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Ignore:
Timestamp:
Nov 12, 2014 3:39:53 PM (10 years ago)
Author:
kanani
Message:

updates due to new code structure and steering of canopy model

File:
1 edited

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  • palm/trunk/TUTORIAL/SOURCE/canopy_model.tex

    r1205 r1493  
    2525  morecomment=[l]{!\ }% Comment only with space after !
    2626}
    27 
     27\usepackage{tabto}
    2828
    2929\institute{Institut fÌr Meteorologie und Klimatologie, Leibniz UniversitÀt Hannover}
    … …  
    6262\subsection{The embedded Canopy Model}
    6363
     64
    6465%Folie 01
    6566\begin{frame}
    … …  
    7273         \item<4->{scalar exchange processes between canopy and atmosphere.}
    7374      \end{itemize}
    74       \item<5->{Within the canopy model, the plant canopy acts as a sink for momentum and as a source/sink for active (e.g. temperature) and passive (e.g. tracer) scalars.}
    75       \item<6->{The canopy model does not account for each plant element, but rather accounts for a volume averaged effect on the flow and scalar concentration, depending on:}
     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.:}
    7677      \begin{itemize}
    7778         \item<7->{leaf area density,}
    78          \item<8->{drag coefficient.}
     79         \item<8->{drag coefficient,}
     80         \item<9->{wind speed.}
    7981      \end{itemize}
    8082   \end{itemize}
    … …  
    9092      \item<1->{A plant canopy affects the flow by acting as a momentum sink due to form and viscous drag forces.}
    9193      \item<2->{The effectiveness of momentum absorption depends on the amount of leaf area per unit volume and the aerodynamic drag.}
    92       \item<3->{Due to the aerodynamic drag, the flow is decelerated within the canopy, leading to an inflection point in the vertical profile of the horizontal velocity at the canopy top.
     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.
    9395         \begin{center}
    9496            \includegraphics[width=0.5\textwidth]{canopy_model_figures/abb1.png}
    … …  
    132134      }
    133135      \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 ($u_{1}=u$, $u_{2}=v$, $u_{3}=w$)}
     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 ($u_{1}=u$, $u_{2}=v$, $u_{3}=w$)}
    138140      \end{itemize}
    139141   \end{itemize}
    140    \uncover<7->{Note: The canopy model does not resolve the effect of single plant elements.}
     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.}
    141143   \end{footnotesize}
    142144\end{frame}
    … …  
    149151   \begin{footnotesize}
    150152   \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:\\
     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:\\
    152154         \begin{align*}
    153155            \frac{\partial e}{\partial t} = \text{...} - 2 c_{d} a U e
    154156         \end{align*}
    155157      }
    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).}
     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).}
    157159   \end{itemize}
    158160   \end{footnotesize}
    … …  
    171173         \end{align*}
    172174      }
    173       \item<2->{It is assumed that the foliage is warmed by the penetrating solar radiation and, in turn, warms the surrounding air.}
     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.}
    174176      \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):\\
    175177         \begin{align*}
    … …  
    211213   \frametitle{Basics (I)}
    212214   \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}}).}
     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}}.}
    214216      \item<2->{All parameters for steering the canopy model are described in:\\
    215       {\scriptsize Documentation $\rightarrow$ Model steering $\rightarrow$ Parameters $\rightarrow$ Initialization $\rightarrow$ Canopy}\\
     217      {\scriptsize Documentation $\rightarrow$ Model steering $\rightarrow$ Parameters $\rightarrow$ Plant canopy}\\
    216218      (http://palm.muk.uni-hannover.de)
    217219      }
    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}}.}
     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}}.}
    219221   \end{itemize}
    220222\end{frame}
    … …  
    224226%Folie 09
    225227\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   \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}}).\\
    228230    \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.}
     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.}
    230232    \end{itemize}
    231233   \vspace{10pt}
    … …  
    363365%Folie 10
    364366\begin{frame}
    365    \frametitle{Basic canopy parameter (II)}
     367   \frametitle{Basic canopy parameters (II)}
    366368    \begin{itemize}
    367369       \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                  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).}
    370536    \end{itemize}
    371537   \vspace{10pt}
    … …  
    559725
    560726
    561 
    562 %Folie 11
    563 \begin{frame}
    564    \frametitle{Basic canopy parameter (III)}
     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)}
    565908   \begin{footnotesize}
    566909    \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.}
     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.}
    568911    \end{itemize}
    569912   
    … …  
    599942
    600943
    601 %Folie 12
    602 \begin{frame}
    603    \frametitle{Basic canopy parameter (IV)}
     944%Folie 14
     945\begin{frame}
     946   \frametitle{Basic canopy parameters (IV)}
    604947   \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)).}
     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)).}
    607950   \end{itemize}
    608951\end{frame}
    … …  
    610953
    611954
    612 %Folie 13
     955%Folie 15
    613956\begin{frame}
    614957   \frametitle{User-defined canopy}
    … …  
    7531096       
    7541097        % % 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}}};}
     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}}};}
    7561099\end{tikzpicture}
    7571100
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