \begin{center}
115            \includegraphics[width=0.5\textwidth]{canopy_model_figures/abb2.png}
116         \end{center}
117      }
118   \end{itemize}
119   \end{footnotesize}
120\end{frame}
121
122
123
124%Folie 04
125\begin{frame}
126   \frametitle{Methods (I)}
127   \begin{footnotesize}
128   \begin{itemize}
129      \item<1->{The canopy model in PALM is based on the models used by Shaw and Schumann (1992) and Watanabe (2004).}
130      \item<2->{The aerodynamic effect of the canopy on the turbulent flow is accounted for by an additional term in the momentum equations:\\
131         \begin{align*}
132            \frac{\partial \bar{u}_{i}}{\partial t} = \text{...} - c_{d} a U \bar{u}_{i}
133         \end{align*}
134      }
135      \begin{itemize}
136         \item<3->{ $c_{d}$\tabto{.5cm}: drag coefficient}
137         \item<4->{ $a $\tabto{.5cm}:    leaf area density $[m^{2}m^{-3}]$}
138         \item<5->{ $U$\tabto{.5cm}:     $(u^{2} + v^{2} + w^{2})^{1/2}$ $[m s^{-1}]$}
139         \item<6->{ $u_{i}$\tabto{.5cm}: velocity component ($u_{1}=u$, $u_{2}=v$, $u_{3}=w$)}
140      \end{itemize}
141   \end{itemize}
142   \uncover<7->{Note: The canopy model does not resolve single plant elements, it rather models a volume-averaged effect of the forest drag on the flow.}
143   \end{footnotesize}
144\end{frame}
145
146
147
148%Folie 05
149\begin{frame}
150   \frametitle{Methods (II)}
151   \begin{footnotesize}
152   \begin{itemize}
153      \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:\\
154         \begin{align*}
155            \frac{\partial e}{\partial t} = \text{...} - 2 c_{d} a U e
156         \end{align*}
157      }
158      \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 plant elements (e.g. Watanabe, 2004).}
159   \end{itemize}
160   \end{footnotesize}
161\end{frame}
162
163
164
165%Folie 06
166\begin{frame}
167   \frametitle{Methods (III)}
168   \begin{footnotesize}
169   \begin{itemize}
170      \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:\\
171         \begin{align*}
172            \frac{\partial \bar{\theta}}{\partial t} = \text{...} +  S_{\theta}
173         \end{align*}
174      }
175      \item<2->{It is assumed that the foliage is warmed by the penetrating solar radiation. In turn, the heated foliage warms the surrounding air.}
176      \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):\\
177         \begin{align*}
178            Q_{\theta}(z) = Q_{\theta}(h) exp(-\alpha F) \text{ , } Q_{\theta}(h) \text{ : Heat flux at canopy top}
179         \end{align*}
180      }
181      \begin{itemize}
182         \item<4->{ $\alpha = 0.6$ (extinction coefficient)}
183         \item<5->{ $F = \int\limits_{z}^{h} a \: dz$ (downward cumulative leaf area index)}
184      \end{itemize}
185   \end{itemize}
186   \end{footnotesize}
187\end{frame}
188
189
190
191%Folie 07
192\begin{frame}
193   \frametitle{Methods (IV)}
194   \begin{footnotesize}
195   \begin{itemize}
196      \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:\\
197         \begin{align*}
198            \frac{\partial \bar{q}}{\partial t} = \text{...} - c_{q} a U (\bar{q} - q_{c})
199         \end{align*}
200      }
201      \begin{itemize}
202         \item<2->{ $c_{q}$ : scalar exchange coefficient}
203         \item<3->{ $q_{c}$ : scalar concentration at leaf surface}
204      \end{itemize}
205   \end{itemize}
206   \end{footnotesize}
207\end{frame}
208
209
210
211%Folie 08
212\begin{frame}
213   \frametitle{Basics (I)}
214   \begin{itemize}
215      \item<1->{The canopy model is enabled by adding {\small \texttt{NAMELIST}} group {\small \texttt{\&canopy\_par}} to the parameter file ({\small \texttt{PARIN}}), subsequently to {\small \texttt{NAMELIST}} group {\small \texttt{\&d3par}}.}
216      \item<2->{All parameters for steering the canopy model are described in:\\
217      {\scriptsize Documentation $\rightarrow$ Model steering $\rightarrow$ Parameters $\rightarrow$ Plant canopy}\\
218      (http://palm.muk.uni-hannover.de)
219      }
220      \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 {\small \texttt{\&canopy\_par}} {\small \texttt{NAMELIST}}.}
221   \end{itemize}
222\end{frame}
223
224
225
226%Folie 09
227\begin{frame}
228   \frametitle{Basic canopy parameters (I)}
229   The parameters for steering the canopy model have to be added to the {\small \texttt{\&canopy\_par}} {\small \texttt{NAMELIST}} in the parameter file ({\small \texttt{PARIN}}).\\
230    \begin{itemize}
231       \item<1->{Step I: Define the upper boundary of the plant canopy volume 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.}
232    \end{itemize}
233   \vspace{10pt}
234
235   \tikzstyle{background} = [rectangle, fill=gray!10, text width=1\textwidth, text centered, rounded corners, minimum height=10em]
236   \tikzstyle{Key1} = [rectangle, draw, fill=gray!70, text width=0.05, minimum size=0.05, font=\tiny]
237   \tikzstyle{Key2} = [rectangle, draw, fill=green!90, text width=0.05, minimum size=0.05, font=\tiny]
238   \tikzstyle{Key3} = [rectangle, text width=3.0cm, minimum size=16pt, font=\tiny]
239
240\begin{tikzpicture}[>=latex']
241        %%% Edit the following coordinate to change the shape of your
242        %%% cuboid
243
244        %% Vanishing points for perspective handling
245        \coordinate (P1) at (-4cm,1.5cm); % left vanishing point (To pick)
246        \coordinate (P2) at (10cm,1.5cm); % right vanishing point (To pick)
247
248        %% (A1) and (A2) defines the 2 central points of the cuboid
249        \coordinate (A1) at (0cm,0cm); % central top point (To pick)
250        \coordinate (A2) at (0cm,-2cm); % central bottom point (To pick)
251       
252        %% (A3) to (A8) are computed given a unique parameter (or 2) .8
253        % You can vary .8 from 0 to 1 to change perspective on left side
254        \coordinate (A3) at ($(P1)!.8!(A2)$); % To pick for perspective
255        \coordinate (A4) at ($(P1)!.8!(A1)$);
256
257        % You can vary .8 from 0 to 1 to change perspective on right side
258        \coordinate (A7) at ($(P2)!.7!(A2)$);
259        \coordinate (A8) at ($(P2)!.7!(A1)$);
260
261        %% Automatically compute the last 2 points with intersections
262        \coordinate (A5) at
263          (intersection cs: first line={(A8) -- (P1)},
264                            second line={(A4) -- (P2)});
265        \coordinate (A6) at
266          (intersection cs: first line={(A7) -- (P1)},
267                            second line={(A3) -- (P2)});
268
269        %% Drawing the canopy layer
270        \coordinate (A9) at (0em,-1.7cm); % central bottom point (To pick)
271        \coordinate (A10) at ($(P2)!.7!(A9)$);
272        \coordinate (A12) at ($(P1)!.8!(A9)$); % To pick for perspective
273        \coordinate (A11) at
274          (intersection cs: first line={(A10) -- (P1)},
275                            second line={(A12) -- (P2)});
276
277        %%% Depending of what you want to display, you can comment/edit
278        %%% the following lines
279
280        {\node [background, right=-0.8cm of A12] (background) {};}
281
282        %% Possibly draw back faces
283
284        \fill[gray!70] (A2) -- (A3) -- (A6) -- (A7) -- cycle; % face 6
285        \node at (barycentric cs:A2=1,A3=1,A6=1,A7=1) {\tiny };
286       
287        \fill[gray!30] (A3) -- (A4) -- (A5) -- (A6) -- cycle; % face 3
288        \node at (barycentric cs:A3=1,A4=1,A5=1,A6=1) {\tiny };
289       
290        \fill[gray!10] (A5) -- (A6) -- (A7) -- (A8) -- cycle; % face 4
291        \node at (barycentric cs:A5=1,A6=1,A7=1,A8=1) {\tiny };
292       
293       
294        \fill[green!90] (A9) -- (A10) -- (A11) -- (A12) -- cycle; % face 7
295        \node at (barycentric cs:A9=1,A10=1,A11=1,A12=1) {\tiny };
296       
297        \fill[green!100] (A9) -- (A12) -- (A3) -- (A2) -- cycle; % face 8
298        \node at (barycentric cs:A9=1,A12=1,A3=1,A2=1) {\tiny };
299       
300        \fill[green!100] (A9) -- (A10) -- (A7) -- (A2) -- cycle; % face 9
301        \node at (barycentric cs:A9=1,A10=1,A7=1,A2=1) {\tiny };
302       
303        \draw[thin,dashed] (A5) -- (A6);
304        \draw[thin,dashed] (A3) -- (A6);
305        \draw[thin,dashed] (A7) -- (A6);
306
307        \draw[thin,dashed] (A11) -- (A12);
308        \draw[thin,dashed] (A10) -- (A11);
309       
310        %% Possibly draw front faces
311
312        % \fill[orange] (A1) -- (A8) -- (A7) -- (A2) -- cycle; % face 1
313        % \node at (barycentric cs:A1=1,A8=1,A7=1,A2=1) {\tiny f1};
314        \fill[gray!50,opacity=0.2] (A1) -- (A2) -- (A3) -- (A4) -- cycle; % f2
315        \node at (barycentric cs:A1=1,A2=1,A3=1,A4=1) {\tiny };
316        \fill[gray!90,opacity=0.2] (A1) -- (A4) -- (A5) -- (A8) -- cycle; % f5
317        \node at (barycentric cs:A1=1,A4=1,A5=1,A8=1) {\tiny };
318
319        %% Possibly draw front lines
320        \draw[thin] (A1) -- (A2);
321        \draw[thin] (A3) -- (A4);
322        \draw[thin] (A7) -- (A8);
323        \draw[thin] (A1) -- (A4);
324        \draw[thin] (A1) -- (A8);
325        \draw[thin] (A2) -- (A3);
326        \draw[thin] (A2) -- (A7);
327        \draw[thin] (A4) -- (A5);
328        \draw[thin] (A8) -- (A5);
329       
330        \draw[thin] (A9) -- (A10);
331        \draw[thin] (A9) -- (A12);
332       
333        % Possibly draw points
334        % (it can help you understand the cuboid structure)
335        \foreach \i in {1,2,...,12}
336        {
337        %  \draw[fill=black] (A\i) circle (0.05em)
338        %    node[above right] {\tiny \i};
339        }
340        % \draw[fill=black] (P1) circle (0.1em) node[below] {\tiny p1};
341        % \draw[fill=black] (P2) circle (0.1em) node[below] {\tiny p2};
342       
343        %Key   
344        \coordinate (K1) at (0.5cm,-2.3cm);
345        \coordinate (K2) at (0.5cm,-2.7cm);
346       
347       
348        \node [Key1, right=0.0cm of K1] (key1) {};
349        \node [Key2, right=0.0cm of K2] (key2) {};
350        \node [Key3, right=0.4cm of K1] (key11) {Total model domain};
351        \node [Key3, right=0.4cm of K2] (key21) {Plant canopy volume};
352       
353        %% frame specific elements
354        \node [Key3, right=0.45cm of A10] (label1) {\texttt{zw(pch\_index)} = canopy top};
355        \node [Key3, right=0.05cm of A10] (label0) {};
356       
357        \draw[<-] (label0) -- (label1);
358\end{tikzpicture}
359
360
361\end{frame}
362
363
364
365%Folie 10
366\begin{frame}
367   \frametitle{Basic canopy parameters (II)}
368    \begin{itemize}
369       \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.\\
370                  Two methods are available to prescribe an lad profile:}
371       \begin{itemize}
372          \item<2->{Create piecewise linear segments by prescribing vertical lad gradients,} 
373          \item<3->{Prescribe a beta probability distribution.} 
374       \end{itemize}
375
376    \end{itemize}
377   \vspace{10pt}
378
379   \tikzstyle{background} = [rectangle, fill=gray!10, text width=1\textwidth, text centered, rounded corners, minimum height=10em]
380   \tikzstyle{Key1} = [rectangle, draw, fill=gray!70, text width=0.05, minimum size=0.05, font=\tiny]
381   \tikzstyle{Key2} = [rectangle, draw, fill=green!90, text width=0.05, minimum size=0.05, font=\tiny]
382   \tikzstyle{Key3} = [rectangle, text width=4.5cm, minimum size=16pt, font=\tiny]
383   \tikzstyle{label} = [rectangle, text width=2.0cm, align=center, minimum size=16pt, font=\tiny]
384
385\begin{tikzpicture}[>=latex']
386        %%% Edit the following coordinate to change the shape of your
387        %%% cuboid
388
389        %% Vanishing points for perspective handling
390        \coordinate (P1) at (-4cm,1.5cm); % left vanishing point (To pick)
391        \coordinate (P2) at (10cm,1.5cm); % right vanishing point (To pick)
392
393        %% (A1) and (A2) defines the 2 central points of the cuboid
394        \coordinate (A1) at (0cm,0cm); % central top point (To pick)
395        \coordinate (A2) at (0cm,-2cm); % central bottom point (To pick)
396       
397        %% (A3) to (A8) are computed given a unique parameter (or 2) .8
398        % You can vary .8 from 0 to 1 to change perspective on left side
399        \coordinate (A3) at ($(P1)!.8!(A2)$); % To pick for perspective
400        \coordinate (A4) at ($(P1)!.8!(A1)$);
401
402        % You can vary .8 from 0 to 1 to change perspective on right side
403        \coordinate (A7) at ($(P2)!.7!(A2)$);
404        \coordinate (A8) at ($(P2)!.7!(A1)$);
405
406        %% Automatically compute the last 2 points with intersections
407        \coordinate (A5) at
408          (intersection cs: first line={(A8) -- (P1)},
409                            second line={(A4) -- (P2)});
410        \coordinate (A6) at
411          (intersection cs: first line={(A7) -- (P1)},
412                            second line={(A3) -- (P2)});
413
414        %% Drawing the canopy layer
415        \coordinate (A9) at (0em,-1.7cm); % central bottom point (To pick)
416        \coordinate (A10) at ($(P2)!.7!(A9)$);
417        \coordinate (A12) at ($(P1)!.8!(A9)$); % To pick for perspective
418        \coordinate (A11) at
419          (intersection cs: first line={(A10) -- (P1)},
420                            second line={(A12) -- (P2)});
421
422        %%% Depending of what you want to display, you can comment/edit
423        %%% the following lines
424
425        {\node [background, right=-0.8cm of A12] (background) {};}
426
427        %% Possibly draw back faces
428
429        \fill[gray!70] (A2) -- (A3) -- (A6) -- (A7) -- cycle; % face 6
430        \node at (barycentric cs:A2=1,A3=1,A6=1,A7=1) {\tiny };
431       
432        \fill[gray!30] (A3) -- (A4) -- (A5) -- (A6) -- cycle; % face 3
433        \node at (barycentric cs:A3=1,A4=1,A5=1,A6=1) {\tiny };
434       
435        \fill[gray!10] (A5) -- (A6) -- (A7) -- (A8) -- cycle; % face 4
436        \node at (barycentric cs:A5=1,A6=1,A7=1,A8=1) {\tiny };
437       
438       
439        \fill[green!90] (A9) -- (A10) -- (A11) -- (A12) -- cycle; % face 7
440        \node at (barycentric cs:A9=1,A10=1,A11=1,A12=1) {\tiny };
441       
442        \fill[green!100] (A9) -- (A12) -- (A3) -- (A2) -- cycle; % face 8
443        \node at (barycentric cs:A9=1,A12=1,A3=1,A2=1) {\tiny };
444       
445        \fill[green!100] (A9) -- (A10) -- (A7) -- (A2) -- cycle; % face 9
446        \node at (barycentric cs:A9=1,A10=1,A7=1,A2=1) {\tiny };
447       
448        \draw[thin,dashed] (A5) -- (A6);
449        \draw[thin,dashed] (A3) -- (A6);
450        \draw[thin,dashed] (A7) -- (A6);
451
452        \draw[thin,dashed] (A11) -- (A12);
453        \draw[thin,dashed] (A10) -- (A11);
454       
455        %% Possibly draw front faces
456
457        % \fill[orange] (A1) -- (A8) -- (A7) -- (A2) -- cycle; % face 1
458        % \node at (barycentric cs:A1=1,A8=1,A7=1,A2=1) {\tiny f1};
459        \fill[gray!50,opacity=0.2] (A1) -- (A2) -- (A3) -- (A4) -- cycle; % f2
460        \node at (barycentric cs:A1=1,A2=1,A3=1,A4=1) {\tiny };
461        \fill[gray!90,opacity=0.2] (A1) -- (A4) -- (A5) -- (A8) -- cycle; % f5
462        \node at (barycentric cs:A1=1,A4=1,A5=1,A8=1) {\tiny };
463
464        %% Possibly draw front lines
465        \draw[thin] (A1) -- (A2);
466        \draw[thin] (A3) -- (A4);
467        \draw[thin] (A7) -- (A8);
468        \draw[thin] (A1) -- (A4);
469        \draw[thin] (A1) -- (A8);
470        \draw[thin] (A2) -- (A3);
471        \draw[thin] (A2) -- (A7);
472        \draw[thin] (A4) -- (A5);
473        \draw[thin] (A8) -- (A5);
474       
475        \draw[thin] (A9) -- (A10);
476        \draw[thin] (A9) -- (A12);
477       
478        % Possibly draw points
479        % (it can help you understand the cuboid structure)
480        \foreach \i in {1,2,...,12}
481        {
482        %  \draw[fill=black] (A\i) circle (0.05em)
483        %    node[above right] {\tiny \i};
484        }
485        % \draw[fill=black] (P1) circle (0.1em) node[below] {\tiny p1};
486        % \draw[fill=black] (P2) circle (0.1em) node[below] {\tiny p2};
487       
488        %Key   
489        \coordinate (K1) at (0.5cm,-2.3cm);
490        \coordinate (K2) at (0.5cm,-2.7cm);
491       
492       
493        \node [Key1, right=0.0cm of K1] (key1) {};
494        \node [Key2, right=0.0cm of K2] (key2) {};
495        \node [Key3, right=0.4cm of K1] (key11) {Total model domain};
496        \node [Key3, right=0.4cm of K2] (key21) {Plant canopy volume};
497       
498        %% frame specific elements
499       
500        %% boundary layer profile 2D
501        \coordinate (B1) at (4.0cm,0.3cm);
502        \coordinate (B2) at (4.0cm,-2.5cm);
503       
504        \coordinate (B3) at (4.0cm,0.6cm);
505        \coordinate (B4) at (6.6cm,-2.5cm);
506       
507        \draw[thin, dotted] (A10) -- (B1);
508        \draw[thin, dotted] (A7) -- (B2);
509        \draw[<-] (B3) -- (B2);
510        \draw[<-] (B4) -- (B2);
511       
512        \coordinate (xlab) at (5.3cm,-2.5cm);
513        \coordinate (ylab) at (4.0cm,-1.1cm);
514        \node [label, below=0.0cm of xlab] (xlabel) {lad $[m^{2}m^{-3}]$};
515        \node [label, rotate=90, above=0.0cm of ylab] (ylabel) {z$[m]$};
516       
517       
518        \coordinate (B5) at (4.5cm,-2.5cm);
519%       \draw [-,color=red] (B1) to [out=-10,in=90,looseness=2.0, relative=false] .. controls (4,0) and (5,0) .. (B5);
520        \draw {(B1) .. controls (8.0,-0.2) and (4.5,-1.0) .. (B5)};
521       
522
523\end{tikzpicture}
524
525
526\end{frame}
527
528
529
530%Folie 11
531\begin{frame}
532   \frametitle{Basic canopy parameters (II)}
533    \begin{itemize}
534       \item<1->{ Method I: Create lad profile from piecewise linear segments by prescribing vertical lad gradients.}
535       \item[]{The canopy top is located at {\small \texttt{zw(pch\_index)}} (w-grid), which is in the center between {\small \texttt{zu(pch\_index)}} and {\small \texttt{zu(pch\_index + 1)}} (u-grid).}
536    \end{itemize}
537   \vspace{10pt}
538
539   \tikzstyle{background} = [rectangle, fill=gray!10, text width=1\textwidth, text centered, rounded corners, minimum height=10em]
540   \tikzstyle{Key1} = [rectangle, draw, fill=gray!70, text width=0.05, minimum size=0.05, font=\tiny]
541   \tikzstyle{Key2} = [rectangle, draw, fill=green!90, text width=0.05, minimum size=0.05, font=\tiny]
542   \tikzstyle{Key3} = [rectangle, text width=4.5cm, minimum size=16pt, font=\tiny]
543   \tikzstyle{label} = [rectangle, text width=2.0cm, align=center, minimum size=16pt, font=\tiny]
544
545\begin{tikzpicture}[>=latex']
546        %%% Edit the following coordinate to change the shape of your
547        %%% cuboid
548
549        %% Vanishing points for perspective handling
550        \coordinate (P1) at (-4cm,1.5cm); % left vanishing point (To pick)
551        \coordinate (P2) at (10cm,1.5cm); % right vanishing point (To pick)
552
553        %% (A1) and (A2) defines the 2 central points of the cuboid
554        \coordinate (A1) at (0cm,0cm); % central top point (To pick)
555        \coordinate (A2) at (0cm,-2cm); % central bottom point (To pick)
556       
557        %% (A3) to (A8) are computed given a unique parameter (or 2) .8
558        % You can vary .8 from 0 to 1 to change perspective on left side
559        \coordinate (A3) at ($(P1)!.8!(A2)$); % To pick for perspective
560        \coordinate (A4) at ($(P1)!.8!(A1)$);
561
562        % You can vary .8 from 0 to 1 to change perspective on right side
563        \coordinate (A7) at ($(P2)!.7!(A2)$);
564        \coordinate (A8) at ($(P2)!.7!(A1)$);
565
566        %% Automatically compute the last 2 points with intersections
567        \coordinate (A5) at
568          (intersection cs: first line={(A8) -- (P1)},
569                            second line={(A4) -- (P2)});
570        \coordinate (A6) at
571          (intersection cs: first line={(A7) -- (P1)},
572                            second line={(A3) -- (P2)});
573
574        %% Drawing the canopy layer
575        \coordinate (A9) at (0em,-1.7cm); % central bottom point (To pick)
576        \coordinate (A10) at ($(P2)!.7!(A9)$);
577        \coordinate (A12) at ($(P1)!.8!(A9)$); % To pick for perspective
578        \coordinate (A11) at
579          (intersection cs: first line={(A10) -- (P1)},
580                            second line={(A12) -- (P2)});
581
582        %%% Depending of what you want to display, you can comment/edit
583        %%% the following lines
584
585        {\node [background, right=-0.8cm of A12] (background) {};}
586
587        %% Possibly draw back faces
588
589        \fill[gray!70] (A2) -- (A3) -- (A6) -- (A7) -- cycle; % face 6
590        \node at (barycentric cs:A2=1,A3=1,A6=1,A7=1) {\tiny };
591       
592        \fill[gray!30] (A3) -- (A4) -- (A5) -- (A6) -- cycle; % face 3
593        \node at (barycentric cs:A3=1,A4=1,A5=1,A6=1) {\tiny };
594       
595        \fill[gray!10] (A5) -- (A6) -- (A7) -- (A8) -- cycle; % face 4
596        \node at (barycentric cs:A5=1,A6=1,A7=1,A8=1) {\tiny };
597       
598       
599        \fill[green!90] (A9) -- (A10) -- (A11) -- (A12) -- cycle; % face 7
600        \node at (barycentric cs:A9=1,A10=1,A11=1,A12=1) {\tiny };
601       
602        \fill[green!100] (A9) -- (A12) -- (A3) -- (A2) -- cycle; % face 8
603        \node at (barycentric cs:A9=1,A12=1,A3=1,A2=1) {\tiny };
604       
605        \fill[green!100] (A9) -- (A10) -- (A7) -- (A2) -- cycle; % face 9
606        \node at (barycentric cs:A9=1,A10=1,A7=1,A2=1) {\tiny };
607       
608        \draw[thin,dashed] (A5) -- (A6);
609        \draw[thin,dashed] (A3) -- (A6);
610        \draw[thin,dashed] (A7) -- (A6);
611
612        \draw[thin,dashed] (A11) -- (A12);
613        \draw[thin,dashed] (A10) -- (A11);
614       
615        %% Possibly draw front faces
616
617        % \fill[orange] (A1) -- (A8) -- (A7) -- (A2) -- cycle; % face 1
618        % \node at (barycentric cs:A1=1,A8=1,A7=1,A2=1) {\tiny f1};
619        \fill[gray!50,opacity=0.2] (A1) -- (A2) -- (A3) -- (A4) -- cycle; % f2
620        \node at (barycentric cs:A1=1,A2=1,A3=1,A4=1) {\tiny };
621        \fill[gray!90,opacity=0.2] (A1) -- (A4) -- (A5) -- (A8) -- cycle; % f5
622        \node at (barycentric cs:A1=1,A4=1,A5=1,A8=1) {\tiny };
623
624        %% Possibly draw front lines
625        \draw[thin] (A1) -- (A2);
626        \draw[thin] (A3) -- (A4);
627        \draw[thin] (A7) -- (A8);
628        \draw[thin] (A1) -- (A4);
629        \draw[thin] (A1) -- (A8);
630        \draw[thin] (A2) -- (A3);
631        \draw[thin] (A2) -- (A7);
632        \draw[thin] (A4) -- (A5);
633        \draw[thin] (A8) -- (A5);
634       
635        \draw[thin] (A9) -- (A10);
636        \draw[thin] (A9) -- (A12);
637       
638        % Possibly draw points
639        % (it can help you understand the cuboid structure)
640        \foreach \i in {1,2,...,12}
641        {
642        %  \draw[fill=black] (A\i) circle (0.05em)
643        %    node[above right] {\tiny \i};
644        }
645        % \draw[fill=black] (P1) circle (0.1em) node[below] {\tiny p1};
646        % \draw[fill=black] (P2) circle (0.1em) node[below] {\tiny p2};
647       
648        %Key   
649        \coordinate (K1) at (0.5cm,-2.3cm);
650        \coordinate (K2) at (0.5cm,-2.7cm);
651       
652       
653        \node [Key1, right=0.0cm of K1] (key1) {};
654        \node [Key2, right=0.0cm of K2] (key2) {};
655        \node [Key3, right=0.4cm of K1] (key11) {Total model domain};
656        \node [Key3, right=0.4cm of K2] (key21) {Plant canopy volume};
657       
658        %% frame specific elements
659       
660        %% boundary layer profile 2D
661        \coordinate (B1) at (4.0cm,0.3cm);
662        \coordinate (B2) at (4.0cm,-2.5cm);
663       
664        \coordinate (B3) at (4.0cm,0.6cm);
665        \coordinate (B4) at (6.6cm,-2.5cm);
666       
667        \draw[thin, dotted] (A10) -- (B1);
668        \draw[thin, dotted] (A7) -- (B2);
669        \draw[<-] (B3) -- (B2);
670        \draw[<-] (B4) -- (B2);
671       
672        \coordinate (xlab) at (5.3cm,-2.5cm);
673        \coordinate (ylab) at (4.0cm,-1.1cm);
674        \node [label, below=0.0cm of xlab] (xlabel) {lad $[m^{2}m^{-3}]$};
675        \node [label, rotate=90, above=0.0cm of ylab] (ylabel) {z$[m]$};
676       
677       
678        \coordinate (B5) at (4.5cm,-2.5cm);
679%       \draw [-,color=red] (B1) to [out=-10,in=90,looseness=2.0, relative=false] .. controls (4,0) and (5,0) .. (B5);
680        \draw {(B1) .. controls (8.0,-0.2) and (4.5,-1.0) .. (B5)};
681       
682        \draw [decorate, decoration={markings,
683                mark=at position 00mm with{\draw[fill=black] (0,0) circle (0.1em);},
684                mark=at position 04mm with{\draw[fill=black] (0,0) circle (0.1em);},
685                mark=at position 08mm with{\draw[fill=black] (0,0) circle (0.1em);},
686                mark=at position 12mm with{\draw[fill=black] (0,0) circle (0.1em);},
687                mark=at position 16mm with{\draw[fill=black] (0,0) circle (0.1em);},
688                mark=at position 20mm with{\draw[fill=black] (0,0) circle (0.1em);},
689                mark=at position 24mm with{\draw[fill=black] (0,0) circle (0.1em);},
690                mark=at position 28mm with{\draw[fill=black] (0,0) circle (0.1em);},
691                mark=at position 32mm with{\draw[fill=black] (0,0) circle (0.1em);},
692                mark=at position 36mm with{\draw[fill=black] (0,0) circle (0.1em);},
693                mark=at position 40mm with{\draw[fill=black] (0,0) circle (0.1em);},
694                mark=at position 44mm with{\draw[fill=black] (0,0) circle (0.1em);},
695                }]
696                {(B5) .. controls (4.5,-1.0) and (8.0,-0.2) .. (B1)};
697
698        \node [Key3, right=1.1cm of B1] (label1) {\texttt{zu(pch\_index + 1)}: lad = 0.0 (default)};
699        \node [Key3, left=0.1cm of B1] (label0) {};
700        \draw[-, dashed] (label0) -- (label1);
701       
702        \coordinate (curvelabel00) at (4.65cm,-2.45cm);
703        \coordinate (curvelabel01) at (5.0cm,-2.25cm);
704        \draw[<-] (curvelabel00) -- (curvelabel01);
705        \node [Key3, right=0.0cm of curvelabel01] (curvelabel02) {\texttt{lad\_surface} (default 0.0)};
706       
707        \coordinate (curvelabel10) at (5.4cm,-1.3cm);
708        \coordinate (curvelabel11) at (5.6cm,-1.6cm);
709        \draw[<-] (curvelabel10) -- (curvelabel11);
710        \node [Key3, right=0.0cm of curvelabel11] (curvelabel12) {\texttt{lad\_vertical\_gradient\_level} (5)};
711       
712        \coordinate (curvelabel10) at (5.47cm,-1.05cm);
713        \coordinate (curvelabel11) at (5.8cm,-1.3cm);
714        \draw[<-] (curvelabel10) -- (curvelabel11);
715        \node [Key3, right=0.0cm of curvelabel11] (curvelabel12) {\texttt{lad\_vertical\_gradient} (5)};
716       
717        \coordinate (curvelabel10) at (5.7cm,-0.93cm);
718        \coordinate (curvelabel11) at (5.9cm,-1.0cm);
719        \draw[<-] (curvelabel10) -- (curvelabel11);
720        \node [Key3, right=0.0cm of curvelabel11] (curvelabel12) {\texttt{lad\_vertical\_gradient\_level} (6)};
721\end{tikzpicture}
722
723
724\end{frame}
725
726
727%Folie 12
728\begin{frame}
729   \frametitle{Basic canopy parameters (II)}
730    \begin{itemize}
731       \item<1->{ Method II: Create \textit{lad} profile by prescribing a distribution, following this beta probability density function:}
732    \end{itemize}
733
734
735   %equation for beta distribution:
736   \vspace{-3pt}
737   \scriptsize
738   \begin{equation*}
739    f_{PDF}(\frac{z}{H},\alpha,\beta) = \frac{(\frac{z}{H})^{\alpha-1}\;(1-\frac{z}{H})^{\beta-1}}{\int_{0}^{1}\;(\frac{z}{H})^{\alpha-1}\;(1-\frac{z}{H})^{\beta-1}\;d(\frac{z}{H})} 
740   \end{equation*}
741   \vspace{5pt}
742   \begin{equation*}
743    \rightarrow \hspace{5pt} lad(z) = LAI\cdot f_{PDF}(\frac{z}{H})\cdot H
744   \end{equation*}
745   \normalsize
746
747
748
749   %draw figure:
750   \tikzstyle{background} = [rectangle, fill=gray!10, text width=1\textwidth, text centered, rounded corners, minimum height=10em]
751   \tikzstyle{Key1} = [rectangle, draw, fill=gray!70, text width=0.05, minimum size=0.05, font=\tiny]
752   \tikzstyle{Key2} = [rectangle, draw, fill=green!90, text width=0.05, minimum size=0.05, font=\tiny]
753   \tikzstyle{Key3} = [rectangle, text width=4.5cm, minimum size=16pt, font=\tiny]
754   \tikzstyle{label} = [rectangle, text width=2.0cm, align=center, minimum size=16pt, font=\tiny]
755
756\begin{tikzpicture}[>=latex']
757        %%% Edit the following coordinate to change the shape of your
758        %%% cuboid
759
760        %% Vanishing points for perspective handling
761        \coordinate (P1) at (-4cm,1.5cm); % left vanishing point (To pick)
762        \coordinate (P2) at (10cm,1.5cm); % right vanishing point (To pick)
763
764        %% (A1) and (A2) defines the 2 central points of the cuboid
765        \coordinate (A1) at (0cm,0cm); % central top point (To pick)
766        \coordinate (A2) at (0cm,-2cm); % central bottom point (To pick)
767       
768        %% (A3) to (A8) are computed given a unique parameter (or 2) .8
769        % You can vary .8 from 0 to 1 to change perspective on left side
770        \coordinate (A3) at ($(P1)!.8!(A2)$); % To pick for perspective
771        \coordinate (A4) at ($(P1)!.8!(A1)$);
772
773        % You can vary .8 from 0 to 1 to change perspective on right side
774        \coordinate (A7) at ($(P2)!.7!(A2)$);
775        \coordinate (A8) at ($(P2)!.7!(A1)$);
776
777        %% Automatically compute the last 2 points with intersections
778        \coordinate (A5) at
779          (intersection cs: first line={(A8) -- (P1)},
780                            second line={(A4) -- (P2)});
781        \coordinate (A6) at
782          (intersection cs: first line={(A7) -- (P1)},
783                            second line={(A3) -- (P2)});
784
785        %% Drawing the canopy layer
786        \coordinate (A9) at (0em,-1.7cm); % central bottom point (To pick)
787        \coordinate (A10) at ($(P2)!.7!(A9)$);
788        \coordinate (A12) at ($(P1)!.8!(A9)$); % To pick for perspective
789        \coordinate (A11) at
790          (intersection cs: first line={(A10) -- (P1)},
791                            second line={(A12) -- (P2)});
792
793        %%% Depending of what you want to display, you can comment/edit
794        %%% the following lines
795
796        {\node [background, right=-0.8cm of A12] (background) {};}
797
798        %% Possibly draw back faces
799
800        \fill[gray!70] (A2) -- (A3) -- (A6) -- (A7) -- cycle; % face 6
801        \node at (barycentric cs:A2=1,A3=1,A6=1,A7=1) {\tiny };
802       
803        \fill[gray!30] (A3) -- (A4) -- (A5) -- (A6) -- cycle; % face 3
804        \node at (barycentric cs:A3=1,A4=1,A5=1,A6=1) {\tiny };
805       
806        \fill[gray!10] (A5) -- (A6) -- (A7) -- (A8) -- cycle; % face 4
807        \node at (barycentric cs:A5=1,A6=1,A7=1,A8=1) {\tiny };
808       
809       
810        \fill[green!90] (A9) -- (A10) -- (A11) -- (A12) -- cycle; % face 7
811        \node at (barycentric cs:A9=1,A10=1,A11=1,A12=1) {\tiny };
812       
813        \fill[green!100] (A9) -- (A12) -- (A3) -- (A2) -- cycle; % face 8
814        \node at (barycentric cs:A9=1,A12=1,A3=1,A2=1) {\tiny };
815       
816        \fill[green!100] (A9) -- (A10) -- (A7) -- (A2) -- cycle; % face 9
817        \node at (barycentric cs:A9=1,A10=1,A7=1,A2=1) {\tiny };
818       
819        \draw[thin,dashed] (A5) -- (A6);
820        \draw[thin,dashed] (A3) -- (A6);
821        \draw[thin,dashed] (A7) -- (A6);
822
823        \draw[thin,dashed] (A11) -- (A12);
824        \draw[thin,dashed] (A10) -- (A11);
825       
826        %% Possibly draw front faces
827
828        % \fill[orange] (A1) -- (A8) -- (A7) -- (A2) -- cycle; % face 1
829        % \node at (barycentric cs:A1=1,A8=1,A7=1,A2=1) {\tiny f1};
830        \fill[gray!50,opacity=0.2] (A1) -- (A2) -- (A3) -- (A4) -- cycle; % f2
831        \node at (barycentric cs:A1=1,A2=1,A3=1,A4=1) {\tiny };
832        \fill[gray!90,opacity=0.2] (A1) -- (A4) -- (A5) -- (A8) -- cycle; % f5
833        \node at (barycentric cs:A1=1,A4=1,A5=1,A8=1) {\tiny };
834
835        %% Possibly draw front lines
836        \draw[thin] (A1) -- (A2);
837        \draw[thin] (A3) -- (A4);
838        \draw[thin] (A7) -- (A8);
839        \draw[thin] (A1) -- (A4);
840        \draw[thin] (A1) -- (A8);
841        \draw[thin] (A2) -- (A3);
842        \draw[thin] (A2) -- (A7);
843        \draw[thin] (A4) -- (A5);
844        \draw[thin] (A8) -- (A5);
845       
846        \draw[thin] (A9) -- (A10);
847        \draw[thin] (A9) -- (A12);
848       
849        % Possibly draw points
850        % (it can help you understand the cuboid structure)
851        \foreach \i in {1,2,...,12}
852        {
853        %  \draw[fill=black] (A\i) circle (0.05em)
854        %    node[above right] {\tiny \i};
855        }
856        % \draw[fill=black] (P1) circle (0.1em) node[below] {\tiny p1};
857        % \draw[fill=black] (P2) circle (0.1em) node[below] {\tiny p2};
858       
859        %Key   
860        \coordinate (K1) at (0.5cm,-2.3cm);
861        \coordinate (K2) at (0.5cm,-2.7cm);
862       
863       
864        \node [Key1, right=0.0cm of K1] (key1) {};
865        \node [Key2, right=0.0cm of K2] (key2) {};
866        \node [Key3, right=0.4cm of K1] (key11) {Total model domain};
867        \node [Key3, right=0.4cm of K2] (key21) {Plant canopy volume};
868       
869        %% frame specific elements
870       
871        %% boundary layer profile 2D
872        \coordinate (B1) at (4.0cm,0.3cm);
873        \coordinate (B2) at (4.0cm,-2.5cm);
874       
875        \coordinate (B3) at (4.0cm,0.6cm);
876        \coordinate (B4) at (6.6cm,-2.5cm);
877       
878        \draw[thin, dotted] (A10) -- (B1);
879        \draw[thin, dotted] (A7) -- (B2);
880        \draw[<-] (B3) -- (B2);
881        \draw[<-] (B4) -- (B2);
882       
883        \coordinate (xlab) at (5.3cm,-2.5cm);
884        \coordinate (ylab) at (4.0cm,-1.1cm);
885        \node [label, below=0.0cm of xlab] (xlabel) {lad $[m^{2}m^{-3}]$};
886        \node [label, rotate=90, above=0.0cm of ylab] (ylabel) {z$[m]$};
887       
888       
889        \coordinate (B5) at (4.5cm,-2.5cm);
890%       \draw [-,color=red] (B1) to [out=-10,in=90,looseness=2.0, relative=false] .. controls (4,0) and (5,0) .. (B5);
891        \draw {(B1) .. controls (8.0,-0.2) and (4.5,-1.0) .. (B5)};
892       
893        %parameters to be prescribed:
894        \node [Key3, right=2.1cm of B1] (label1) {Prescribe values for coefficients\\ $\alpha$, $\beta$ and for $LAI$:};
895
896        \coordinate (curvelabel11) at (5.9cm,-0.5cm);
897        \node [Key3, right=1.0cm of curvelabel11] (curvelabel12) {\texttt{alpha\_lad},\\ \texttt{beta\_lad},\\ \texttt{lai\_beta}.};
898\end{tikzpicture}
899
900
901\end{frame}
902
903
904
905%Folie 13
906\begin{frame}
907   \frametitle{Basic canopy parameters (III)}
908   \begin{footnotesize}
909    \begin{itemize}
910       \item<1->{Step III: Prescribe a value for the parameter {\small \texttt{canopy\_drag\_coeff (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.}
911    \end{itemize}
912   
913
914   \begin{minipage}{0.47\textwidth}
915      \begin{center}
916         \includegraphics[width=1\textwidth]{canopy_model_figures/large.png}\\
917      \end{center}
918   \end{minipage}
919   \hfill
920   \begin{minipage}{0.47\textwidth}
921      \begin{center}
922         \includegraphics[width=1\textwidth]{canopy_model_figures/small.png}\\
923      \end{center}
924   \end{minipage}
925   
926   \begin{minipage}{0.47\textwidth}
927      \begin{center}
928         Strong trees offer a larger form drag to the flow.
929      \end{center}
930   \end{minipage}
931   \hfill
932   \begin{minipage}{0.47\textwidth}
933      \begin{center}
934         Young / small trees offer a smaller form drag to the flow because they are more flexible.
935      \end{center}
936   \end{minipage}
937   
938   \end{footnotesize}
939
940\end{frame}
941
942
943
944%Folie 14
945\begin{frame}
946   \frametitle{Basic canopy parameters (IV)}
947   \begin{itemize}
948      \item<1->{For steering the effect of the sensible heat transfer inside the canopy, prescribe a value for the sensible heat flux at the canopy top, using the parameter \texttt{cthf} (see Methods (III)).}
949      \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\_conc} and \texttt{leaf\_scalar\_exch\_coeff} (see Methods (IV)).}
950   \end{itemize}
951\end{frame}
952
953
954
955%Folie 15
956\begin{frame}
957   \frametitle{User-defined canopy}
958   \begin{footnotesize}
959   Do you want to simulate a more customized canopy, which e.g. covers only half the model surface?\\
960    \begin{itemize}
961       \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')}}.}
962       \item<3->{Step II: In your parameter file set: {\scriptsize \texttt{canopy\_mode = 'user\_defined\_canopy\_1'}}}
963    \end{itemize}
964   \end{footnotesize}
965   \vspace{7pt}
966
967   \tikzstyle{background} = [rectangle, fill=gray!10, text width=1\textwidth, text centered, rounded corners, minimum height=10em]
968   \tikzstyle{Key1} = [rectangle, draw, fill=gray!70, text width=0.05, minimum size=0.05, font=\tiny]
969   \tikzstyle{Key2} = [rectangle, draw, fill=green!90, text width=0.05, minimum size=0.05, font=\tiny]
970   \tikzstyle{Key3} = [rectangle, text width=2.0cm, minimum size=4pt, font=\tiny]
971   \tikzstyle{text1} = [rectangle, text width=0.4\textwidth, minimum height=10em]
972\begin{tikzpicture}[>=latex']
973        %%% Edit the following coordinate to change the shape of your
974        %%% cuboid
975     
976        %% Vanishing points for perspective handling
977        \coordinate (P1) at (-4cm,1.5cm); % left vanishing point (To pick)
978        \coordinate (P2) at (10cm,1.5cm); % right vanishing point (To pick)
979
980        %% (A1) and (A2) defines the 2 central points of the cuboid
981        \coordinate (A1) at (0cm,0cm); % central top point (To pick)
982        \coordinate (A2) at (0cm,-2cm); % central bottom point (To pick)
983
984        %% (A3) to (A8) are computed given a unique parameter (or 2) .8
985        % You can vary .8 from 0 to 1 to change perspective on left side
986        \coordinate (A3) at ($(P1)!.8!(A2)$); % To pick for perspective
987        \coordinate (A4) at ($(P1)!.8!(A1)$);
988
989        % You can vary .8 from 0 to 1 to change perspective on right side
990        \coordinate (A7) at ($(P2)!.7!(A2)$);
991        \coordinate (A8) at ($(P2)!.7!(A1)$);
992
993        %% Automatically compute the last 2 points with intersections
994        \coordinate (A5) at
995          (intersection cs: first line={(A8) -- (P1)},
996                            second line={(A4) -- (P2)});
997        \coordinate (A6) at
998          (intersection cs: first line={(A7) -- (P1)},
999                            second line={(A3) -- (P2)});
1000
1001        %% Drawing the canopy layer
1002        \coordinate (A9) at (0em,-1.7cm); % central bottom point (To pick)
1003        \coordinate (A10) at ($(P2)!.7!(A9)$);
1004        \coordinate (A12) at ($(P1)!.8!(A9)$); % To pick for perspective
1005        \coordinate (A11) at
1006          (intersection cs: first line={(A10) -- (P1)},
1007                            second line={(A12) -- (P2)});
1008       
1009        \coordinate (A13) at ($(A9)!.54!(A10)$);
1010        \coordinate (A14) at ($(A2)!.54!(A7)$);
1011       
1012        \coordinate (A15) at
1013                  (intersection cs: first line={(A13) -- (P1)},
1014                                    second line={(A12) -- (P2)});
1015        \coordinate (A16) at
1016                  (intersection cs: first line={(A14) -- (P1)},
1017                                    second line={(A3) -- (P2)});
1018        %%% Depending of what you want to display, you can comment/edit
1019        %%% the following lines
1020       
1021        {\node [background, right=-0.8cm of A12] (background) {};}
1022
1023        %% Possibly draw back faces
1024
1025        \fill[gray!70] (A2) -- (A3) -- (A6) -- (A7) -- cycle; % face 6
1026        \node at (barycentric cs:A2=1,A3=1,A6=1,A7=1) {\tiny };
1027       
1028        \fill[gray!30] (A3) -- (A4) -- (A5) -- (A6) -- cycle; % face 3
1029        \node at (barycentric cs:A3=1,A4=1,A5=1,A6=1) {\tiny };
1030       
1031        \fill[gray!10] (A5) -- (A6) -- (A7) -- (A8) -- cycle; % face 4
1032        \node at (barycentric cs:A5=1,A6=1,A7=1,A8=1) {\tiny };
1033       
1034       
1035        \fill[green!90] (A13) -- (A10) -- (A11) -- (A15) -- cycle; % face 4
1036        \node at (barycentric cs:A9=1,A10=1,A11=1,A12=1) {\tiny };
1037       
1038        \fill[green!100] (A13) -- (A15) -- (A16) -- (A14) -- cycle; % face 4
1039        \node at (barycentric cs:A9=1,A12=1,A3=1,A2=1) {\tiny };
1040       
1041        \fill[green!100] (A13) -- (A10) -- (A7) -- (A14) -- cycle; % face 4
1042        \node at (barycentric cs:A9=1,A10=1,A7=1,A2=1) {\tiny };
1043       
1044        \draw[thin,dashed] (A5) -- (A6);
1045        \draw[thin,dashed] (A3) -- (A6);
1046        \draw[thin,dashed] (A7) -- (A6);
1047
1048        \draw[thin,dashed] (A11) -- (A15);
1049        \draw[thin,dashed] (A10) -- (A11);
1050       
1051        %% Possibly draw front faces
1052
1053        % \fill[orange] (A1) -- (A8) -- (A7) -- (A2) -- cycle; % face 1
1054        % \node at (barycentric cs:A1=1,A8=1,A7=1,A2=1) {\tiny f1};
1055        \fill[gray!50,opacity=0.2] (A1) -- (A2) -- (A3) -- (A4) -- cycle; % f2
1056        \node at (barycentric cs:A1=1,A2=1,A3=1,A4=1) {\tiny };
1057        \fill[gray!90,opacity=0.2] (A1) -- (A4) -- (A5) -- (A8) -- cycle; % f5
1058        \node at (barycentric cs:A1=1,A4=1,A5=1,A8=1) {\tiny };
1059
1060        %% Possibly draw front lines
1061        \draw[thin] (A1) -- (A2);
1062        \draw[thin] (A3) -- (A4);
1063        \draw[thin] (A7) -- (A8);
1064        \draw[thin] (A1) -- (A4);
1065        \draw[thin] (A1) -- (A8);
1066        \draw[thin] (A2) -- (A3);
1067        \draw[thin] (A2) -- (A7);
1068        \draw[thin] (A4) -- (A5);
1069        \draw[thin] (A8) -- (A5);
1070       
1071        \draw[thin] (A13) -- (A10);
1072        \draw[thin] (A13) -- (A15);
1073        \draw[thin] (A14) -- (A16);
1074        \draw[thin] (A13) -- (A14);
1075        \draw[thin] (A15) -- (A16);
1076       
1077        % Possibly draw points
1078        % (it can help you understand the cuboid structure)
1079        \foreach \i in {1,2,...,16}
1080        {
1081        %  \draw[fill=black] (A\i) circle (0.05em)
1082        %    node[above right] {\tiny \i};
1083        }
1084        % \draw[fill=black] (P1) circle (0.1em) node[below] {\tiny p1};
1085        % \draw[fill=black] (P2) circle (0.1em) node[below] {\tiny p2};
1086       
1087        %Key   
1088        \coordinate (K1) at (0.5cm,-2.3cm);
1089        \coordinate (K2) at (0.5cm,-2.7cm);
1090       
1091       
1092        \node [Key1, right=0.0cm of K1] (key1) {};
1093        \node [Key2, right=0.0cm of K2] (key2) {};
1094        \node [Key3, right=0.4cm of K1] (key11) {Total model domain};
1095        \node [Key3, right=0.4cm of K2] (key21) {Plant canopy volume};
1096       
1097        % % Text
1098        \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 in: \texttt{user\_init\_plant\_canopy.f90}}};}
1099\end{tikzpicture}
1100
1101
1102\end{frame}
1103
1104\end{document}
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