source: palm/trunk/TUTORIAL/SOURCE/canopy_model.tex @ 1597

Last change on this file since 1597 was 1515, checked in by boeske, 10 years ago

several updates in the tutorial

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1%$Id: canopy_model.tex 1515 2015-01-02 11:35:51Z gronemeier $
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{Institute of Meteorology and Climatology, Leibniz UniversitÀt Hannover}
30\selectlanguage{english}
31\date{last update: \today}
32\event{PALM Seminar}
33\setbeamertemplate{navigation symbols}{}
34
35\setbeamertemplate{footline}
36  {%
37    \begin{beamercolorbox}[rightskip=-0.1cm]&
38     {\includegraphics[height=0.65cm]{imuk_logo.pdf}\hfill \includegraphics[height=0.65cm]{luh_logo.pdf}}
39    \end{beamercolorbox}
40    \begin{beamercolorbox}[ht=2.5ex,dp=1.125ex,%
41      leftskip=.3cm,rightskip=0.3cm plus1fil]{title in head/foot}%
42      {\leavevmode{\usebeamerfont{author in head/foot}\insertshortauthor} \hfill \eventname \hfill \insertframenumber \; / \inserttotalframenumber}%
43    \end{beamercolorbox}%
44%    \begin{beamercolorbox}[colsep=1.5pt]{lower separation line foot}%
45%    \end{beamercolorbox}
46  }
47%\logo{\includegraphics[width=0.3\textwidth]{luhimuk_logo.png}}
48
49\title[PALM's Canopy Model]{PALM's Canopy Model}
50\author{PALM group}
51
52
53% Notes:
54% jede subsection bekommt einen punkt im menu (vertikal ausgerichtet.
55% jeder frame in einer subsection bekommt einen punkt (horizontal ausgerichtet)
56\begin{document}
57
58\begin{frame}
59\titlepage
60\end{frame}
61
62\section{PALM's Canopy Model}
63\subsection{The embedded Canopy Model}
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->{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.}
76      \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:}
77      \begin{itemize}
78         \item<7->{leaf area density,}
79         \item<8->{drag coefficient.}
80      \end{itemize}
81   \end{itemize}
82\end{frame}
83
84
85
86%Folie 02
87\begin{frame}
88   \frametitle{Theory (I)}
89   \begin{footnotesize}
90   \begin{itemize}
91      \item<1->{A plant canopy affects the flow by acting as a momentum sink due to form and viscous drag forces.}
92      \item<2->{The effectiveness of momentum absorption depends on the amount of leaf area per unit volume and the aerodynamic drag.}
93      \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.
94         \begin{center}
95            \includegraphics[width=0.5\textwidth]{canopy_model_figures/abb1.png}
96         \end{center}
97      }
98   \end{itemize}
99   \end{footnotesize}
100\end{frame}
101
102
103
104%Folie 03
105\begin{frame}
106   \frametitle{Theory (II)}
107   \begin{footnotesize}
108   \begin{itemize}
109      \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}}).}
110      \item<2->{Wave breaking induces further instabilities, whereby a longitudinal component is added to the developing turbulence structures (\textcircled{{\tiny 2}} \& \textcircled{{\tiny 3}}).}
111      \item<3->{Due to the persistent instabilities the turbulence structures develop a distinct three-dimensionality (\textcircled{{\tiny 4}}).}
112      \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.
113         \begin{center}
114            \includegraphics[width=0.5\textwidth]{canopy_model_figures/abb2.png}
115         \end{center}
116      }
117   \end{itemize}
118   \end{footnotesize}
119\end{frame}
120
121
122
123%Folie 04
124\begin{frame}
125   \frametitle{Methods (I)}
126   \begin{footnotesize}
127   \begin{itemize}
128      \item<1->{The canopy model in PALM is based on the models used by Shaw and Schumann (1992) and Watanabe (2004).}
129      \item<2->{The aerodynamic effect of the canopy on the turbulent flow is accounted for by an additional term in the momentum equations:\\
130         \begin{align*}
131            \frac{\partial \bar{u}_{i}}{\partial t} = \text{...} - c_{d} a U \bar{u}_{i}
132         \end{align*}
133      }
134      \begin{itemize}
135         \item<3->{ $c_{d}$ : drag coefficient}
136         \item<4->{ $a $ : leaf area density $[m^{2}m^{-3}]$}
137         \item<5->{ $U$ : $(u^{2} + v^{2} + w^{2})^{1/2}$ $[m s^{-1}]$}
138         \item<6->{ $u_{i}$ : velocity component ($u_{1}=u$, $u_{2}=v$, $u_{3}=w$)}
139      \end{itemize}
140   \end{itemize}
141   \uncover<7->{Note: The canopy model does not resolve the effect of single plant elements.}
142   \end{footnotesize}
143\end{frame}
144
145
146
147%Folie 05
148\begin{frame}
149   \frametitle{Methods (II)}
150   \begin{footnotesize}
151   \begin{itemize}
152      \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:\\
153         \begin{align*}
154            \frac{\partial e}{\partial t} = \text{...} - 2 c_{d} a U e
155         \end{align*}
156      }
157      \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).}
158   \end{itemize}
159   \end{footnotesize}
160\end{frame}
161
162
163
164%Folie 06
165\begin{frame}
166   \frametitle{Methods (III)}
167   \begin{footnotesize}
168   \begin{itemize}
169      \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:\\
170         \begin{align*}
171            \frac{\partial \bar{\theta}}{\partial t} = \text{...} +  S_{\theta}
172         \end{align*}
173      }
174      \item<2->{It is assumed that the foliage is warmed by the penetrating solar radiation and, in turn, warms the surrounding air.}
175      \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):\\
176         \begin{align*}
177            Q_{\theta}(z) = Q_{\theta}(h) exp(-\alpha F) \text{ , } Q_{\theta}(h) \text{ : Heat flux at canopy top}
178         \end{align*}
179      }
180      \begin{itemize}
181         \item<4->{ $\alpha = 0.6$ (extinction coefficient)}
182         \item<5->{ $F = \int\limits_{z}^{h} a \: dz$ (downward cumulative leaf area index)}
183      \end{itemize}
184   \end{itemize}
185   \end{footnotesize}
186\end{frame}
187
188
189
190%Folie 07
191\begin{frame}
192   \frametitle{Methods (IV)}
193   \begin{footnotesize}
194   \begin{itemize}
195      \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:\\
196         \begin{align*}
197            \frac{\partial \bar{q}}{\partial t} = \text{...} - c_{q} a U (\bar{q} - q_{c})
198         \end{align*}
199      }
200      \begin{itemize}
201         \item<2->{ $c_{q}$ : scalar exchange coefficient}
202         \item<3->{ $q_{c}$ : scalar concentration at leaf surface}
203      \end{itemize}
204   \end{itemize}
205   \end{footnotesize}
206\end{frame}
207
208
209
210%Folie 08
211\begin{frame}
212   \frametitle{Basics (I)}
213   \begin{itemize}
214      \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}}).}
215      \item<2->{All parameters for steering the canopy model are described in:\\
216      {\scriptsize Documentation $\rightarrow$ Model steering $\rightarrow$ Parameters $\rightarrow$ Initialization $\rightarrow$ Canopy}\\
217      (http://palm.muk.uni-hannover.de)
218      }
219      \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}}.}
220   \end{itemize}
221\end{frame}
222
223
224
225%Folie 09
226\begin{frame}
227   \frametitle{Basic canopy parameter (I)}
228   The parameters for steering the canopy model have to be added to the \&inipar {\small \texttt{NAMELIST}} in the parameter file ({\small \texttt{PARIN}}).\\
229    \begin{itemize}
230       \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.}
231    \end{itemize}
232   \vspace{10pt}
233
234   \tikzstyle{background} = [rectangle, fill=gray!10, text width=1\textwidth, text centered, rounded corners, minimum height=10em]
235   \tikzstyle{Key1} = [rectangle, draw, fill=gray!70, text width=0.05, minimum size=0.05, font=\tiny]
236   \tikzstyle{Key2} = [rectangle, draw, fill=green!90, text width=0.05, minimum size=0.05, font=\tiny]
237   \tikzstyle{Key3} = [rectangle, text width=3.0cm, minimum size=16pt, font=\tiny]
238
239\begin{tikzpicture}[>=latex']
240        %%% Edit the following coordinate to change the shape of your
241        %%% cuboid
242
243        %% Vanishing points for perspective handling
244        \coordinate (P1) at (-4cm,1.5cm); % left vanishing point (To pick)
245        \coordinate (P2) at (10cm,1.5cm); % right vanishing point (To pick)
246
247        %% (A1) and (A2) defines the 2 central points of the cuboid
248        \coordinate (A1) at (0cm,0cm); % central top point (To pick)
249        \coordinate (A2) at (0cm,-2cm); % central bottom point (To pick)
250       
251        %% (A3) to (A8) are computed given a unique parameter (or 2) .8
252        % You can vary .8 from 0 to 1 to change perspective on left side
253        \coordinate (A3) at ($(P1)!.8!(A2)$); % To pick for perspective
254        \coordinate (A4) at ($(P1)!.8!(A1)$);
255
256        % You can vary .8 from 0 to 1 to change perspective on right side
257        \coordinate (A7) at ($(P2)!.7!(A2)$);
258        \coordinate (A8) at ($(P2)!.7!(A1)$);
259
260        %% Automatically compute the last 2 points with intersections
261        \coordinate (A5) at
262          (intersection cs: first line={(A8) -- (P1)},
263                            second line={(A4) -- (P2)});
264        \coordinate (A6) at
265          (intersection cs: first line={(A7) -- (P1)},
266                            second line={(A3) -- (P2)});
267
268        %% Drawing the canopy layer
269        \coordinate (A9) at (0em,-1.7cm); % central bottom point (To pick)
270        \coordinate (A10) at ($(P2)!.7!(A9)$);
271        \coordinate (A12) at ($(P1)!.8!(A9)$); % To pick for perspective
272        \coordinate (A11) at
273          (intersection cs: first line={(A10) -- (P1)},
274                            second line={(A12) -- (P2)});
275
276        %%% Depending of what you want to display, you can comment/edit
277        %%% the following lines
278
279        {\node [background, right=-0.8cm of A12] (background) {};}
280
281        %% Possibly draw back faces
282
283        \fill[gray!70] (A2) -- (A3) -- (A6) -- (A7) -- cycle; % face 6
284        \node at (barycentric cs:A2=1,A3=1,A6=1,A7=1) {\tiny };
285       
286        \fill[gray!30] (A3) -- (A4) -- (A5) -- (A6) -- cycle; % face 3
287        \node at (barycentric cs:A3=1,A4=1,A5=1,A6=1) {\tiny };
288       
289        \fill[gray!10] (A5) -- (A6) -- (A7) -- (A8) -- cycle; % face 4
290        \node at (barycentric cs:A5=1,A6=1,A7=1,A8=1) {\tiny };
291       
292       
293        \fill[green!90] (A9) -- (A10) -- (A11) -- (A12) -- cycle; % face 7
294        \node at (barycentric cs:A9=1,A10=1,A11=1,A12=1) {\tiny };
295       
296        \fill[green!100] (A9) -- (A12) -- (A3) -- (A2) -- cycle; % face 8
297        \node at (barycentric cs:A9=1,A12=1,A3=1,A2=1) {\tiny };
298       
299        \fill[green!100] (A9) -- (A10) -- (A7) -- (A2) -- cycle; % face 9
300        \node at (barycentric cs:A9=1,A10=1,A7=1,A2=1) {\tiny };
301       
302        \draw[thin,dashed] (A5) -- (A6);
303        \draw[thin,dashed] (A3) -- (A6);
304        \draw[thin,dashed] (A7) -- (A6);
305
306        \draw[thin,dashed] (A11) -- (A12);
307        \draw[thin,dashed] (A10) -- (A11);
308       
309        %% Possibly draw front faces
310
311        % \fill[orange] (A1) -- (A8) -- (A7) -- (A2) -- cycle; % face 1
312        % \node at (barycentric cs:A1=1,A8=1,A7=1,A2=1) {\tiny f1};
313        \fill[gray!50,opacity=0.2] (A1) -- (A2) -- (A3) -- (A4) -- cycle; % f2
314        \node at (barycentric cs:A1=1,A2=1,A3=1,A4=1) {\tiny };
315        \fill[gray!90,opacity=0.2] (A1) -- (A4) -- (A5) -- (A8) -- cycle; % f5
316        \node at (barycentric cs:A1=1,A4=1,A5=1,A8=1) {\tiny };
317
318        %% Possibly draw front lines
319        \draw[thin] (A1) -- (A2);
320        \draw[thin] (A3) -- (A4);
321        \draw[thin] (A7) -- (A8);
322        \draw[thin] (A1) -- (A4);
323        \draw[thin] (A1) -- (A8);
324        \draw[thin] (A2) -- (A3);
325        \draw[thin] (A2) -- (A7);
326        \draw[thin] (A4) -- (A5);
327        \draw[thin] (A8) -- (A5);
328       
329        \draw[thin] (A9) -- (A10);
330        \draw[thin] (A9) -- (A12);
331       
332        % Possibly draw points
333        % (it can help you understand the cuboid structure)
334        \foreach \i in {1,2,...,12}
335        {
336        %  \draw[fill=black] (A\i) circle (0.05em)
337        %    node[above right] {\tiny \i};
338        }
339        % \draw[fill=black] (P1) circle (0.1em) node[below] {\tiny p1};
340        % \draw[fill=black] (P2) circle (0.1em) node[below] {\tiny p2};
341       
342        %Key   
343        \coordinate (K1) at (0.5cm,-2.3cm);
344        \coordinate (K2) at (0.5cm,-2.7cm);
345       
346       
347        \node [Key1, right=0.0cm of K1] (key1) {};
348        \node [Key2, right=0.0cm of K2] (key2) {};
349        \node [Key3, right=0.4cm of K1] (key11) {Total model domain};
350        \node [Key3, right=0.4cm of K2] (key21) {Plant canopy volume};
351       
352        %% frame specific elements
353        \node [Key3, right=0.45cm of A10] (label1) {\texttt{zw(pch\_index)} = canopy top};
354        \node [Key3, right=0.05cm of A10] (label0) {};
355       
356        \draw[<-] (label0) -- (label1);
357\end{tikzpicture}
358
359
360\end{frame}
361
362
363
364%Folie 10
365\begin{frame}
366   \frametitle{Basic canopy parameter (II)}
367    \begin{itemize}
368       \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.\\
369       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.
370       }
371    \end{itemize}
372   \vspace{10pt}
373
374   \tikzstyle{background} = [rectangle, fill=gray!10, text width=1\textwidth, text centered, rounded corners, minimum height=10em]
375   \tikzstyle{Key1} = [rectangle, draw, fill=gray!70, text width=0.05, minimum size=0.05, font=\tiny]
376   \tikzstyle{Key2} = [rectangle, draw, fill=green!90, text width=0.05, minimum size=0.05, font=\tiny]
377   \tikzstyle{Key3} = [rectangle, text width=4.5cm, minimum size=16pt, font=\tiny]
378   \tikzstyle{label} = [rectangle, text width=2.0cm, align=center, minimum size=16pt, font=\tiny]
379
380\begin{tikzpicture}[>=latex']
381        %%% Edit the following coordinate to change the shape of your
382        %%% cuboid
383
384        %% Vanishing points for perspective handling
385        \coordinate (P1) at (-4cm,1.5cm); % left vanishing point (To pick)
386        \coordinate (P2) at (10cm,1.5cm); % right vanishing point (To pick)
387
388        %% (A1) and (A2) defines the 2 central points of the cuboid
389        \coordinate (A1) at (0cm,0cm); % central top point (To pick)
390        \coordinate (A2) at (0cm,-2cm); % central bottom point (To pick)
391       
392        %% (A3) to (A8) are computed given a unique parameter (or 2) .8
393        % You can vary .8 from 0 to 1 to change perspective on left side
394        \coordinate (A3) at ($(P1)!.8!(A2)$); % To pick for perspective
395        \coordinate (A4) at ($(P1)!.8!(A1)$);
396
397        % You can vary .8 from 0 to 1 to change perspective on right side
398        \coordinate (A7) at ($(P2)!.7!(A2)$);
399        \coordinate (A8) at ($(P2)!.7!(A1)$);
400
401        %% Automatically compute the last 2 points with intersections
402        \coordinate (A5) at
403          (intersection cs: first line={(A8) -- (P1)},
404                            second line={(A4) -- (P2)});
405        \coordinate (A6) at
406          (intersection cs: first line={(A7) -- (P1)},
407                            second line={(A3) -- (P2)});
408
409        %% Drawing the canopy layer
410        \coordinate (A9) at (0em,-1.7cm); % central bottom point (To pick)
411        \coordinate (A10) at ($(P2)!.7!(A9)$);
412        \coordinate (A12) at ($(P1)!.8!(A9)$); % To pick for perspective
413        \coordinate (A11) at
414          (intersection cs: first line={(A10) -- (P1)},
415                            second line={(A12) -- (P2)});
416
417        %%% Depending of what you want to display, you can comment/edit
418        %%% the following lines
419
420        {\node [background, right=-0.8cm of A12] (background) {};}
421
422        %% Possibly draw back faces
423
424        \fill[gray!70] (A2) -- (A3) -- (A6) -- (A7) -- cycle; % face 6
425        \node at (barycentric cs:A2=1,A3=1,A6=1,A7=1) {\tiny };
426       
427        \fill[gray!30] (A3) -- (A4) -- (A5) -- (A6) -- cycle; % face 3
428        \node at (barycentric cs:A3=1,A4=1,A5=1,A6=1) {\tiny };
429       
430        \fill[gray!10] (A5) -- (A6) -- (A7) -- (A8) -- cycle; % face 4
431        \node at (barycentric cs:A5=1,A6=1,A7=1,A8=1) {\tiny };
432       
433       
434        \fill[green!90] (A9) -- (A10) -- (A11) -- (A12) -- cycle; % face 7
435        \node at (barycentric cs:A9=1,A10=1,A11=1,A12=1) {\tiny };
436       
437        \fill[green!100] (A9) -- (A12) -- (A3) -- (A2) -- cycle; % face 8
438        \node at (barycentric cs:A9=1,A12=1,A3=1,A2=1) {\tiny };
439       
440        \fill[green!100] (A9) -- (A10) -- (A7) -- (A2) -- cycle; % face 9
441        \node at (barycentric cs:A9=1,A10=1,A7=1,A2=1) {\tiny };
442       
443        \draw[thin,dashed] (A5) -- (A6);
444        \draw[thin,dashed] (A3) -- (A6);
445        \draw[thin,dashed] (A7) -- (A6);
446
447        \draw[thin,dashed] (A11) -- (A12);
448        \draw[thin,dashed] (A10) -- (A11);
449       
450        %% Possibly draw front faces
451
452        % \fill[orange] (A1) -- (A8) -- (A7) -- (A2) -- cycle; % face 1
453        % \node at (barycentric cs:A1=1,A8=1,A7=1,A2=1) {\tiny f1};
454        \fill[gray!50,opacity=0.2] (A1) -- (A2) -- (A3) -- (A4) -- cycle; % f2
455        \node at (barycentric cs:A1=1,A2=1,A3=1,A4=1) {\tiny };
456        \fill[gray!90,opacity=0.2] (A1) -- (A4) -- (A5) -- (A8) -- cycle; % f5
457        \node at (barycentric cs:A1=1,A4=1,A5=1,A8=1) {\tiny };
458
459        %% Possibly draw front lines
460        \draw[thin] (A1) -- (A2);
461        \draw[thin] (A3) -- (A4);
462        \draw[thin] (A7) -- (A8);
463        \draw[thin] (A1) -- (A4);
464        \draw[thin] (A1) -- (A8);
465        \draw[thin] (A2) -- (A3);
466        \draw[thin] (A2) -- (A7);
467        \draw[thin] (A4) -- (A5);
468        \draw[thin] (A8) -- (A5);
469       
470        \draw[thin] (A9) -- (A10);
471        \draw[thin] (A9) -- (A12);
472       
473        % Possibly draw points
474        % (it can help you understand the cuboid structure)
475        \foreach \i in {1,2,...,12}
476        {
477        %  \draw[fill=black] (A\i) circle (0.05em)
478        %    node[above right] {\tiny \i};
479        }
480        % \draw[fill=black] (P1) circle (0.1em) node[below] {\tiny p1};
481        % \draw[fill=black] (P2) circle (0.1em) node[below] {\tiny p2};
482       
483        %Key   
484        \coordinate (K1) at (0.5cm,-2.3cm);
485        \coordinate (K2) at (0.5cm,-2.7cm);
486       
487       
488        \node [Key1, right=0.0cm of K1] (key1) {};
489        \node [Key2, right=0.0cm of K2] (key2) {};
490        \node [Key3, right=0.4cm of K1] (key11) {Total model domain};
491        \node [Key3, right=0.4cm of K2] (key21) {Plant canopy volume};
492       
493        %% frame specific elements
494       
495        %% boundary layer profile 2D
496        \coordinate (B1) at (4.0cm,0.3cm);
497        \coordinate (B2) at (4.0cm,-2.5cm);
498       
499        \coordinate (B3) at (4.0cm,0.6cm);
500        \coordinate (B4) at (6.6cm,-2.5cm);
501       
502        \draw[thin, dotted] (A10) -- (B1);
503        \draw[thin, dotted] (A7) -- (B2);
504        \draw[<-] (B3) -- (B2);
505        \draw[<-] (B4) -- (B2);
506       
507        \coordinate (xlab) at (5.3cm,-2.5cm);
508        \coordinate (ylab) at (4.0cm,-1.1cm);
509        \node [label, below=0.0cm of xlab] (xlabel) {lad $[m^{2}m^{-3}]$};
510        \node [label, rotate=90, above=0.0cm of ylab] (ylabel) {z$[m]$};
511       
512       
513        \coordinate (B5) at (4.5cm,-2.5cm);
514%       \draw [-,color=red] (B1) to [out=-10,in=90,looseness=2.0, relative=false] .. controls (4,0) and (5,0) .. (B5);
515        \draw {(B1) .. controls (8.0,-0.2) and (4.5,-1.0) .. (B5)};
516       
517        \draw [decorate, decoration={markings,
518                mark=at position 00mm with{\draw[fill=black] (0,0) circle (0.1em);},
519                mark=at position 04mm with{\draw[fill=black] (0,0) circle (0.1em);},
520                mark=at position 08mm with{\draw[fill=black] (0,0) circle (0.1em);},
521                mark=at position 12mm with{\draw[fill=black] (0,0) circle (0.1em);},
522                mark=at position 16mm with{\draw[fill=black] (0,0) circle (0.1em);},
523                mark=at position 20mm with{\draw[fill=black] (0,0) circle (0.1em);},
524                mark=at position 24mm with{\draw[fill=black] (0,0) circle (0.1em);},
525                mark=at position 28mm with{\draw[fill=black] (0,0) circle (0.1em);},
526                mark=at position 32mm with{\draw[fill=black] (0,0) circle (0.1em);},
527                mark=at position 36mm with{\draw[fill=black] (0,0) circle (0.1em);},
528                mark=at position 40mm with{\draw[fill=black] (0,0) circle (0.1em);},
529                mark=at position 44mm with{\draw[fill=black] (0,0) circle (0.1em);},
530                }]
531                {(B5) .. controls (4.5,-1.0) and (8.0,-0.2) .. (B1)};
532
533        \node [Key3, right=1.1cm of B1] (label1) {\texttt{zu(pch\_index + 1)}: lad = 0.0 (default)};
534        \node [Key3, left=0.1cm of B1] (label0) {};
535        \draw[-, dashed] (label0) -- (label1);
536       
537        \coordinate (curvelabel00) at (4.65cm,-2.45cm);
538        \coordinate (curvelabel01) at (5.0cm,-2.25cm);
539        \draw[<-] (curvelabel00) -- (curvelabel01);
540        \node [Key3, right=0.0cm of curvelabel01] (curvelabel02) {\texttt{lad\_surface} (default 0.0)};
541       
542        \coordinate (curvelabel10) at (5.4cm,-1.3cm);
543        \coordinate (curvelabel11) at (5.6cm,-1.6cm);
544        \draw[<-] (curvelabel10) -- (curvelabel11);
545        \node [Key3, right=0.0cm of curvelabel11] (curvelabel12) {\texttt{lad\_vertical\_gradient\_level} (5)};
546       
547        \coordinate (curvelabel10) at (5.47cm,-1.05cm);
548        \coordinate (curvelabel11) at (5.8cm,-1.3cm);
549        \draw[<-] (curvelabel10) -- (curvelabel11);
550        \node [Key3, right=0.0cm of curvelabel11] (curvelabel12) {\texttt{lad\_vertical\_gradient} (5)};
551       
552        \coordinate (curvelabel10) at (5.7cm,-0.93cm);
553        \coordinate (curvelabel11) at (5.9cm,-1.0cm);
554        \draw[<-] (curvelabel10) -- (curvelabel11);
555        \node [Key3, right=0.0cm of curvelabel11] (curvelabel12) {\texttt{lad\_vertical\_gradient\_level} (6)};
556\end{tikzpicture}
557
558
559\end{frame}
560
561
562
563%Folie 11
564\begin{frame}
565   \frametitle{Basic canopy parameter (III)}
566   \begin{footnotesize}
567    \begin{itemize}
568       \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.}
569    \end{itemize}
570   
571
572   \begin{minipage}{0.47\textwidth}
573      \begin{center}
574         \includegraphics[width=1\textwidth]{canopy_model_figures/large.png}\\
575      \end{center}
576   \end{minipage}
577   \hfill
578   \begin{minipage}{0.47\textwidth}
579      \begin{center}
580         \includegraphics[width=1\textwidth]{canopy_model_figures/small.png}\\
581      \end{center}
582   \end{minipage}
583   
584   \begin{minipage}{0.47\textwidth}
585      \begin{center}
586         Strong trees offer a larger form drag to the flow.
587      \end{center}
588   \end{minipage}
589   \hfill
590   \begin{minipage}{0.47\textwidth}
591      \begin{center}
592         Young / small trees offer a smaller form drag to the flow because they are more flexible.
593      \end{center}
594   \end{minipage}
595   
596   \end{footnotesize}
597
598\end{frame}
599
600
601
602%Folie 12
603\begin{frame}
604   \frametitle{Basic canopy parameter (IV)}
605   \begin{itemize}
606      \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)).}
607      \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)).}
608   \end{itemize}
609\end{frame}
610
611
612
613%Folie 13
614\begin{frame}
615   \frametitle{User-defined canopy}
616   \begin{footnotesize}
617   Do you want to simulate a more customized canopy, which e.g. covers only half the model surface?\\
618    \begin{itemize}
619       \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')}}.}
620       \item<3->{Step II: In your parameter file set: {\scriptsize \texttt{canopy\_mode = 'user\_defined\_canopy\_1'}}}
621    \end{itemize}
622   \end{footnotesize}
623   \vspace{7pt}
624
625   \tikzstyle{background} = [rectangle, fill=gray!10, text width=1\textwidth, text centered, rounded corners, minimum height=10em]
626   \tikzstyle{Key1} = [rectangle, draw, fill=gray!70, text width=0.05, minimum size=0.05, font=\tiny]
627   \tikzstyle{Key2} = [rectangle, draw, fill=green!90, text width=0.05, minimum size=0.05, font=\tiny]
628   \tikzstyle{Key3} = [rectangle, text width=2.0cm, minimum size=4pt, font=\tiny]
629   \tikzstyle{text1} = [rectangle, text width=0.4\textwidth, minimum height=10em]
630\begin{tikzpicture}[>=latex']
631        %%% Edit the following coordinate to change the shape of your
632        %%% cuboid
633     
634        %% Vanishing points for perspective handling
635        \coordinate (P1) at (-4cm,1.5cm); % left vanishing point (To pick)
636        \coordinate (P2) at (10cm,1.5cm); % right vanishing point (To pick)
637
638        %% (A1) and (A2) defines the 2 central points of the cuboid
639        \coordinate (A1) at (0cm,0cm); % central top point (To pick)
640        \coordinate (A2) at (0cm,-2cm); % central bottom point (To pick)
641
642        %% (A3) to (A8) are computed given a unique parameter (or 2) .8
643        % You can vary .8 from 0 to 1 to change perspective on left side
644        \coordinate (A3) at ($(P1)!.8!(A2)$); % To pick for perspective
645        \coordinate (A4) at ($(P1)!.8!(A1)$);
646
647        % You can vary .8 from 0 to 1 to change perspective on right side
648        \coordinate (A7) at ($(P2)!.7!(A2)$);
649        \coordinate (A8) at ($(P2)!.7!(A1)$);
650
651        %% Automatically compute the last 2 points with intersections
652        \coordinate (A5) at
653          (intersection cs: first line={(A8) -- (P1)},
654                            second line={(A4) -- (P2)});
655        \coordinate (A6) at
656          (intersection cs: first line={(A7) -- (P1)},
657                            second line={(A3) -- (P2)});
658
659        %% Drawing the canopy layer
660        \coordinate (A9) at (0em,-1.7cm); % central bottom point (To pick)
661        \coordinate (A10) at ($(P2)!.7!(A9)$);
662        \coordinate (A12) at ($(P1)!.8!(A9)$); % To pick for perspective
663        \coordinate (A11) at
664          (intersection cs: first line={(A10) -- (P1)},
665                            second line={(A12) -- (P2)});
666       
667        \coordinate (A13) at ($(A9)!.54!(A10)$);
668        \coordinate (A14) at ($(A2)!.54!(A7)$);
669       
670        \coordinate (A15) at
671                  (intersection cs: first line={(A13) -- (P1)},
672                                    second line={(A12) -- (P2)});
673        \coordinate (A16) at
674                  (intersection cs: first line={(A14) -- (P1)},
675                                    second line={(A3) -- (P2)});
676        %%% Depending of what you want to display, you can comment/edit
677        %%% the following lines
678       
679        {\node [background, right=-0.8cm of A12] (background) {};}
680
681        %% Possibly draw back faces
682
683        \fill[gray!70] (A2) -- (A3) -- (A6) -- (A7) -- cycle; % face 6
684        \node at (barycentric cs:A2=1,A3=1,A6=1,A7=1) {\tiny };
685       
686        \fill[gray!30] (A3) -- (A4) -- (A5) -- (A6) -- cycle; % face 3
687        \node at (barycentric cs:A3=1,A4=1,A5=1,A6=1) {\tiny };
688       
689        \fill[gray!10] (A5) -- (A6) -- (A7) -- (A8) -- cycle; % face 4
690        \node at (barycentric cs:A5=1,A6=1,A7=1,A8=1) {\tiny };
691       
692       
693        \fill[green!90] (A13) -- (A10) -- (A11) -- (A15) -- cycle; % face 4
694        \node at (barycentric cs:A9=1,A10=1,A11=1,A12=1) {\tiny };
695       
696        \fill[green!100] (A13) -- (A15) -- (A16) -- (A14) -- cycle; % face 4
697        \node at (barycentric cs:A9=1,A12=1,A3=1,A2=1) {\tiny };
698       
699        \fill[green!100] (A13) -- (A10) -- (A7) -- (A14) -- cycle; % face 4
700        \node at (barycentric cs:A9=1,A10=1,A7=1,A2=1) {\tiny };
701       
702        \draw[thin,dashed] (A5) -- (A6);
703        \draw[thin,dashed] (A3) -- (A6);
704        \draw[thin,dashed] (A7) -- (A6);
705
706        \draw[thin,dashed] (A11) -- (A15);
707        \draw[thin,dashed] (A10) -- (A11);
708       
709        %% Possibly draw front faces
710
711        % \fill[orange] (A1) -- (A8) -- (A7) -- (A2) -- cycle; % face 1
712        % \node at (barycentric cs:A1=1,A8=1,A7=1,A2=1) {\tiny f1};
713        \fill[gray!50,opacity=0.2] (A1) -- (A2) -- (A3) -- (A4) -- cycle; % f2
714        \node at (barycentric cs:A1=1,A2=1,A3=1,A4=1) {\tiny };
715        \fill[gray!90,opacity=0.2] (A1) -- (A4) -- (A5) -- (A8) -- cycle; % f5
716        \node at (barycentric cs:A1=1,A4=1,A5=1,A8=1) {\tiny };
717
718        %% Possibly draw front lines
719        \draw[thin] (A1) -- (A2);
720        \draw[thin] (A3) -- (A4);
721        \draw[thin] (A7) -- (A8);
722        \draw[thin] (A1) -- (A4);
723        \draw[thin] (A1) -- (A8);
724        \draw[thin] (A2) -- (A3);
725        \draw[thin] (A2) -- (A7);
726        \draw[thin] (A4) -- (A5);
727        \draw[thin] (A8) -- (A5);
728       
729        \draw[thin] (A13) -- (A10);
730        \draw[thin] (A13) -- (A15);
731        \draw[thin] (A14) -- (A16);
732        \draw[thin] (A13) -- (A14);
733        \draw[thin] (A15) -- (A16);
734       
735        % Possibly draw points
736        % (it can help you understand the cuboid structure)
737        \foreach \i in {1,2,...,16}
738        {
739        %  \draw[fill=black] (A\i) circle (0.05em)
740        %    node[above right] {\tiny \i};
741        }
742        % \draw[fill=black] (P1) circle (0.1em) node[below] {\tiny p1};
743        % \draw[fill=black] (P2) circle (0.1em) node[below] {\tiny p2};
744       
745        %Key   
746        \coordinate (K1) at (0.5cm,-2.3cm);
747        \coordinate (K2) at (0.5cm,-2.7cm);
748       
749       
750        \node [Key1, right=0.0cm of K1] (key1) {};
751        \node [Key2, right=0.0cm of K2] (key2) {};
752        \node [Key3, right=0.4cm of K1] (key11) {Total model domain};
753        \node [Key3, right=0.4cm of K2] (key21) {Plant canopy volume};
754       
755        % % Text
756        \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}}};}
757\end{tikzpicture}
758
759
760\end{frame}
761
762\end{document}
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