--- manual/s_phys_pkgs/text/fizhi.tex	2005/07/18 20:45:27	1.9
+++ manual/s_phys_pkgs/text/fizhi.tex	2005/08/02 15:43:59	1.10
@@ -21,7 +21,7 @@
 \label{sec:fizhi:mc}
 
 Sub-grid scale cumulus convection is parameterized using the Relaxed Arakawa
-Schubert (RAS) scheme of Moorthi and Suarez (1992), which is a linearized Arakawa Schubert
+Schubert (RAS) scheme of \cite{moorsz:92}, which is a linearized Arakawa Schubert
 type scheme.  RAS predicts the mass flux from an ensemble of clouds.  Each subensemble is identified
 by its entrainment rate and level of neutral bouyancy which are determined by the grid-scale properties.
 
@@ -43,7 +43,7 @@
 The entrainment parameter, $\lambda$, characterizes a particular subensemble based on its
 detrainment level, and is obtained by assuming that the level of detrainment is the level of neutral
 buoyancy, ie., the level at which the moist static energy of the cloud, $h_c$, is equal 
-to the saturation moist static energy of the environment, $h^*$.  Following Moorthi and Suarez (1992),
+to the saturation moist static energy of the environment, $h^*$.  Following \cite{moorsz:92},
 $\lambda$ may be written as
 \[
 \lambda = { {h_B - h^*_D} \over { {c_p \over g} {\int_{P_D}^{P_B}\theta(h^*_D-h)dP^{\kappa}}} } ,
@@ -101,7 +101,7 @@
 towards equillibrium.  
 
 In addition to the RAS cumulus convection scheme, the fizhi package employs a
-Kessler-type scheme for the re-evaporation of falling rain (Sud and Molod, 1988), which
+Kessler-type scheme for the re-evaporation of falling rain (\cite{sudm:88}), which
 correspondingly adjusts the temperature assuming $h$ is conserved. RAS in its current
 formulation assumes that all cloud water is deposited into the detrainment level as rain.
 All of the rain is available for re-evaporation, which begins in the level below detrainment. 
@@ -221,7 +221,7 @@
 and a $CO_2$ mixing ratio of 330 ppm. 
 For the ozone mixing ratio, monthly mean zonally averaged 
 climatological values specified as a function
-of latitude and height (Rosenfield, et al., 1987) are linearly interpolated to the current time.
+of latitude and height (\cite{rosen:87}) are linearly interpolated to the current time.
 
 
 \paragraph{Shortwave Radiation}
@@ -231,11 +231,11 @@
 clouds, and aerosols and due to the
 scattering by clouds, aerosols, and gases.
 The shortwave radiative processes are described by 
-Chou (1990,1992). This shortwave package
+\cite{chou:90,chou:92}. This shortwave package
 uses the Delta-Eddington approximation to compute the
 bulk scattering properties of a single layer following King and Harshvardhan (JAS, 1986).
 The transmittance and reflectance of diffuse radiation
-follow the procedures of Sagan and Pollock (JGR, 1967) and Lacis and Hansen (JAS, 1974).
+follow the procedures of Sagan and Pollock (JGR, 1967) and \cite{lhans:74}.
 
 Highly accurate heating rate calculations are obtained through the use
 of an optimal grouping strategy of spectral bands.  By grouping the UV and visible regions
@@ -321,7 +321,7 @@
 
 \paragraph{Longwave Radiation}
 
-The longwave radiation package used in the fizhi package is thoroughly described by Chou and Suarez (1994).
+The longwave radiation package used in the fizhi package is thoroughly described by \cite{chsz:94}.
 As described in that document, IR fluxes are computed due to absorption by water vapor, carbon
 dioxide, and ozone.  The spectral bands together with their absorbers and parameterization methods,
 configured for the fizhi package, are shown in Table \ref{tab:fizhi:longwave}.
@@ -357,7 +357,7 @@
 \end{tabular}
 \end{center}
 \vspace{0.1in}
-\caption{IR Spectral Bands, Absorbers, and Parameterization Method (from Chou and Suarez, 1994)}
+\caption{IR Spectral Bands, Absorbers, and Parameterization Method (from \cite{chzs:94})}
 \label{tab:fizhi:longwave}
 \end{table}
 
@@ -459,7 +459,7 @@
 of second turbulent moments is explicitly modeled by representing the third moments in terms of 
 the first and second moments.  This approach is known as a second-order closure modeling.
 To simplify and streamline the computation of the second moments, the level 2.5 assumption
-of Mellor and Yamada (1974) and Yamada (1977) is employed, in which only the turbulent 
+of Mellor and Yamada (1974) and \cite{yam:77} is employed, in which only the turbulent 
 kinetic energy (TKE),
 
 \[ {\h}{q^2}={\overline{{u^{\prime}}^2}}+{\overline{{v^{\prime}}^2}}+{\overline{{w^{\prime}}^2}}, \]
@@ -493,8 +493,8 @@
 
 In the level 2.5 approach, the vertical fluxes of the scalars $\theta_v$ and $q$ and the
 wind components $u$ and $v$ are expressed in terms of the diffusion coefficients $K_h$ and
-$K_m$, respectively.  In the statisically realizable level 2.5 turbulence scheme of Helfand
-and Labraga (1988), these diffusion coefficients are expressed as
+$K_m$, respectively.  In the statisically realizable level 2.5 turbulence scheme of 
+\cite{helflab:88}, these diffusion coefficients are expressed as
 
 \[
 K_h 
@@ -569,12 +569,12 @@
 \]
 Here $\phi_h$ is the similarity function of $\zeta$, which expresses the stability dependance of
 the temperature and moisture gradients, and is specified differently for stable and unstable
-layers according to Helfand and Schubert, 1995.
+layers according to \cite{helfschu:95}.
 
 $\psi_g$ is the non-dimensional temperature or moisture gradient in the viscous sublayer, 
 which is the mosstly laminar region between the surface and the tops of the roughness 
 elements, in which temperature and moisture gradients can be quite large.
-Based on Yaglom and Kader (1974):
+Based on \cite{yagkad:74}:
 \[
 \psi_{g} = { 0.55 (Pr^{2/3} - 0.2) \over \nu^{1/2} }
 (h_{0}u_{*} - h_{0_{ref}}u_{*_{ref}})^{1/2}
@@ -588,13 +588,13 @@
 {z_0} = c_1u^3_* + c_2u^2_* + c_3u_* + c_4 + {c_5 \over {u_*}}
 \]
 where the constants are chosen to interpolate between the reciprocal relation of
-Kondo(1975) for weak winds, and the piecewise linear relation of Large and Pond(1981)
+\cite{kondo:75} for weak winds, and the piecewise linear relation of \cite{larpond:81}
 for moderate to large winds.  Roughness lengths over land are specified
-from the climatology of Dorman and Sellers (1989).
+from the climatology of \cite{dorsell:89}.
 
 For an unstable surface layer, the stability functions, chosen to interpolate between the
 condition of small values of $\beta$ and the convective limit, are the KEYPS function 
-(Panofsky, 1973) for momentum, and its generalization for heat and moisture:  
+(\cite{pano:73}) for momentum, and its generalization for heat and moisture:  
 \[
 {\phi_m}^4 - 18 \zeta {\phi_m}^3 = 1 \hspace{1cm} ; \hspace{1cm} 
 {\phi_h}^2 - 18 \zeta {\phi_h}^3 = 1 \hspace{1cm} .
@@ -603,7 +603,7 @@
 speed approaches zero. 
 
 For a stable surface layer, the stability functions are the observationally 
-based functions of Clarke (1970),  slightly modified for
+based functions of \cite{clarke:70},  slightly modified for
 the momemtum flux:  
 \[
 {\phi_m} = { { 1 + 5 {{\zeta}_1} } \over { 1 + 0.00794 {{\zeta}_1}
@@ -661,7 +661,7 @@
 surface temperature of the ice.
 
 $C_g$ is the total heat capacity of the ground, obtained by solving a heat diffusion equation
-for the penetration of the diurnal cycle into the ground (Blackadar, 1977), and is given by:
+for the penetration of the diurnal cycle into the ground (\cite{black:77}), and is given by:
 \[
 C_g = \sqrt{ {\lambda C_s \over 2\omega} } = \sqrt{(0.386 + 0.536W + 0.15W^2)2\times10^{-3}
 {86400 \over 2 \pi} } \, \, .
@@ -676,13 +676,13 @@
 Land Surface Processes:
 
 \paragraph{Surface Type}
-The fizhi package surface Types are designated using the Koster-Suarez (1992) mosaic
-philosophy which allows multiple ``tiles'', or multiple surface types, in any one
-grid cell. The Koster-Suarez Land Surface Model (LSM) surface type classifications
+The fizhi package surface Types are designated using the Koster-Suarez (\cite{ks:91,ks:92}) 
+Land Surface Model (LSM) mosaic philosophy which allows multiple ``tiles'', or multiple surface 
+types, in any one grid cell. The Koster-Suarez LSM surface type classifications
 are shown in Table \ref{tab:fizhi:surftype}. The surface types and the percent of the grid
 cell occupied by any surface type were derived from the surface classification of
-Defries and Townshend (1994), and information about the location of permanent
-ice was obtained from the classifications of Dorman and Sellers (1989).
+\cite{deftow:94}, and information about the location of permanent
+ice was obtained from the classifications of \cite{dorsell:89}.
 The surface type for the \txt GCM grid is shown in Figure \ref{fig:fizhi:surftype}.
 The determination of the land or sea category of surface type was made from NCAR's
 10 minute by 10 minute Navy topography 
@@ -736,13 +736,13 @@
 
 \paragraph{Surface Roughness}
 The surface roughness length over oceans is computed iteratively with the wind
-stress by the surface layer parameterization (Helfand and Schubert, 1991).
-It employs an interpolation between the functions of Large and Pond (1981)
-for high winds and of Kondo (1975) for weak winds.
+stress by the surface layer parameterization (\cite{helfschu:95}).
+It employs an interpolation between the functions of \cite{larpond:81}
+for high winds and of \cite{kondo:75} for weak winds.
 
 
 \paragraph{Albedo}
-The surface albedo computation, described in Koster and Suarez (1991),
+The surface albedo computation, described in \cite{ks:91},
 employs the ``two stream'' approximation used in Sellers' (1987) Simple Biosphere (SiB)
 Model which distinguishes between the direct and diffuse albedos in the visible
 and in the near infra-red spectral ranges. The albedos are functions of the observed
@@ -753,7 +753,7 @@
 
 Gravity Wave Drag:
 
-The fizhi package employs the gravity wave drag scheme of Zhou et al. (1996).
+The fizhi package employs the gravity wave drag scheme of \cite{zhouetal:96}).
 This scheme is a modified version of Vernekar et al. (1992),
 which was based on Alpert et al. (1988) and Helfand et al. (1987).  
 In this version, the gravity wave stress at the surface is
@@ -770,7 +770,7 @@
 escape through the top of the model, although this effect is small for the current 70-level model.  
 The subgrid scale standard deviation is defined by $h$, and is not allowed to exceed 400 m. 
 
-The effects of using this scheme within a GCM are shown in Takacs and Suarez (1996).
+The effects of using this scheme within a GCM are shown in \cite{taksz:96}.
 Experiments using the gravity wave drag parameterization yielded significant and
 beneficial impacts on both the time-mean flow and the transient statistics of the
 a GCM climatology, and have eliminated most of the worst dynamically driven biases 
@@ -827,62 +827,10 @@
 Surface geopotential heights are provided from an averaging of the Navy 10 minute
 by 10 minute dataset supplied by the National Center for Atmospheric Research (NCAR) to the
 model's grid resolution. The original topography is first rotated to the proper grid-orientation
-which is being run, and then  
-averages the data to the model resolution.  
-The averaged topography is then passed through a Lanczos (1966) filter in both dimensions 
-which removes the smallest
-scales while inhibiting Gibbs phenomena.  
-
-In one dimension, we may define a cyclic function in $x$ as:
-\begin{equation}
-f(x) = {a_0 \over 2} + \sum_{k=1}^N \left( a_k \cos(kx) + b_k \sin(kx) \right)
-\label{eq:fizhi:filt}
-\end{equation}
-where $N = { {\rm IM} \over 2 }$ and ${\rm IM}$ is the total number of points in the $x$ direction.
-Defining $\Delta x = { 2 \pi \over {\rm IM}}$, we may define the average of $f(x)$ over a 
-$2 \Delta x$ region as:
-
-\begin{equation}
-\overline {f(x)} = {1 \over {2 \Delta x}} \int_{x-\Delta x}^{x+\Delta x} f(x^{\prime}) dx^{\prime}
-\label{eq:fizhi:fave1}
-\end{equation}
-
-Using equation (\ref{eq:fizhi:filt}) in equation (\ref{eq:fizhi:fave1}) and integrating, we may write:
- 
-\begin{equation}
-\overline {f(x)} = {a_0 \over 2} + {1 \over {2 \Delta x}}
-\sum_{k=1}^N \left [
-\left. a_k { \sin(kx^{\prime}) \over k } \right /_{x-\Delta x}^{x+\Delta x} -
-\left. b_k { \cos(kx^{\prime}) \over k } \right /_{x-\Delta x}^{x+\Delta x} 
-\right]
-\end{equation}
-or
-
-\begin{equation}
-\overline {f(x)} = {a_0 \over 2} + \sum_{k=1}^N {\sin(k \Delta x) \over {k \Delta x}}
-\left( a_k \cos(kx) + b_k \sin(kx) \right)
-\label{eq:fizhi:fave2}
-\end{equation}
-
-Thus, the Fourier wave amplitudes are simply modified by the Lanczos filter response
-function ${\sin(k\Delta x) \over {k \Delta x}}$.  This may be compared with an $mth$-order 
-Shapiro (1970) filter response function, defined as $1-\sin^m({k \Delta x \over 2})$,
-shown in Figure \ref{fig:fizhi:lanczos}.
-It should be noted that negative values in the topography resulting from
-the filtering procedure are {\em not} filled.
-
-\begin{figure*}[htbp]
-  \centerline{  \epsfysize=7.0in  \epsfbox{part6/lanczos.ps}}
-  \caption{ \label{fig:fizhi:lanczos} Comparison between the Lanczos and $mth$-order Shapiro filter 
-  response functions for $m$ = 2, 4, and 8. }
-\end{figure*}
+which is being run, and then  averages the data to the model resolution.  
 
-The standard deviation of the subgrid-scale topography
-is computed from a modified version of the the Navy 10 minute by 10 minute dataset.
-The 10 minute by 10 minute topography is passed through a wavelet
-filter in both dimensions which removes the scale smaller than 20 minutes.
-The topography is then averaged to $1^\circ x 1^\circ$ grid resolution, and then
-re-interpolated back to the 10 minute by 10 minute resolution. 
+The standard deviation of the subgrid-scale topography is computed by interpolating the 10 minute 
+data to the model's resolution and re-interpolating back to the 10 minute by 10 minute resolution. 
 The sub-grid scale variance is constructed based on this smoothed dataset.
 
 
@@ -1588,7 +1536,7 @@
 \noindent
 $\phi_h$ is the similarity function of $\zeta$, which expresses the stability dependance of
 the temperature and moisture gradients, specified differently for stable and unstable 
-layers according to Helfand and Schubert, 1993. k is the Von Karman constant, $\zeta$ is the 
+layers according to \cite{helfschu:95}. k is the Von Karman constant, $\zeta$ is the 
 non-dimensional stability parameter, Pr is the Prandtl number for air, $\nu$ is the molecular 
 viscosity, $z_{0}$ is the surface roughness length, $u_*$ is the surface stress velocity 
 (see diagnostic number 67), and the subscript ref refers to a reference value.
@@ -1610,7 +1558,7 @@
 \noindent
 $\phi_m$ is the similarity function of $\zeta$, which expresses the stability dependance of
 the temperature and moisture gradients, specified differently for stable and unstable layers
-according to Helfand and Schubert, 1993. k is the Von Karman constant, $\zeta$ is the 
+according to \cite{helfschu:95}. k is the Von Karman constant, $\zeta$ is the 
 non-dimensional stability parameter, $u_*$ is the surface stress velocity 
 (see diagnostic number 67), and $W_s$ is the magnitude of the surface layer wind.
 \\
@@ -1622,7 +1570,7 @@
 In the level 2.5 version of the Mellor-Yamada (1974) hierarchy, the turbulent heat or
 moisture flux for the atmosphere above the surface layer can be expressed as a turbulent 
 diffusion coefficient $K_h$ times the negative of the gradient of potential temperature 
-or moisture. In the Helfand and Labraga (1988) adaptation of this closure, $K_h$ 
+or moisture. In the \cite{helflab:88} adaptation of this closure, $K_h$ 
 takes the form:
 \[
 {\bf ET} = K_h = -{( {\overline{w^{\prime}\theta_v^{\prime}}}) \over {\pp{\theta_v}{z}} }
@@ -1641,7 +1589,7 @@
 
 \noindent
 For the detailed equations and derivations of the modified level 2.5 closure scheme,
-see Helfand and Labraga, 1988.
+see \cite{helflab:88}.
 
 \noindent
 In the surface layer, ${\bf {ET}}$ is the exchange coefficient for heat and moisture,
@@ -1663,7 +1611,7 @@
 In the level 2.5 version of the Mellor-Yamada (1974) hierarchy, the turbulent heat
 momentum flux for the atmosphere above the surface layer can be expressed as a turbulent
 diffusion coefficient $K_m$ times the negative of the gradient of the u-wind.
-In the Helfand and Labraga (1988) adaptation of this closure, $K_m$
+In the \cite{helflab:88} adaptation of this closure, $K_m$
 takes the form:
 \[
 {\bf EU} = K_m = -{( {\overline{u^{\prime}w^{\prime}}}) \over {\pp{U}{z}} }
@@ -1683,7 +1631,7 @@
 
 \noindent
 For the detailed equations and derivations of the modified level 2.5 closure scheme,
-see Helfand and Labraga, 1988.
+see \cite{helflab:88}.
  
 \noindent
 In the surface layer, ${\bf {EU}}$ is the exchange coefficient for momentum,
@@ -2073,7 +2021,7 @@
 sea ice, $H$ is the upward sensible heat flux, $LE$ is the upward latent heat
 flux, and $C_g$ is the total heat capacity of the ground. 
 $C_g$ is obtained by solving a heat diffusion equation 
-for the penetration of the diurnal cycle into the ground (Blackadar, 1977), and is given by:
+for the penetration of the diurnal cycle into the ground (\cite{black:77}), and is given by:
 \[
 C_g = \sqrt{ {\lambda C_s \over {2 \omega} } } = \sqrt{(0.386 + 0.536W + 0.15W^2)2x10^{-3}
 { 86400. \over {2 \pi} } } \, \, .
@@ -2428,7 +2376,7 @@
 
 \noindent
 Over the land surface, the surface roughness length is interpolated to the local
-time from the monthly mean data of Dorman and Sellers (1989). Over the ocean,
+time from the monthly mean data of \cite{dorsell:89}. Over the ocean,
 the roughness length is a function of the surface-stress velocity, $u_*$.
 \[
 {\bf Z0} = c_1u^3_* + c_2u^2_* + c_3u_* + c_4 + {c_5 \over {u_*}}
@@ -2436,7 +2384,7 @@
 
 \noindent
 where the constants are chosen to interpolate between the reciprocal relation of
-Kondo(1975) for weak winds, and the piecewise linear relation of Large and Pond(1981) 
+\cite{kondo:75} for weak winds, and the piecewise linear relation of \cite{larpond:81}
 for moderate to large winds.
 \\