source: palm/trunk/TUTORIAL/SOURCE/canopy_model.tex @ 1264

Last change on this file since 1264 was 1205, checked in by kanani, 11 years ago

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

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[1080]1%$Id: canopy_model.tex 1205 2013-07-15 10:55:47Z fricke $
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}
[1205]68      \item<1->{The canopy model embedded in PALM can be used to study the effect of a plant canopy on e.g.:}
[1080]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}
[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.}
[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:}
76      \begin{itemize}
[1205]77         \item<7->{leaf area density,}
[1080]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.}
[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.
[1080]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}
[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}}).}
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}}).}
[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.
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.}
[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):\\
[1080]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      }
[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}}.}
[1080]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}
[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 };
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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