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\title{Re: ``Interactive comment on `Effects of vegetation structure
  on biomass accumulation in a Balanced Optimality Structure
  Vegetation Model (BOSVM v1.0)', Anonymous Referee \#1"}

%The role of vegetation structure and fire in bistabilities of
%  woody cover from savanna to rainforest}
\author{Z. Yin, S.~C. Dekker, B.~J.~J.~M. van den Hurk, H.~A. Dijkstra}
\date{} % Activate to display a given date or no date (if empty),
         % otherwise the current date is printed 

\begin{document}
\maketitle

1.``This is a very interesting paper about the theoretical physical
description of the impact of canopy patchiness on biomass production
along aridity gradients. A new model able to represent key feedback
mechanisms is presented. The F90 source code is provided as a
supplement material. The model capitalizes on the LPJ dynamic
vegetation model and on pre-existing land surface models (ISBA-A-gs
and TESSEL).''\\
% 
A: Thanks for your positive comments on our work.\\
\\
2.``For example, the limitations of the approach are not sufficiently described.''\\
% 
A: A paragraph will be added to discuss the limitation of this
research at the end of the discussion section, as``As our interest is
to study the effects of vegetation structure on their total biomass
between different climate regime, we realize that numerous factors
that can significantly influence biomass dynamics are not taken into
account. For instance, \citet{dardel2014} found that the heterogeneities
in soil types is an important driver of vegetation-climate
interactions. The property of the soil determines soil water holding
capacity, which in turn affects the soil water balance. Also we did
not include grass-tree competition. Due to this competition, maximum
biomass of grasses and woody plants can be limited. Further grasses
prohibit the colonization rate of seedlings \citep{baudena2010} as
they compete for the same resources and grasses provide fuel for fire
occurrence \citep{staver2011a} in savanna systems, which further limit
the biomass of woody plants. Moreover, human activities
\citep{kleidon2006} and topography \citep{klausmeier1999} have
potential effects on dynamics of the ecosystem under certain climate
regime, which are not considered in this work. Understanding the
importance of climate regimes versus different heterogeneity of local
conditions and other important mechanisms in savanna ecosystems soil
types to simulate biomass
dynamics will be a interesting and important new step.''\\
\\
3.``In the present version of the text, it is difficult to understand
whether or not soil hydrology (2 layers) is consistent with a detailed
root profile.''\\
% 
A: In BOSVM, we didn't include detailed root
  profile. We only consider the effects of total amount of root
  biomass ($C_\text{root}$) per canopy area (CA) on soil water
  stress. We will clarify this in the new version.\\
\\
4.``It is difficult to understand whether or not radiative transfer
within vegetation is consistent with patchiness (impact of clumping
on light absorption ?).''\\
  % 
A: Here we assume a spherical leaf angle
  distribution. Thus, the radiative transfer within vegetation is
only influenced by leaf area index (see Appendix B4) and not with
clumping effects. We have chosen for this, to keep the model balanced,
i.e. that the complexity of climate, physiology, ecology and hydrology
mechanisms are balanced within our model. We will clarify in the
manuscript that leaf angles are randomly distributed and that we do
not account for clumping.\\
\\
5.``Although the new model represents many feedbacks, other
(biological / soil) feedbacks may be at stake in the real world. For
example, what about competition between grass and trees ? Impact of
the soil water holding capacity ?''\\
%
A: The vegetation dynamics is influenced by numerous internal/external
variables and complex interactions among them. Detailed ecological
models of savanna systems are developed (e.g. \citet{scheiter2009}),
but these models are too complex to couple to global climate models to
understand climate-vegetation feedbacks. Alternatively, the current
dynamic vegetation models used in earth system models do not account
for important ecological mechanisms as small scale vegetation
structure, different vegetation types and different plant specific
defensive/offensive water use mechanisms with different impacts on
fire and e.g. hetereogeneities of microtopography and soil
properties. As mentioned under point 2, we will add a paragraph in the
discussion on the limitation and other potential impacts and
mechanisms such as tree-grass competition.\\
\\
6.``PP. 4603-4604: Title sounds different from the contents of the
abstract. Is the objective of the paper to present a new model or to
propose an interpretation of the vegetation patchiness in semiarid
regions ? "BOSVM" is used in the title only. For the sake of
clarity, title should be modified.''\\
  % 
A: The primary objective is to investigate the effect of vegetation
structure on its total biomass and find the optimal structure that can
lead to the maximum total biomass under given climate. To address this
question, the new water-carbon-energy balanced model is
developed. Most important reason for developing this model is that it
can be linked to an atmospheric model for further land-atmosphere
interactions research. The name of the model was added temporarily as
a requirement before publication on GMDD. The model's name and the
rationale for the development of the
model will be updated in the introduction of the manuscript.\\
\\
  % 
  7.``P. 4606, L. 16: the work of Dardel et al., Re-greening Sahel: 30
  years of remote sensing data and field observations (Mali, Niger),
  Remote Sens. Environ., 2014, could be cited as it shows that soil
  type is a key driver of the vegetation response to climate in
  Sahel.''\\
  % 
  A: Will be cited. Also we will add in the introduction:
    ``Although soil types do play an important role in vegetation
    response to climate \citep{dardel2014}, its distribution is
    independent to the precipitation gradient. Thus, we only applied
    medium soil texture \citep{balsamo2009} in this study and
    ignore effects of soil types on biomass dynamics.''\\
  \\
  % 
  8.``P. 4610 (Sect. 2.2): It is not clear how plant growth is related
  to photosynthesis.''\\
  % 
  A: In Section 2.2, we will add: ``During the photosynthesis
  simulation, we calculate NPP (see Appendix B). Then based on Eq 3,
  the total biomass is updated, after which vegetation structural
  variables are updated by equations listed in Section 2.2. First,
  $C_\text{root}$ and $C_\text{leaf} + C_\text{stem}$ can be
  calculated by $\alpha$ (Eq 5). Second, $C_\text{leaf}+C_\text{stem}$
  can be represented as a function of LAI and CA by combining Eq 6 and
  7. Then, LAI and CA can be retrieved by the combined equation and
  Equation 8. Third, CA is compared to
    CA$_\text{ref}$. If CA$>$CA$_\text{ref}$, LAI will be
  recalculated by the combined equation while keeping
  CA=CA$_\text{ref}$ (CA cannot exceed CA$_\text{ref}$). At last,
  $f_\text{c}$ and $\varphi$ can be
  obtained by Eq 9 and 10 respectively.''\\
  In the Section 2.8, we will add: `` ... After updating the
  $C_\text{veg}$, other structural variables can be updated as
  described above.''\\
  \\
% 
9.``P. 4611 (Table 1): please check the Dmax units in Table 1.''\\
% 
A: Corrected (see Table~1 below).\\
\\
10.``P. 4611 (Eq. 9): The vegetation cover fraction changes with time. Is
the (carbon) mass conservation ensured ? How ? Same question for soil
water mass conservation.''\\
% 
A: Yes. The carbon mass conservation is governed by Eq
  3. At the end of each time step, the total biomass is updated by Eq
  3. Then the vegetation structural variables are updated (see the
  reply to comment 8). The soil water mass conservation is governed
  by Eq 2.\\
\\
11.``P. 4612, L. 21 (Table 1): the gamma value for grass indicates
that C3 grasses are considered, not C4 grasses. In west Africa, are C3
grasses frequent ? I would expect C4 grass species are more
frequent than C3 grass species.''\\
  % 
A: True. C4 grasses are more common than C3 grasses in
  Africa. We revised the parameterization and simulation of
  grasses. Parameterization in Table 1 is updated (see below). Figure
  2, 7, 8, 9 and 10 are updated (see below). In Figure 7, we can find
  that areas of survival patterns of C4 grasses are larger than C3
  grasses (Figure 7 in previous version), which coincides with that C4
  species is more common that C3 species in arid and semi-arid
  areas. However, the new parameterization of C4 grasses has no
  different effect on model behavior.\\
\\
12.``P. 4617, L. 11: "stomatal opening until very dry"; I suppose
that this depends on the parameters of the model and how the
drought-tolerant parameterization is implemented ?''\\
  % 
A: True. The threshold ($f_\text{wc}$ in Table 1) here is determined
by the parameterization based on observations \citep{calvet2000,
  calvet2004}. Also, it depends on soil types and root density (see Eq
12). Although the soil type is fixed (medium) in our research, the
biomass dynamics can change the threshold
significantly (by Eq 12). We will change this accordingly.\\
\\
13.``P. 4620, L. 19: It would be useful here to detail the time steps
of the various processes (e.g. hourly for photosynthesis ?  Daily for
biomass ?)''\\
A: In this work, we use half an hour time step in the simulation for
all processes. It is modified as: ``... modifies the soil temperature
(Appendix~C2). The time step ($\mathrm{d}t$) of the
simulation is half an hour for all processes.''\\
\\
14. ``P. 4620, L. 21: This is the first and the last time we see a map
of west Africa. This is confusing. Were continuous model simulations
performed over this area ? If yes, what do the simulated variables
(e.g. LAI) look like ? Are they consistent with published satellite
or in situ observations ?''\\
A: No. We didn't apply the model for the whole area shown in the map,
as our interest is the sensitivity of total biomass to vegetation
structure. The spatial implementation is provided in the next paper
including fire behaviour (in Earth System Dynamics Discussion now,
doi:10.5194/esdd-5-83-2014). A paragraph will be added in Section 2.9
as: ``Since this study focuses on the effect of vegetation structure
on total biomass across the precipitation gradient, the BOSVM model is
not applied to the whole region of West Africa. In the second
experiment (Section 3.2), four grid cells with mean annual
precipitation of 200\,mm\,yr$^{-1}$, 400\,mm\,yr$^{-1}$,
800\,mm\,yr$^{-1}$ and 1200\,mm\,yr$^{-1}$ (black points in Fig~5) are
chosen as climate forcing to represent the gradient of rainfall. In
the third experiment (Section 3.3), we provide the model simulation
for a sub region (the dashed rectangle in Fig~5).'' Finally we will
add an extra model testing based on observations of woody cover across
climate regimes from 100 to 1500 mm\,yr$^{-1}$, also requested by
Referee \#2. Details are given in the
reply of Referee \#2, resulting in a new figure 11.\\
The caption of Fig 5 is revised as: ``Annual mean precipitation and
incoming shortwave radiation distribution in West Africa. The four
black points are chosen as climate forcings for the second experiment
(Section 3.2). The Rectangle marked is the study domain in the third
experiment (Section 3.3), ranging [20$^\circ$W,
30$^\circ$E]$\times$[5$^\circ$S, 20$^\circ$N] in West Africa. Data
is from the ALMIP forcing data set \citep{boone2009}.''\\
\\
15. ``P. 4621, L. 15: using CA/CAref in Fig. 6 (instead of CA) would
be more appropriate.''\\
  % 
A: True. Revised. The caption of Fig~6 is modified
  as:`` Patterns of woody vegetation for different combinations of
  $\alpha$ and $D$. $\alpha$ is varied from 0 to 0.5. $D$ is set from
  0.1 to 5. Total biomass is 30\,kg\,C per pixel of 15\,m$^2$. Panel
  \textbf{(a)}: LAI; \textbf{(b)}: relative CA; \textbf{(c)}:
  $f_\text{c}$; \textbf{(d)}: relative $\varphi$. Relative CA is
  defined as CA$/$CA$_\text{ref}$. Relative $\varphi$ is defined as
  $\varphi/\varphi_\text{max}$. When $\varphi>\varphi_\text{max}$,
  value of relative $\varphi$ is set to one.''\\
\\
16. ``P. 4622, L. 24: please explain why WUE increases.''\\
  % 
  A: The explicit explanation is in Section 2.6 and
    Figure 2. Here it will be modified as:``...  the water use efficiency
    increases with extractable water (Section~2.6 and Fig~2).''\\
\\
  17. ``P. 4626, L. 5: why 87 grid cells ?''\\
  % 
  A: 87 grid cells are those grid cells in the
    research region (dashed rectangle in the Fig.~5) where woody
    plants are able to exist. It will be revised to:``To depict the
    variability of the response mechanisms as a function of the
    climate regime, we calculated Spearman's correlation coefficients
    between averaged biomass and variables LAI, $f_\text{c}$ and WUE
    under each given climate regime for each vegetation
    strategy. For each grid cell in the research region (dashed
    rectangle in Fig~5) and for each vegetation strategy, we
    simulated biomass of 100 vegetation structures as defined in
    Sect. 3.2. Thus we have 100 samples of simulated average biomass,
    LAI, $f_\text{c}$ and WUE, which are used to calculate correlation
    coefficients.''\\
  \\
  18. ``P. 4627, L. 24: "fc-Rspace feedback" should be defined
  here. Do you refer to Eq. (25) ?''\\
  % 
  A: Since we introduce and discuss $f_\text{c}$-$R_\text{WU}$ and
  $f_\text{c}$-$R_\text{space}$ together, we think it's better to keep
  the definition of $R_\text{space}$ in
  Section~2.7. Here we will mention Eq.~25 when
    $f_\text{c}$-$R_\text{space}$ is introduced.\\
  \\
  19. ``P. 4632 (A2, Table 1): why are the "defensive / offensive"
  columns omitted for grass ? The two parameterizations are considered
  in a number of figures. The corresponding parameters should be
  indicated in Table 1.''\\
  % 
  A: True. Corrected (see below in the new table captions).\\
\\
 20. ``Figures 7-9: (a, c) why not exploring values of alpha higher
  than 0.5 ? (b, d) what is the meaning of the crosses ? Do they
  correspond to various values of D and alpha ? Please explain''\\
  % 
  A: Because if $\alpha$ is larger than 0.5, above ground biomass will
  be larger than the rooting biomass, which is not normal (see the LPJ
  model \citep{sitch2003}). We will clarify this in the new
  manuscript.\\
    Yes. Crosses in sub figures (b,d) are averaged value of variables
    ($C_\text{veg}$, LAI, $f_\text{c}$, WUE, etc.) corresponding to
    100 vegetation structures.\\
    It will be revised as: ``Figure~7b shows relations of
    $C_\text{veg}$-LAI, $C_\text{veg}$-$f_\text{c}$,
    $C_\text{veg}$-WUE and $f_\text{c}$-$R_\text{WU}$. Each cross
    corresponds to a specific vegetation structure.''\\
  \\
  21. ``Figures 6-9: the scale for D is quite strange. It seems that
  what is plotted is a complex function of D, not D.''\\
  % 
  A: Yes. As $D$ is a ratio of relative LAI to
    relative CA, it can vary from 0 to $\infty$. Thus the
    distribution of $D$ value in Fig~6--9 is determined by an inverse
    tangent function. It will be revised as: ``The scale of $D$ (y-axis)
    follows an inverse tangent function. Same for Fig.~7--9.''\\
  \\
  22. ``P. 4608, L. 3: "Obkhov" ?''\\
 % 
A: Corrected.\\
\\
23. ``P. 4608, L. 19: "In stead" ?''\\
% 
 A: Corrected.\\
\\
24. ``P. 4610, L. 10: "exists of" or "consists of" ?''\\
% 
 A: Corrected.\\
\\
25. ``P. 4610, L. 12 (Fig. 1): please explain Fig. 1 more
  extensively. This figure could be split into 4 figures.''\\
  % 
  A: Figure 1 will be referred in places where it is mentioned.\\
  \\
  26. ``P. 4610, L. 17 (and Eq. 5): this is not "shoot-root ratio",
  Eq. (5) corresponds to the "shoot-total biomass ratio". This is
  confusing. Either change Eq. (5) or rename alpha.''\\
  % 
  A: Renamed $\alpha$ as ``shoot-total biomass ratio''.\\
\\
 27. ``P. 4611, L. 13 (and Eq. 8): is it "between relative LAI and
  relative CA" or "between relative LAI and relative CA" ? This is
  confusing. Either change Eq. (8) or rename D.''\\
  % 
  A: It is modified as: ``The second control
    parameter, representing the trade-off between CA and LAI, is the
    ratio of relative CA to relative LAI (Eq. 8)."\\
  \\
  28. ``P. 4612, L. 2-6: this is difficult to understand as it was not
  explained in which order the variables are calculated. Refer to
  Figure 4 here ?''\\
  % 
  A: Here we want to explain that the canopy structure of vegetation
  will change when CA=CA$_\text{ref}$. When CA$<$CA$_\text{ref}$, both
  CA and LAI increase with the growth of biomass to keep the
  vegetation structure parameter $D$ as a constant. However, when CA
  reaches CA$_\text{ref}$, vegetation cannot spread laterally
  anymore. Only LAI can increase with the growth of biomass,
  suggesting that canopy structure becomes more vertical and $D$
  increases (Eq 8). This special case is explicitly explained in the
  end of Section 2.2. See reply to comment 8.\\
  \\
  29. ``P. 4617, L. 11: "remaining" or "maintaining" ?''\\
  % 
  A: Corrected.\\
  \\
  30. ``P. 4618, L. 15 (Fig. 3): please use colors.''\\
  % 
  A: Updated.\\
\\
  31. ``P. 4622, L. 21: "coefficiences" ?''\\
  % 
  A: Corrected.\\
\\
  32. ``P. 4623, L. 11: "different with" ?''\\
  % 
  A: Corrected.\\
\\
  33. ``P. 4626, L. 23: "effect" or "affect" ?''\\
  % 
  A: Corrected.\\
\\
  34. ``P. 4627, L. 19; "addtion" ?''\\
  % 
  A: Corrected.


\bibliographystyle{plainnat}
\bibliography{reference}

\newpage

\begin{table}[t]
  \caption{Parameterization of vegetation with two strategies.}\label{tab:gw}
  \begin{tabular}{llrrrrp{3.8cm}}
    \toprule
    & &\multicolumn{4}{c}{Vegetation Type} \\
    \cline{3-6}
    Parameters &Unit &\multicolumn{2}{c}{Grass} &\multicolumn{2}{c}{Woody} &Reference\\
    \cline{3-4} \cline{5-6}
    & &Defensive &Offensive &Defensive &Offensive  \\
    \midrule
    $A_\text{max}$(25\,$^\circ$C) & mg\,C\,m$^{-2}$\,s$^{-1}$
    &0.464 &0.464 &0.49 &0.49 & Boussetta et al.~(2013)\\
    $a_\text{l}$ & kg\,C\,m$^{-2}$ &-- &-- &0.65 &0.65 & Cox~(2001)\\
    $D_\text{max}$ &g\,kg$^{-1}$ &-- &-- &100 &100 & Calvet et al.~(2004)\\
    $D_\text{max}^N$ & g\,kg$^{-1}$ &55 &-- &-- &-- & Calvet~(2000)\\
    $D_\text{max}^X$ & g\,kg$^{-1}$ &-- &300 &-- &-- &Calvet~(2000)\\
    $f_0^*$ &-- &-- &-- &0.606 &0.46 &
 Calvet~(2000); \\
&&&&&&Calvet et al.~(2004)\\
    $f_0$ &-- &0.6 &0.6 &-- &-- & Boussetta et al.~(2013)\\
    $f_\text{wc}$ & m$^2$\,m$^{-2}$ &0.5 &0.5 &0.1 &0.6 &
    Calvet~(2000);\\
    &&&&&&Calvet et al.~(2004)\\
    $g_\text{m}^*$(25\,$^\circ$C) &mm\,s$^{-1}$ &2.38 &2.38  &1.6 &4.4 &
    Calvet~(2000);\\
    &&&&&&Calvet et al.~(2004)\\
    $\Gamma$(25\,$^\circ$C) & ppm &2.8 &2.8 &42 &42 &Boussetta et al.~(2013)\\
    $\epsilon_0^*$ &$10^{-3}$\,mg\,C\,J$^{-1}$ &3.82 &3.82 &4.64 &4.64 &Boussetta et al.~(2013)\\
    $T_\text{1,Am}$ &$^\circ$C &13 &13 &8 &8 &Calvet~(2000)\\
    $T_\text{2,Am}$ &$^\circ$C &38 &38 &38 &38 &Calvet~(2000)\\
    $T_\text{1,g}$ &$^\circ$C &13 &13 &5 &5 &Calvet~(2000)\\
    $T_\text{2,g}$ &$^\circ$C &36 &36 &36 &36 &Calvet~(2000)\\
    $\tau_\text{leaf}$ & yr &1 &1 &1 &1 &--\\
    $\tau_\text{stem}$ & yr &-- &-- &10 &10 &--\\
    $\tau_\text{root}$ &yr &1 &1 &10 &10 &--\\
    $\varphi_\text{max}$ &kg\,C\,m$^{-2}$ &1 &1 &10 &10 &--\\
    \bottomrule
  \end{tabular}
\end{table}

\setcounter{figure}{1}

\begin{figure}[htbp]
  \centering
  \includegraphics[height=9cm]{fig/fig2.pdf}
  \caption{Intrinsic WUE as a function of extractable
    water. Extractable water ($f_\text{w}$) is defined as
    Eq.~(12). Solid and dot-dashed lines represent defensive
    and offensive strategies respectively. Thick and thin lines
    represents grass and woody plants
    respectively. vpD\,=\,12\,g\,kg$^{-1}$, LAI\,=\,1,
    $R_\text{swd}=800$\,W\,m$^{-2}$, $c_\text{a}$\,=\,380\,ppm and
    $T_\text{s}$\,=\,25\,$^\circ$C.}
  \label{fig:sm_wue}
\end{figure}

%  \begin{figure}[htbp]
%    \centering
%   \includegraphics[height=4cm]{fig/fig3.pdf}
%    \caption{Impacts of $\alpha$ and $D$ on vegetation biomass via six
%      variables. Solid and dashed lines represent positive and negative
%      impact respectively. $R_\text{WU}$ is the relative water use,
%      defined in Eq.~(24). $\varphi$ is root density. WUE
%      is water use efficiency defined in Eq.~(23).}
% \label{fig:flow}
% \end{figure}

\setcounter{figure}{4}

\begin{figure}[htbp]
  \centering
  \includegraphics[height=9cm]{fig/fig5.pdf}
  \caption{Annual mean precipitation and incoming shortwave radiation
    distribution in West Africa. The four black points are chosen as
    climate forcings in the second experiment (Section~3.2). The
    Rectangle marked is the study domain in the third experiment
    (Section~3.3), ranging between 20$^\circ$\,W to
    30$^\circ$\,E and from 5$^\circ$\,S to 20$^\circ$\,N in West
    Africa. Data is from the ALMIP forcing data set \citep{boone2009}.}
  \label{fig:map}
\end{figure}

\begin{figure}[htbp]
  \centering
  \includegraphics[height=9cm]{fig/fig6.pdf}
  \caption{Patterns of woody vegetation for different combinations of
    $\alpha$ and $D$. $\alpha$ is varied from 0 to 0.5. $D$ is set
    from 0.1 to 5. Total biomass is 30\,kg\,C per pixel of
    15\,m$^2$. Panel \textbf{(a)}: LAI; \textbf{(b)}: relative CA;
    \textbf{(c)}: $f_\text{c}$; \textbf{(d)}: relative
    $\varphi$. Relative CA is defined as
    CA$/$CA$_\text{ref}$. Relative $\varphi$ is defined as
    $\varphi/\varphi_\text{max}$. When $\varphi>\varphi_\text{max}$,
    value of relative $\varphi$ is set to one. The
      scale of $D$ (y-axis) follows an inverse tangent function. Same
      for Fig.~7 to 9.}
  \label{fig:structure}
 \end{figure}

\begin{figure}[htbp]
  \centering
  \includegraphics[height=6cm]{fig/fig7a.pdf}
  \includegraphics[height=6cm]{fig/fig7b.pdf}
  \includegraphics[height=6cm]{fig/fig7c.pdf}
  \includegraphics[height=6cm]{fig/fig7d.pdf}
  \caption{Sensitivity analysis of equilibrium biomass to vegetation
    structure: A. Panels \textbf{(a)} and \textbf{(c)} present
    six-year averaged total biomass that changes with different
    vegetation structures of two strategies. Patterns represent
    survival structures under the specified regime. Panels
    \textbf{(b)} and \textbf{(d)} display several variables (LAI,
    $f_\text{c}$ and WUE) as a function of biomass and a comparison
    between $f_\text{c}$ and $R_\text{WU}$. Solid lines in Panels
    \textbf{(b)} and \textbf{(d)} are one-one line. Panels
    \textbf{(a)} and \textbf{(b)} are for defensive grass case under
    200\,mm\,yr$^{-1}$. Panels \textbf{(c)} and \textbf{(d)} are for
    offensive grass case. The parameterization is
      based on C4 plants.}
\label{fig:grass}
\end{figure}

\begin{figure}[htbp]
  \centering
  \includegraphics[height=6cm]{fig/fig8a.pdf}
  \includegraphics[height=6cm]{fig/fig8b.pdf}
  \includegraphics[height=6cm]{fig/fig8c.pdf}
  \includegraphics[height=6cm]{fig/fig8d.pdf}
  \caption{Sensitivity analysis of equilibrium biomass to
    vegetation structure: B. As Fig.~7,
    defensive woody vegetation case for 200\,mm\,yr$^{-1}$ (panels \textbf{a}
    and \textbf{b}) and 400\,mm\,yr$^{-1}$ (\textbf{c} and \textbf{d}).}
  \label{fig:dw200}
\end{figure}

\begin{figure}[htbp]
  \centering
  \includegraphics[height=6cm]{fig/fig9a.pdf}
  \includegraphics[height=6cm]{fig/fig9b.pdf}
  \includegraphics[height=6cm]{fig/fig9c.pdf}
  \includegraphics[height=6cm]{fig/fig9d.pdf}
  \caption{Sensitivity analysis of equilibrium biomass to vegetation
    structure: C. As Fig.~7 for 800\,mm\,yr$^{-1}$
    (panels \textbf{a} and \textbf{b}) and 1200\,mm\,yr$^{-1}$
    (\textbf{c} and \textbf{d}).}
  \label{fig:dw800}
\end{figure}

\begin{figure}[htbp]
  \centering
  \includegraphics[height=12cm]{fig/fig10.pdf}
  \caption{Dominant factor change with precipitation. Correlation
    coefficients between averaged biomass and three parameters as a
    function of mean annual precipitation. Panels \textbf{(a)},
    \textbf{(b)}, \textbf{(c)} and \textbf{(d)} represent defensive
    grass, offensive grass, defensive woody and offensive woody
    respectively. Dot-dashed, dashed and solid lines are for
    correlation between biomass and $f_\text{c}$, LAI and WUE,
    respectively.}
  \label{fig:rain_cor}
\end{figure}

\end{document}