/[MITgcm]/manual/s_phys_pkgs/text/fizhi.tex

Diff of /manual/s_phys_pkgs/text/fizhi.tex

Parent Directory | Revision Log | View Revision Graph Revision Graph | View Patch Patch

-revision 1.9 by molod,
Mon Jul 18 20:45:27 2005 UTC
+revision 1.10 by molod,
Tue Aug  2 15:43:59 2005 UTC
 Line 21 
 Moist Convective Processes:
  \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.
 Line 43 
 where we have used the hydrostatic equat
  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}}} } ,
 Line 101 
 $\alpha$ of the total adjustment. The pa
  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.
 Line 221 
 The solar constant value used in the pac
  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}
 Line 231 
 heating due to the absoption by water va
  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
 Line 321 
 low/middle/high classification, and appr
  \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}.
 Line 357 
 Band & Spectral Range (cm$^{-1}$) & Abso
  \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}
 Line 459 
 Within the atmosphere, the time evolutio
  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),
  \[ {\h}{q^2}={\overline{{u^{\prime}}^2}}+{\overline{{v^{\prime}}^2}}+{\overline{{w^{\prime}}^2}}, \]
 Line 493 
 of TKE.
  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
+ $K_m$, respectively.  In the statisically realizable level 2.5 turbulence scheme of
- and Labraga (1988), these diffusion coefficients are expressed as
+ \cite{helflab:88}, these diffusion coefficients are expressed as
  \[
  K_h
 Line 569 
 where $\psi_h$ is the surface layer non-
  \]
  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}:
  \[
  \psi_{g} = { 0.55 (Pr^{2/3} - 0.2) \over \nu^{1/2} }
  (h_{0}u_{*} - h_{0_{ref}}u_{*_{ref}})^{1/2}
 Line 588 
 The surface roughness length over oceans
  {z_0} = c_1u^3_* + c_2u^2_* + c_3u_* + c_4 + {c_5 \over {u_*}}
  \]
  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} .
 Line 603 
 The function for heat and moisture assur
  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}
 Line 661 
 be $3 \hspace{.1cm} m$ where sea ice is
  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} } \, \, .
 Line 676 
 is a function of the ground wetness, $W$
  Land Surface Processes:
  \paragraph{Surface Type}
- The fizhi package surface Types are designated using the Koster-Suarez (1992) mosaic
+ The fizhi package surface Types are designated using the Koster-Suarez (\cite{ks:91,ks:92})
- philosophy which allows multiple ``tiles'', or multiple surface types, in any one
+ Land Surface Model (LSM) mosaic philosophy which allows multiple ``tiles'', or multiple surface
- grid cell. The Koster-Suarez Land Surface Model (LSM) surface type classifications
+ 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
+ \cite{deftow:94}, and information about the location of permanent
- ice was obtained from the classifications of Dorman and Sellers (1989).
+ 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
 minute by 10 minute Navy topography
 Line 736 
 and surface albedo.}
  \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).
+ stress by the surface layer parameterization (\cite{helfschu:95}).
- It employs an interpolation between the functions of Large and Pond (1981)
+ It employs an interpolation between the functions of \cite{larpond:81}
- for high winds and of Kondo (1975) for weak winds.
+ 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
 Line 753 
 to the height of the vegetation elements
  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
 Line 770 
 A modification introduced by Zhou et al.
  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
 Line 827 
 current years and frequencies available.
  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
+ which is being run, and then  averages the data to the model resolution.
- 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*}
- The standard deviation of the subgrid-scale topography
+ The standard deviation of the subgrid-scale topography is computed by interpolating the 10 minute
- is computed from a modified version of the the Navy 10 minute by 10 minute dataset.
+ data to the model's resolution and re-interpolating back to the 10 minute by 10 minute resolution.
- 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 sub-grid scale variance is constructed based on this smoothed dataset.
-Line 1588 
 $h_{0} = 30z_{0}$ with a maximum value o
+Line 1536 
 $h_{0} = 30z_{0}$ with a maximum value o
  \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.
-Line 1610 
 where $\psi_m$ is the surface layer non-
+Line 1558 
 where $\psi_m$ is the surface layer non-
  \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.
  \\
-Line 1622 
 non-dimensional stability parameter, $u_
+Line 1570 
 non-dimensional stability parameter, $u_
  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}} }
-Line 1641 
 are functions of the Richardson number.
+Line 1589 
 are functions of the Richardson number.
  \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,
-Line 1663 
 and $W_s$ is the magnitude of the surfac
+Line 1611 
 and $W_s$ is the magnitude of the surfac
  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}} }
-Line 1683 
 are functions of the Richardson number.
+Line 1631 
 are functions of the Richardson number.
  \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,
-Line 2073 
 net surface upward longwave radiative fl
+Line 2021 
 net surface upward longwave radiative fl
  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} } } \, \, .
-Line 2428 
 number 10), and $W_s$ is the surface win
+Line 2376 
 number 10), and $W_s$ is the surface win
  \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_*}}
-Line 2436 
 the roughness length is a function of th
+Line 2384 
 the roughness length is a function of th
  \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.
  \\

 Legend:



Removed from v.1.9
 


changed lines


 
Added in v.1.10
 Legend:



Removed from v.1.9
 


changed lines


 
Added in v.1.10
-Removed from v.1.9
+Added in v.1.10

	ViewVC Help
Powered by ViewVC 1.1.22