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Add reference list using BibTeX
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t-nitta committed Mar 19, 2021
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3 changes: 3 additions & 0 deletions convert/descript.tex
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\usepackage{booktabs}
\usepackage{ltablex,booktabs}
\usepackage[dvipdfm,hidelinks]{hyperref}
\usepackage[round]{natbib}

\makeatletter
\def\maxwidth{\ifdim\Gin@nat@width>\linewidth\linewidth\else\Gin@nat@width\fi}
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\include{descript/matsiro}
%
%
\bibliography{descript/reference}
\bibliographystyle{abbrvnat}
\end{document}
26 changes: 14 additions & 12 deletions descript/matsiro.md
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## Calculation of canopy albedo and transmissivity

The calculation of canopy albedo and transmissivity is based on the calculation of radiation within a canopy layer proposed by Watanabe and Ohtani (1995).
The calculation of canopy albedo and transmissivity is based on the calculation of radiation within a canopy layer proposed by \citet{Watanabe1995-je}.

Considering the canopy as vertically uniform and making use of several assumptions for simplification, the transfer equations of insolation within the canopy and the boundary condition are expressed as

Expand Down Expand Up @@ -572,7 +572,7 @@ Next, the turbulence parameter (bulk coefficient) is calculated.

## Calculation of roughness with respect to momentum and heat

The calculation of roughness is based on Watanabe (1994). In that study, using the results of a multilayer canopy model by Kondo and Watanabe (1992) as a function form for the roughness of a bulk model best fitting those results, Watanabe (1994) proposed the following:
The calculation of roughness is based on \citet{Watanabe1994-sx}. In that study, using the results of a multilayer canopy model by \citet{Kondo1992-ut} as a function form for the roughness of a bulk model best fitting those results, \citet{Watanabe1994-sx} proposed the following:

$$
\left(\ln \frac{h-d}{z_0}\right)^{-1} &=&
Expand Down Expand Up @@ -612,7 +612,7 @@ $c_d$ and $c_h$ are parameters determined by the leaf shape, and are given as ex

## Calculation of bulk coefficient with respect to momentum and heat

After Watanabe (1994), the bulk coefficient is also calculated using Monin-Obukhov similarity as
After \citet{Watanabe1994-sx}, the bulk coefficient is also calculated using Monin-Obukhov similarity as

$$
C_M &=& k^2 \left[ \ln \frac{z_a-d}{z_0} + \Psi_m(\zeta) \right]^{-2} \\
Expand Down Expand Up @@ -671,7 +671,7 @@ In addition, when there is no stomatal resistance, etc. (such as evaporation fro

# Stomatal resistance

For the calculation of stomatal resistance, a photosynthesis-stomatal model based on Farquhar et al. (1980), Ball (1988), and Collatz et al. (1990, 1991, 1992) is used. The code of SiB2 (Sellers et al., 1996) is used virtually unchanged, with the exception of the method for solving the resistance of the overall canopy. A Jarvis-type empirical equation could be used instead; however, the explanation of this point is omitted here.
For the calculation of stomatal resistance, a photosynthesis-stomatal model based on \citet{Farquhar1980-dm}, \citet{Ball1988-jh}, and \citet{Collatz1990-pw,Collatz1991-lz,Collatz1992-hc} is used. The code of SiB2 \citep{Sellers1996-xi} is used virtually unchanged, with the exception of the method for solving the resistance of the overall canopy. A Jarvis-type empirical equation could be used instead; however, the explanation of this point is omitted here.

## Calculation of soil moisture stress factor

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## Calculation of stomatal resistance (2)

The net photosynthesis ($A_n$) and stomatal conductance ($g_s$) are related by the semiempirical equation of Ball (1988) as follows:
The net photosynthesis ($A_n$) and stomatal conductance ($g_s$) are related by the semiempirical equation of \citet{Ball1988-jh} as follows:

$$
g_s = m \frac {A_n}{c_s} h_s + b f_w \tag{eq93}
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$W_{c\max}$ is set at 0.2 mm as a standard value, and the same value is used with respect to the liquid and solid phases.

The natural dripping due to gravity $D_g$ is, after Rutter et al. (1975), assumed to be
The natural dripping due to gravity $D_g$ is, after \citet{Rutter1975-bg}, assumed to be

$$
D_g(w_c) = D_1 \exp(D_2 w_c)
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$\alpha_b^{\tau}$ is the albedo of the snow for band $b$ at the time step of $\tau$. Three bands of wavelength, visible (vis), near infrared (nir) and infrared (ifr) are considered in MATSIRO, and here the factors for visible band are used. $\alpha_{b,new}$ is the albedo of newly fallen snow for band $b$ and $\alpha_{b,old}$ is that of old snow. In default, $\alpha_{vis,new}$, $\alpha_{nir,new}$, $\alpha_{ifr,new}$, $\alpha_{vis,old}$, $\alpha_{nir,old}$ and $\alpha_{ifr,old}$ are set to 0.9, 0.7, 0.01, 0.65 (or 0.4), 0.2 and 0.1, respectively.


The age of snow at the next time step ${\tau+1}$ is, after Yang et al. (1997), assumed to be given by the following equation:
The age of snow at the next time step ${\tau+1}$ is, after \citet{Yang1997-va}, assumed to be given by the following equation:

$$
A_g^{\tau+1} = A_g^{\tau} + (f_{age} + f_{age}^{10} + r_{dirt})\Delta t_L / \tau_{age}, \tag{8-58}
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SUBROUTINE: MATROF in matrof.F.

The surface runoff and groundwater runoff are solved using a simplified TOPMODEL (Beven and Kirkby, 1979).
The surface runoff and groundwater runoff are solved using a simplified TOPMODEL \citep{Beven1979-ia}.

## Outline of TOPMODEL

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3. The downward groundwater flow at a certain point on the slope is equal to the accumulated groundwater recharge in the upper slope above that point.

The usage of the symbols below is in accordance with the usual practice in descriptions of TOPMODEL (Sivapalan et al., 1987; Stieglitz et al., 1997).
The usage of the symbols below is in accordance with the usual practice in descriptions of TOPMODEL \citep{Sivapalan1987-dq,Stieglitz1997-sk}.

Assumption 1 can be expressed as

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\right. \tag{eq300}
$$

in which $K_{(k+1/2)}$ is the soil hydraulic conductivity that, referring to Clapp and Hornberger (1978), is expressed as
in which $K_{(k+1/2)}$ is the soil hydraulic conductivity that, referring to \citet{Clapp1978-vf}, is expressed as

$$
K_{(k+1/2)} = K_{s(k+1/2)} (\max(W_{(k)},W_{(k+1)}))^{2b(k)+3} f_i
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where the $\alpha_{SnLk(d,b)}$ is the snow albedo covering the lake, and $R_{SnLk}$ is the snow coverage, respectively.

Second, let us consider the lake surface roughness. The roughnesses of for momentum, heat and vapor are calculated in `SUBROUTINE:[LAKEZ0F]`, based on Miller et al. (1992), same with COCO-OGCM (Hasumi 2015), supposing the ice-free conditions, then modified.
Second, let us consider the lake surface roughness. The roughnesses of for momentum, heat and vapor are calculated in `SUBROUTINE:[LAKEZ0F]`, based on \citet{Miller1992-gi}, same with COCO-OGCM (Hasumi 2015), supposing the ice-free conditions, then modified.

When lake ice is present, each roughness is modified to take into account the lake ice concentration ($R_{IcLk}$)

Expand Down Expand Up @@ -4018,7 +4018,7 @@ The surface heat and water fluxes over lakes have been calculated as one of the

Both potential vegetation and cropland tiles consist of six soil layers, up to three snow layers, and a single canopy layer, driving predictions of the temperature and amount of water in the canopy, soil, and snow.

Potential vegetation is defined according to the vegetation types of the Simple Biosphere Model 2 (SiB2; Sellers et al. 1996) scheme and has 10 categories including land ice. There is no wetland category for land cover in the original SiB2 vegetation types or soil types.
Potential vegetation is defined according to the vegetation types of the Simple Biosphere Model 2 (SiB2; \citealt{Sellers1996-ye}) scheme and has 10 categories including land ice. There is no wetland category for land cover in the original SiB2 vegetation types or soil types.

## Appendix

Expand All @@ -4039,6 +4039,7 @@ Potential vegetation is defined according to the vegetation types of the Simple
| $f_i(i=1,2)$ | Fractional weight of potential vegetation and cropland | SFFRAC1 | IJLDIM,MULTCY | - | - |


<!--
# References
-
Ball, J. T., 1988: An analysis of stomatal conductance. Ph.D. thesis, Stanford University, 89 pp.
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-
渡辺力・大谷義一, 1995: キャノピー層内の日射量分布の近似計算法. <span>農業気象</span>, <span>**51**</span>, 57–60.
-->
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