<p><b>gill</b> 2008-05-06 14:44:59 -0600 (Tue, 06 May 2008)</p><p>3.0 sections for initialization<br>
and nesting - two new figures<br>
<br>
M technote/initialization.tex<br>
A technote/figures/zone12.pdf<br>
AM technote/figures/WPS_real_wrf.pdf<br>
M technote/nest.tex<br>
</p><hr noshade><pre><font color="gray">Added: trunk/wrf/technote/figures/WPS_real_wrf.pdf
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Modified: trunk/wrf/technote/initialization.tex
===================================================================
--- trunk/wrf/technote/initialization.tex 2008-05-05 19:38:13 UTC (rev 64)
+++ trunk/wrf/technote/initialization.tex 2008-05-06 20:44:59 UTC (rev 65)
@@ -1,394 +1,424 @@
-\chapter{Initial Conditions}
-\label{initialization_chap}
-
-The ARW may be run with initial conditions that are defined
-analytically for idealized simulations, or it may be run using
-interpolated data from either a large-scale analysis or forecast for
-real-data cases. Both 2D and 3D tests cases for idealized
-simulations are provided.
-Several sample cases for real-data simulations are provided, which
-rely on pre-processing from an external package that converts
-the large-scale GriB data into a format suitable for ingest by the ARW's
-real-data processor.
-
-The programs that generate the specific initial conditions for the selected
-idealized or real-data case function similarly. They provide the ARW with:
-\begin{itemize}\setlength{\parskip}{-5pt}
-\item input data that is on the correct horizontal and vertical staggering;
-\item hydrostatically balanced reference state and perturbation fields; and
-\item metadata specifying such information as the date, grid physical characteristics,
-and projection details.
-\end{itemize}
-</font>
<font color="red">oindent For neither the idealized nor the real-data cases
-are the initial conditions enhanced with observations. However, output from
-the ARW system initial condition programs is suitable as input to the WRF variational
-assimilation package (see Chapter \ref{var_chap}).
-
-\section{Initialization for Idealized Conditions}
-
-The ARW comes with a number of test cases using idealized
-environments, including mountain waves (em\_hill2d\_x), squall lines
-(em\_squall2d\_x, em\_squall2d\_y), supercell thunderstorms
-(em\_quarter\_ss), gravity currents (em\_grav2d\_x), and baroclinic
-waves (em\_b\_wave). A brief description of these test cases can be
-found in the README\_test\_cases file provided in the ARW release.
-The test cases include examples of atmospheric
-flows at fine scales (e.g., the gravity current example has a grid-spacing of
-100 meters and a time step of 1 second) and examples of flow at large
-scales (e.g., the baroclinic wave test case uses a grid-spacing of 100 km and
-a time step of 600 s), in addition to the traditional mesoscale and
-cloudscale model simulations. The test suite allows an ARW user to
-easily reproduce these known solutions. The test suite is also the
-starting point for constructing idealized flow simulations by modifying
-initializations that closely resemble a desired initialization.
-
-All of these tests use as input a 1D sounding specified as a function of
-geometric height $z$ (except for the baroclinic wave case that uses a 2D
-sounding specified in $[y,z]$), and, with the exception of the baroclinic
-wave test case, the sounding files are in text format that can be
-directly edited by the user. The 1D specification of the sounding in
-these test files requires the surface values of pressure, potential
-temperature, and water vapor mixing ratio, followed by the potential
-temperature, vapor mixing ratio, and horizontal wind components at some
-heights above the surface. The initialization programs for each case
-assume that this moist sounding represents an atmosphere in hydrostatic
-balance.
-
-Two sets of thermodynamic fields are needed for the model--- the
-reference state and the perturbation state (see Chapter
-\ref{equation_chap} for further discussion of the equations). The
-reference state used in the idealized initializations is computed using
-the input sounding from which the moisture is discarded (because the
-reference state is dry). The perturbation state is computed using the full
-moist input sounding. The procedure for computing the hydrostatically-balanced
-ARW reference and perturbation state variables from the input
-sounding is as follows. First, density and both a dry and full
-hydrostatic pressure are computed from the input sounding at the input
-sounding levels $z$. This is accomplished by integrating the
-hydrostatic equation vertically up the column using the surface pressure
-and potential temperature as the lower boundary condition. The
-hydrostatic equation is
-%
-\begin{equation} \delta_z p = - {\overline
-\rho}^z g (1 + (R_d/R_v) {\overline q_v}^z),
-\label{init_hydro}
-\end{equation}
-%
-</font>
<font color="red">oindent
-where $\overline{\rho}^z$ is a two point average between input sounding
-levels, and $\delta_z p$ is the difference of the pressure between input
-sounding levels divided by the height difference. Additionally, the
-equation of state is needed to close the system:
-%
-\begin{equation} \alpha_d = {1 \over \rho_d} = {R_d
-\theta \over p_o} \biggl(1 + {R_d \over R_v}q_v\biggr)
-\biggl({p \over p_o}\biggr)^{-{c_v \over c_p}},
-\label{init_state}
-\end{equation}
-%
-</font>
<font color="red">oindent
-where $q_v$ and $\theta$ are given in the input sounding.
-\eqref{init_hydro} and \eqref{init_state} are a coupled set of nonlinear
-equations for $p$ and $\rho$ in the vertical integration, and they are
-solved by iteration. The dry pressure on input sounding levels is
-computed by integrating the hydrostatic relation down from the top,
-excluding the vapor component.
-
-Having computed the full pressure (dry plus vapor) and dry air pressure
-on the input sounding levels, the pressure at the model top ($p_{dht}$)
-is computed by linear interpolation in height (or possibly
-extrapolation) given the height of the model top (an input variable).
-The column mass $\mu_d$ is computed by interpolating the dry air
-pressure to the surface and subtracting it from $p_{dht}$. Given the
-column mass, the dry-air pressure at each $\eta$ level is known from the
-coordinate definition \eqref{eta_def}, repeated here
-%
-\begin{equation}
-\eta = (p_{dh}-p_{dht})/\mu_d ~~~~~~~{\rm where
- }~~~ \mu_d = p_{dhs}-p_{dht},
-</font>
<font color="red">otag
-\end{equation}
-%
-</font>
<font color="red">oindent
-and the pressures $p_{dhs}$ and $p_{dht}$ refer to the dry atmosphere.
-The potential
-temperature from the input sounding is interpolated to
-each of the model pressure levels, and the equation of state
-\eqref{init_state} is used to compute the inverse density
-$\alpha_d$. Finally, the
-ARW's hydrostatic relation \eqref{hydrostatic_relation},
-in discrete form
-%
-\begin{equation}
-\delta_\eta \phi = - \alpha_d \mu_d
-</font>
<font color="red">otag
-\end{equation}
-</font>
<font color="red">oindent
-is used to compute the geopotential. This procedure is used to compute
-the reference state (assuming a dry atmosphere) and the full state
-(using the full moist sounding). The perturbation variables are
-computed as the difference between the reference and full state. It
-should also be noted that in the nonhydrostatic model integration,
-the inverse density $\alpha_d$ is diagnosed from the geopotential using
-this equation of state, and the pressure is diagnosed from the equation
-of state using the inverse density $\alpha_d$ and the prognostic potential
-temperature $\theta$. Thus, the ARW's prognostic variables $\mu_d$,
-$\theta$, and $\phi$ are in exact hydrostatic balance for the model
-equations (to machine roundoff).
-
-\section{Initialization for Real-Data Conditions}
-
-The initial conditions for the real-data cases are pre-processed through a separate
-package called the Standard Initialization (SI, see Fig. \ref{figure:SI_real_wrf}).
-The output from the SI is passed to the
-real-data pre-processor in the ARW--- program {\it real}--- which generates initial and lateral boundary
-conditions. This section is primarily about the steps taken to build the
-initial and the lateral boundary conditions for a real-data case. Even though the
-SI is outside of the ARW system, a brief description is appropriate to see how the
-raw meteorological and static terrestrial data are brought into the model
-for real-data cases.
-
-\subsection{Use of the Standard Initialization by the ARW}
-
-The SI is a set of programs that takes
-terrestrial and meteorological data (typically in GriB format) and transforms them for input to
-the ARW pre-processor program for real-data cases ({\it real}).
-Figure \ref {figure:SI_real_wrf} shows the flow of data into and out of the SI system.
-The first step for the SI is to define a physical grid (including
-the projection type, location on the globe,
-number of grid points, nest locations, and grid distances) and
-to interpolate static fields to the prescribed domain.
-Independent of the domain configuration,
-an external analysis or forecast is processed by the SI's GriB decoder,
-which diagnoses required fields and
-reformats the GriB data into an internal binary format.
-With a specified domain,
-the SI horizontally interpolates the meteorological data onto the projected domain(s),
-and vertically interpolates the data to the
-ARW's $\eta$ coordinate.
-The output data from the SI supplies a complete 3-dimensional snapshot of the atmosphere
-on the selected model grid's horizontal and vertical staggering at the selected time slices,
-which is sent to the ARW pre-processor program for real-data cases.
-
-%
-% Figure showing SI and real and ARW
-%
-\begin{figure}
- \centering
- \includegraphics[width=6in]{figures/SI_real_wrf.pdf}
- \caption{\label{figure:SI_real_wrf}Schematic showing
-the data flow and program components in the SI, and how the SI feeds initial data to the ARW.
-Letters in the rectangular boxes indicate program names.
-GRID\_GEN: defines the model domain and creates static files of terrestrial data. GRIB\_PREP:
-decodes GriB data. HINTERP: interpolates meteorological data to the model domain. VINTERP:
-vertically interpolates data to model coordinate.}
-\end{figure}
-
-The input to the ARW real-data processor from the
-SI contains 3-dimensional fields of potential temperature (K), mixing ratio
-(kg/kg), and the horizontal components of momentum (m/s, already rotated to the model
-projection).
-The 2-dimensional static terrestrial fields include:
-albedo, Coriolis parameters, terrain elevation, vegetation/land-use type,
-land/water mask, map scale factors, map rotation angle, soil texture category, vegetation greenness fraction,
-annual mean temperature,
-and latitude/longitude.
-The 2-dimensional time-dependent fields from the external model, after processing by the SI, include:
-$\mu_d$ (Pa), layers of soil temperature (K) and soil moisture (kg/kg, either total moisture, or
-binned into total and liquid content),
-snow depth (m), skin temperature (K), and fractional sea ice. All of the fields in the final output from the SI
-are on the correct horizontal and vertical staggering for the ARW.
-The input data from the SI is assumed to be hydrostatically balanced.
-
-
-
-\subsection{Reference and Perturbation State}
-Identical to the idealized initializations, there is a partitioning of some of the
-meteorological data into reference and perturbation fields.
-For real-data cases, the reference state is defined by terrain elevation and the following three constants:
-\begin{itemize}\setlength{\parskip}{-5pt}
-\item $p_{0}$ ($10^5$ Pa) reference sea level pressure;
-\item $T_{0}$ (usually 270 to 300 K) reference sea level temperature; and
-\item $A$ (50 K) temperature difference between the pressure levels of $p_{0}$ and $p_{0}/e$.
-\end{itemize}
-
-</font>
<font color="red">oindent Using these parameters, the dry reference state surface pressure is
-\begin{equation}
-p_{dhs} = p_{0}~exp\Bigg({-T_{0} \over A} +
- \sqrt{ {\bigg( {T_{0} \over A } \bigg)}^2 - ~
- { 2\phi_{sfc} \over { A~R_d}} } \Bigg).
-\label{init_psurf}
-\end{equation}
-
-</font>
<font color="red">oindent From \eqref{init_psurf}, the 3-dimensional reference pressure is computed as
-a function of the vertical coordinate $\eta$ levels and the model top $p_{dht}$
-(input provided by SI for real-data cases):
-\begin{equation}
-\overline{p}_d = \eta ~( p_{dhs} - p_{dht} ) + p_{dht}.
-\label{init_pbar}
-\end{equation}
-
-</font>
<font color="red">oindent With \eqref{init_pbar}, the reference temperature is a straight line on a skew-T plot, defined as
-\begin{equation}
-T = T_0 + A~ln {\overline{p}_d \over p_0}.
-</font>
<font color="red">otag
-\end{equation}
-
-</font>
<font color="red">oindent From the reference temperature and pressure,
-the reference potential temperature is then defined as
-
-</font>
<font color="red">oindent
-\begin{equation}
-\overline{\theta}_d = {\bigg( T_{0} + A~ln{\overline{p}_d \over p_{0} } \bigg) }
-{\bigg( {p_0 \over \overline{p}_d } \bigg) }
-^{R_d \over C_p},
-\label{init_thetad}
-\end{equation}
-
-</font>
<font color="red">oindent and the reciprocal of the reference density using
-\eqref{init_pbar} and \eqref{init_thetad} is given by
-\begin{equation}
-\overline{\alpha}_d = {1 \over \overline{\rho}_d} = {{R_d ~\overline{\theta}_d}\over p_{0} }~\bigg(
-{\overline{p}_d \over p_{0} } \bigg)^{-{C_v \over C_p}}.
-\label{init_alphabar}
-\end{equation}
-
-</font>
<font color="red">oindent The base state difference of the dry surface pressure
-from \eqref{init_psurf} and the model top is
-given as
-\begin{equation}
-\overline{\mu}_d = p_{dhs} - p_{dht}.
-\label{init_mubar}
-\end{equation}
-
-</font>
<font color="red">oindent
-From \eqref{init_alphabar} and \eqref{init_mubar},
-the reference state geopotential defined from the hydrostatic relation is
-\begin{equation}
-\delta_{\eta} \overline{\phi} = -\overline{\alpha}_d~\overline{\mu}_d.
-</font>
<font color="red">otag
-\end{equation}
-
-</font>
<font color="red">oindent One of the total fields provided to the real-data
-cases by the SI is $\mu_d$. The perturbation
-field given the reference value \eqref{init_mubar} is
-\begin{equation}
-\mu_d' = \mu_d - \overline{\mu}_d.
-\label{init_muprime}
-\end{equation}
-
-</font>
<font color="red">oindent Starting with the reference state fields
-(\ref{init_pbar}, \ref{init_alphabar}, and \ref{init_mubar}) and the
-dry surface pressure perturbation (\ref{init_muprime}),
-the perturbation fields for pressure and inverse density are diagnosed.
-The pressure perturbation includes moisture and is diagnosed from
-the hydrostatic equation
-%
-\begin{equation}
-\delta_{\eta} p' = \mu'_d \bigg(1 + {\overline{q_v}^\eta} \bigg) +
- \overline{q_v}^\eta~\overline \mu_d,
-%\label{init_pprime}
-</font>
<font color="red">otag
-\end{equation}
-%
-</font>
<font color="red">oindent
-which is
-integrated down from
-at the model top (where $p'= 0$) to recover $p'$.
-The total dry inverse density is given as
-\begin{equation}
-\alpha_d = {R_d \over p_{0} } ~ \theta~ \bigg( 1 + {R_v \over R_d}q_v \bigg)~
- \bigg( {{p'_d + \overline {p}_d} \over p_{0} } \bigg )^{-{C_v \over C_p}},
-</font>
<font color="red">otag
-\end{equation}
-
-</font>
<font color="red">oindent which defines the perturbation field for inverse density
-
-\begin{equation}
-\alpha'_d = \alpha_d - \overline{\alpha}_d.
-</font>
<font color="red">otag
-\end{equation}
-
-</font>
<font color="red">oindent
-The perturbation geopotential
-is diagnosed from the hydrostatic relation
-\begin{equation}
-\delta_{\eta} \phi' = - \big ( {\mu}_d \alpha'_d + \mu'_d
-\overline{\alpha}_d \big )
-</font>
<font color="red">otag
-\end{equation}
-%
-by upward integration using the terrain elevation as the lower boundary condition.
-In future versions of the real-data pre-processor, $p'$ will
-be re-diagnosed consistent with the method used in the model
-\eqref{ideal_gas_law} as a final step. No modifications to the
-original $\mu_{d}$, $u$, $v$, $q_v$, or $\theta$ from the SI are
-performed. The vertical component of velocity is initialized to zero.
-
-\subsection{Generating Lateral Boundary Data}
-
-This section deals with generating the separate lateral boundary condition file used
-exclusively for the real-data cases. For information
-on which lateral boundary options are available for both the idealized and real-data
-cases, see Chapter \eqref{lbc_chap}.
-
-The specified
-lateral boundary condition for the coarse grid for real-data cases is supplied by an external file that is
-generated by program {\it real}.
-This file contains
-records for the fields $u$, $v$, $\theta$, $q_v$, $\phi'$, and $\mu'_d$ that are used by the ARW to
-constrain the lateral boundaries (other fields are in the boundary file, but are not used).
-The lateral boundary file holds one less time period than was processed by the SI.
-Each of these variables has both
-a valid value at the initial time of the lateral boundary time and a tendency term to get to the
-next boundary time period. For example, assuming a 3-hourly availability of data from the SI,
-the first time period of the lateral boundary file
-for $u$ would contain data for both coupled $u$ (map scale factor and $\mu_d$ interpolated to
-the variable's
-staggering) at the 0 h time
-
-\begin{equation}
-%U_{0h} = {{\mu_u~u}\over{m_u}} \bigg | _{0h}
-U_{0h} = {{\overline{\mu_d}^x u}\over{\overline{m}^x}} \bigg | _{0h},
-</font>
<font color="red">otag
-\end{equation}
-</font>
<font color="red">oindent and a tendency value defined as
-\begin{equation}
-U_t = { U_{3h} - U_{0h} \over 3h},
-</font>
<font color="red">otag
-\end{equation}
-
-</font>
<font color="red">oindent which would take a grid point from the initial value to the value at the next large-scale time
-during 3 simulation hours.
-The horizontal momentum fields are coupled both with $\mu_d$ and the inverse map factor. The
-other 3-dimensional fields ($\theta$, $q_v$, and $\phi'$) are coupled only with $\mu_d$.
-The $\mu'_d$ lateral boundary field is not coupled.
-
-Each lateral boundary field
-is defined along the four sides of the
-rectangular grid (loosely referred to as the north, south, east, and west sides).
-The boundary values and tendencies for vertical velocity and the non-vapor moisture species are included
-in the external lateral boundary file, but act as
-place-holders for the nested boundary data for the fine grids.
-The width of the lateral
-boundary along each of the four sides is user selectable at run-time.
-
-\subsection{Masking of Surface Fields}
-
-Some of the meteorological and static fields are ``masked''. A masked field is one in which
-the values are typically defined only over water (e.g., sea surface temperature) or defined
-only over land (e.g., soil temperature).
-The need to match all of the masked fields consistently to each other requires additional steps
-for the real-data cases due to the masked data's presumed use in various physics packages in the soil,
-at the surface, and in the boundary layer.
-If the land/water
-mask for a location is flagged as a water point, then the vegetation and soil categories must also
-recognize the location as the special water flag for each of their respective categorical indices.
-
-The values for the soil temperature and soil moisture come from the SI on the
-native levels originally defined for those variables
-in the large-scale model. The SI does no vertical interpolation for the
-soil data. While it is typical to try to match the ARW soil scheme with
-the incoming data, that is not a requirement. Pre-processor {\it real} will vertically interpolate
-(linear in depth below the ground) from the incoming levels to the requested soil layers to be
-used within the model.
+\chapter{Initial Conditions}
+\label{initialization_chap}
+
+The ARW may be run with initial conditions that are defined
+analytically for idealized simulations, or it may be run using
+interpolated data from either a large-scale analysis or forecast for
+real-data cases. Both 2D and 3D tests cases for idealized
+simulations are provided.
+Several sample cases for real-data simulations are provided, which
+rely on pre-processing from an external package that converts
+the large-scale GriB data into a format suitable for ingest by the ARW's
+real-data processor.
+
+The programs that generate the specific initial conditions for the selected
+idealized or real-data case function similarly. They provide the ARW with:
+\begin{itemize}\setlength{\parskip}{-5pt}
+\item input data that is on the correct horizontal and vertical staggering;
+\item hydrostatically balanced reference state and perturbation fields; and
+\item metadata specifying such information as the date, grid physical characteristics,
+and projection details.
+\end{itemize}
+</font>
<font color="blue">oindent For neither the idealized nor the real-data cases
+are the initial conditions enhanced with observations. However, output from
+the ARW system initial condition programs is suitable as input to the WRF variational
+assimilation package (see Chapter \ref{var_chap}).
+
+\section{Initialization for Idealized Conditions}
+
+The ARW comes with a number of test cases using idealized
+environments, including large eddy simulations (em\_les),
+sea breezes ( em\_seabreeze), mountain waves (em\_hill2d\_x), squall lines
+(em\_squall2d\_x, em\_squall2d\_y), supercell thunderstorms
+(em\_quarter\_ss), gravity currents (em\_grav2d\_x), baroclinic
+waves (em\_b\_wave), and global systems (em\_heldsuarez).
+A brief description of these test cases can be
+found in the README\_test\_cases file provided in the ARW release.
+The test cases include examples of atmospheric
+flows at fine scales (e.g., the gravity current example has a grid-spacing of
+100 meters and a time step of 1 second) and examples of flow at large
+scales (e.g., the Held Suarez global test case uses a grid-spacing around 600 km and
+a time step of 1800 s), in addition to the traditional mesoscale and
+cloudscale model simulations. The test suite allows an ARW user to
+easily reproduce these known solutions. The test suite is also the
+starting point for constructing idealized flow simulations by modifying
+initializations that closely resemble a desired initialization.
+
+All of these tests use as input a 1D sounding specified as a function of
+geometric height $z$ (except for the baroclinic wave case that uses a 2D
+sounding specified in $[y,z]$), and, with the exception of the baroclinic
+wave test case, the sounding files are in text format that can be
+directly edited by the user. The 1D specification of the sounding in
+these test files requires the surface values of pressure, potential
+temperature, and water vapor mixing ratio, followed by the potential
+temperature, vapor mixing ratio, and horizontal wind components at some
+heights above the surface. The initialization programs for each case
+assume that this moist sounding represents an atmosphere in hydrostatic
+balance.
+
+Two sets of thermodynamic fields are needed for the model--- the
+reference state and the perturbation state (see Chapter
+\ref{equation_chap} for further discussion of the equations). The
+reference state used in the idealized initializations is computed using
+the input sounding from which the moisture is discarded (because the
+reference state is dry). The perturbation state is computed using the full
+moist input sounding. The procedure for computing the hydrostatically-balanced
+ARW reference and perturbation state variables from the input
+sounding is as follows. First, density and both a dry and full
+hydrostatic pressure are computed from the input sounding at the input
+sounding levels $z$. This is accomplished by integrating the
+hydrostatic equation vertically up the column using the surface pressure
+and potential temperature as the lower boundary condition. The
+hydrostatic equation is
+%
+\begin{equation} \delta_z p = - {\overline
+\rho}^z g (1 + (R_d/R_v) {\overline q_v}^z),
+\label{init_hydro}
+\end{equation}
+%
+</font>
<font color="blue">oindent
+where $\overline{\rho}^z$ is a two point average between input sounding
+levels, and $\delta_z p$ is the difference of the pressure between input
+sounding levels divided by the height difference. Additionally, the
+equation of state is needed to close the system:
+%
+\begin{equation} \alpha_d = {1 \over \rho_d} = {R_d
+\theta \over p_o} \biggl(1 + {R_d \over R_v}q_v\biggr)
+\biggl({p \over p_o}\biggr)^{-{c_v \over c_p}},
+\label{init_state}
+\end{equation}
+%
+</font>
<font color="blue">oindent
+where $q_v$ and $\theta$ are given in the input sounding.
+\eqref{init_hydro} and \eqref{init_state} are a coupled set of nonlinear
+equations for $p$ and $\rho$ in the vertical integration, and they are
+solved by iteration. The dry pressure on input sounding levels is
+computed by integrating the hydrostatic relation down from the top,
+excluding the vapor component.
+
+Having computed the full pressure (dry plus vapor) and dry air pressure
+on the input sounding levels, the pressure at the model top ($p_{dht}$)
+is computed by linear interpolation in height (or possibly
+extrapolation) given the height of the model top (an input variable).
+The column mass $\mu_d$ is computed by interpolating the dry air
+pressure to the surface and subtracting from it $p_{dht}$. Given the
+column mass, the dry-air pressure at each $\eta$ level is known from the
+coordinate definition \eqref{eta_def}, repeated here
+%
+\begin{equation}
+\eta = (p_{dh}-p_{dht})/\mu_d ~~~~~~~{\rm where
+ }~~~ \mu_d = p_{dhs}-p_{dht},
+</font>
<font color="blue">otag
+\end{equation}
+%
+</font>
<font color="blue">oindent
+and the pressures $p_{dhs}$ and $p_{dht}$ refer to the dry atmosphere.
+The potential
+temperature from the input sounding is interpolated to
+each of the model pressure levels, and the equation of state
+\eqref{init_state} is used to compute the inverse density
+$\alpha_d$. Finally, the
+ARW's hydrostatic relation \eqref{hydrostatic_relation},
+in discrete form
+%
+\begin{equation}
+\delta_\eta \phi = - \alpha_d \mu_d
+</font>
<font color="blue">otag
+\end{equation}
+</font>
<font color="blue">oindent
+is used to compute the geopotential. This procedure is used to compute
+the reference state (assuming a dry atmosphere) and the full state
+(using the full moist sounding). The perturbation variables are
+computed as the difference between the reference and full state. It
+should also be noted that in the nonhydrostatic model integration,
+the inverse density $\alpha_d$ is diagnosed from the geopotential using
+this equation of state, and the pressure is diagnosed from the equation
+of state using the inverse density $\alpha_d$ and the prognostic potential
+temperature $\theta$. Thus, the ARW's prognostic variables $\mu_d$,
+$\theta$, and $\phi$ are in exact hydrostatic balance for the model
+equations (to machine roundoff).
+
+\section{Initialization for Real-Data Conditions}
+
+The initial conditions for the real-data cases are pre-processed through a separate
+package called the WRF Preprocessing System (WPS, see Fig. \ref{figure:WPS_real_wrf}).
+The output from WPS is passed to the
+real-data pre-processor in the ARW--- program {\it real}--- which generates initial and lateral boundary
+conditions. This section is primarily about the steps taken to build the
+initial and the lateral boundary conditions for a real-data case. Even though the
+WPS is outside of the ARW system, a brief description is appropriate to see how the
+raw meteorological and static terrestrial data are brought into the model
+for real-data cases.
+
+\subsection{Use of the WRF Preprocessing System by the ARW}
+
+The WPS is a set of programs that takes
+terrestrial and meteorological data (typically in GriB format) and transforms them for input to
+the ARW pre-processor program for real-data cases ({\it real}).
+Figure \ref {figure:WPS_real_wrf} shows the flow of data into and out of the WPS system.
+The first step for the WPS is to define a physical grid (including
+the projection type, location on the globe,
+number of grid points, nest locations, and grid distances) and
+to interpolate static fields to the prescribed domain.
+Independent of the domain configuration,
+an external analysis or forecast is processed by the WPS GriB decoder,
+which diagnoses required fields and
+reformats the GriB data into an internal binary format.
+With a specified domain,
+WPS horizontally interpolates the meteorological data onto the projected domain(s).
+The output data from WPS supplies a complete 3-dimensional snapshot of the atmosphere
+on the selected model grid's horizontal staggering at the selected time slices,
+which is sent to the ARW pre-processor program for real-data cases.
+
+%
+% Figure showing WPS and real and ARW
+%
+\begin{figure}
+ \centering
+ \includegraphics[width=6in]{figures/WPS_real_wrf.pdf}
+ \caption{\label{figure:WPS_real_wrf}Schematic showing
+the data flow and program components in WPS, and how WPS feeds initial data to the ARW.
+Letters in the rectangular boxes indicate program names.
+GEOGRID: defines the model domain and creates static files of terrestrial data. UNGRIB:
+decodes GriB data. METGRID: interpolates meteorological data to the model domain.}
+\end{figure}
+
+The input to the ARW real-data processor from
+WPS contains 3-dimensional fields of temperature (K), relative humidity
+(%), geopotential height (m), pressure (Pa),
+and the horizontal components of momentum (m/s, already rotated to the model
+projection).
+The 2-dimensional static terrestrial fields include:
+albedo, Coriolis parameters, terrain elevation, vegetation/land-use type,
+land/water mask, map scale factors, map rotation angle, soil texture category, vegetation greenness fraction,
+annual mean temperature,
+and latitude/longitude.
+The 2-dimensional time-dependent fields from the external model, after processing by WPS, include:
+surface pressure and sea-level pressure (Pa), layers of soil temperature (K) and soil moisture (kg/kg,
+either total moisture, or
+binned into total and liquid content),
+snow depth (m), skin temperature (K), and sea ice.
+
+\subsection{Reference State}
+\label{initialization_real_base_section}
+Identical to the idealized initializations, there is a partitioning of some of the
+meteorological data into reference and perturbation fields.
+For real-data cases, the reference state is defined by terrain elevation and three constants:
+\begin{itemize}\setlength{\parskip}{-5pt}
+\item $p_{0}$ ($10^5$ Pa) reference sea level pressure;
+\item $T_{0}$ (usually 270 to 300 K) reference sea level temperature; and
+\item $A$ (50 K) temperature difference between the pressure levels of $p_{0}$ and $p_{0}/e$.
+\end{itemize}
+
+</font>
<font color="blue">oindent Using these parameters, the dry reference state surface pressure is
+\begin{equation}
+p_{dhs} = p_{0}~exp\Bigg({-T_{0} \over A} +
+ \sqrt{ {\bigg( {T_{0} \over A } \bigg)}^2 - ~
+ { 2\phi_{sfc} \over { A~R_d}} } \Bigg).
+\label{init_psurf}
+\end{equation}
+
+</font>
<font color="blue">oindent From \eqref{init_psurf}, the 3-dimensional reference pressure (dry hydrostatic pressure $p_{dh}$)
+is computed as
+a function of the vertical coordinate $\eta$ levels and the model top $p_{dht}$:
+\begin{equation}
+p_{dh} = \overline{p}_d = \eta ~( p_{dhs} - p_{dht} ) + p_{dht}.
+\label{init_pbar}
+\end{equation}
+
+</font>
<font color="blue">oindent With \eqref{init_pbar}, the reference temperature is a straight line on a skew-T plot, defined as
+\begin{equation}
+T = T_0 + A~ln {\overline{p}_d \over p_0}.
+</font>
<font color="blue">otag
+\end{equation}
+
+</font>
<font color="blue">oindent From the reference temperature and pressure,
+the reference potential temperature is then defined as
+
+</font>
<font color="blue">oindent
+\begin{equation}
+\overline{\theta}_d = {\bigg( T_{0} + A~ln{\overline{p}_d \over p_{0} } \bigg) }
+{\bigg( {p_0 \over \overline{p}_d } \bigg) }
+^{R_d \over C_p},
+\label{init_thetad}
+\end{equation}
+
+</font>
<font color="blue">oindent and the reciprocal of the reference density using
+\eqref{init_pbar} and \eqref{init_thetad} is given by
+\begin{equation}
+\overline{\alpha}_d = {1 \over \overline{\rho}_d} = {{R_d ~\overline{\theta}_d}\over p_{0} }~\bigg(
+{\overline{p}_d \over p_{0} } \bigg)^{-{C_v \over C_p}}.
+\label{init_alphabar}
+\end{equation}
+
+</font>
<font color="blue">oindent The base state difference of the dry surface pressure
+from \eqref{init_psurf} and the model top is
+given as
+\begin{equation}
+\overline{\mu}_d = p_{dhs} - p_{dht}.
+\label{init_mubar}
+\end{equation}
+
+</font>
<font color="blue">oindent
+From \eqref{init_alphabar} and \eqref{init_mubar},
+the reference state geopotential defined from the hydrostatic relation is
+\begin{equation}
+\delta_{\eta} \overline{\phi} = -\overline{\alpha}_d~\overline{\mu}_d.
+</font>
<font color="blue">otag
+\end{equation}
+
+
+\subsection{Vertical Interpolation and Extrapolation}
+The ARW real-data preprocessor vertically interpolates using functions of dry pressure.
+The input data from WPS contains both a total pressure and a moisture field (typically
+relative humidity). Starting at the top each column of input pressure data, the integrated moisture
+is subtracted from the pressure field step-wise down to the surface.
+Then, by removing the pressure at the model
+lid, the total dry surface pressure $p_{sd}$ diagnosed from WPS defines the
+model total dry column pressure
+\begin{equation}
+\mu_d = \overline{\mu}_d + \mu_d' = p_{sd} - p_{dht}.
+\label{init_mutotal}
+\end{equation}
+
+</font>
<font color="blue">oindent
+With the ARW vertical coordinate $\eta$, the model lid $p_{dht}$, and the column dry
+pressure known at each $(i,j,k)$ location, the 3-dimensional arrays are interpolated.
+
+In the free atmosphere up to the model lid, the vertical calculations are always interpolations.
+However, near the model surface, it is possible to have an inconsistency between the input
+surface pressure (based largely on the input surface elevation) and the ARW surface
+pressure (possibly with a much higher resolution topography). These inconsistencies
+may lead to an extrapolation. The default behavior for extrapolating the horizontal winds and
+the relative humidity below the known surface is to keep the values constant, with zero vertical gradient.
+For the potential temperature, by default a -6.5 $K/km$ lapse rate for the temperature is applied.
+The vertical interpolation of the geopotential field is optional and is
+handled separately. Since a known lower boundary condition exists
+(the geopotential is defined as zero at the pressure at sea-level), no extrapolation is required.
+
+
+
+\subsection{Perturbation State}
+In the real-data preprocessor, first a topographically defined reference state is computed,
+then the input 3-dimensional data are vertically
+interpolated in dry pressure space. With the potential temperature $\theta$ and mixing ratio
+$q_v$ available on each $\eta$ level, the pressure, density, and height diagnostics are
+handled.
+</font>
<font color="blue">oindent The perturbation dry column pressure
+field given the reference dry column pressure \eqref{init_mubar} is
+\begin{equation}
+\mu_d' = \mu_d - \overline{\mu}_d,
+\label{init_muprime}
+\end{equation}
+
+</font>
<font color="blue">oindent where $\mu_d$ is the column total dry pressure.
+Starting with the reference state fields
+(\ref{init_pbar}, \ref{init_alphabar}, and \eqref{init_mubar}) and the
+dry surface pressure perturbation (\ref{init_muprime}),
+the perturbation fields for pressure and inverse density are diagnosed.
+The pressure perturbation includes moisture and is diagnosed from
+the hydrostatic equation
+%
+\begin{equation}
+\delta_{\eta} p' = \mu'_d \bigg(1 + {\overline{q_v}^\eta} \bigg) +
+ \overline{q_v}^\eta~\overline \mu_d,
+%\label{init_pprime}
+</font>
<font color="blue">otag
+\end{equation}
+%
+</font>
<font color="blue">oindent
+which is
+integrated down from
+at the model top (where $p'= 0$) to recover $p'$.
+The total dry inverse density is given as
+\begin{equation}
+\alpha_d = {R_d \over p_{0} } ~ \theta~ \bigg( 1 + {R_v \over R_d}q_v \bigg)~
+ \bigg( {{p'_d + \overline {p}_d} \over p_{0} } \bigg )^{-{C_v \over C_p}},
+</font>
<font color="blue">otag
+\end{equation}
+
+</font>
<font color="blue">oindent which defines the perturbation field for inverse density
+
+\begin{equation}
+\alpha'_d = \alpha_d - \overline{\alpha}_d.
+</font>
<font color="blue">otag
+\end{equation}
+
+</font>
<font color="blue">oindent
+The perturbation geopotential
+is diagnosed from the hydrostatic relation
+\begin{equation}
+\delta_{\eta} \phi' = - \big ( {\mu}_d \alpha'_d + \mu'_d
+\overline{\alpha}_d \big )
+</font>
<font color="blue">otag
+\end{equation}
+%
+by upward integration using the terrain elevation as the lower boundary condition.
+
+\subsection{Generating Lateral Boundary Data}
+
+This section deals with generating the separate lateral boundary condition file used
+exclusively for the real-data cases. For information
+on which lateral boundary options are available for both the idealized and real-data
+cases, see Chapter \eqref{lbc_chap}.
+
+The specified
+lateral boundary condition for the coarse grid for real-data cases is supplied by an external file that is
+generated by program {\it real}.
+This file contains
+records for the fields $u$, $v$, $\theta$, $q_v$, $\phi'$, and $\mu'_d$ that are used by the ARW to
+constrain the lateral boundaries (other fields are in the boundary file, but are not used).
+The lateral boundary file holds one less time period than was processed by WPS.
+Each of these variables has both
+a valid value at the initial time of the lateral boundary time and a tendency term to get to the
+next boundary time period. For example, assuming a 3-hourly availability of data from WPS,
+the first time period of the lateral boundary file
+for $u$ would contain data for both coupled $u$ (map scale factor and $\mu_d$ interpolated to
+the variable's
+staggering) at the 0 h time
+
+\begin{equation}
+%U_{0h} = {{\mu_u~u}\over{m_u}} \bigg | _{0h}
+U_{0h} = {{\overline{\mu_d}^x u}\over{\overline{m}^x}} \bigg | _{0h},
+</font>
<font color="blue">otag
+\end{equation}
+</font>
<font color="blue">oindent and a tendency value defined as
+\begin{equation}
+U_t = { U_{3h} - U_{0h} \over 3h},
+</font>
<font color="blue">otag
+\end{equation}
+
+</font>
<font color="gray">oindent which would take a grid point from the initial value to the value at the next large-scale time
+during 3 simulation hours.
+The horizontal momentum fields are coupled both with $\mu_d$ and the inverse map factor. The
+other 3-dimensional fields ($\theta$, $q_v$, and $\phi'$) are coupled only with $\mu_d$.
+The 2-dimensional $\mu'_d$ lateral boundary field is not coupled.
+
+Each lateral boundary field
+is defined along the four sides of the
+rectangular grid (loosely referred to as the north, south, east, and west sides).
+The boundary values and tendencies for vertical velocity and the non-vapor moisture species are included
+in the external lateral boundary file, but act as
+place-holders for the nested boundary data for the fine grids.
+The width of the lateral
+boundary along each of the four sides is user selectable at run-time.
+
+\subsection{Masking of Surface Fields}
+
+Some of the meteorological and static fields are ``masked''. A masked field is one in which
+the values are typically defined only over water (e.g., sea surface temperature) or defined
+only over land (e.g., soil temperature).
+The need to match all of the masked fields consistently to each other requires additional steps
+for the real-data cases due to the masked data's presumed use in various physics packages in the soil,
+at the surface, and in the boundary layer.
+If the land/water
+mask for a location is flagged as a water point, then the vegetation and soil categories must also
+recognize the location as the special water flag for each of their respective categorical indices.
+
+The values for the soil temperature and soil moisture come from WPS on the
+native levels originally defined for those variables
+in the large-scale model. WPS does no vertical interpolation for the
+soil data. While it is typical to try to match the ARW soil scheme with
+the incoming data, that is not a requirement. Pre-processor {\it real} will vertically interpolate
+(linear in depth below the ground) from the incoming levels to the requested soil layers to be
+used within the model.
Modified: trunk/wrf/technote/nest.tex
===================================================================
--- trunk/wrf/technote/nest.tex 2008-05-05 19:38:13 UTC (rev 64)
+++ trunk/wrf/technote/nest.tex 2008-05-06 20:44:59 UTC (rev 65)
@@ -1,414 +1,468 @@
-\chapter{Nesting}
-\label{nesting_chap}
-
-The ARW supports horizontal nesting that allows resolution to be
-focused over a region of interest by introducing an additional grid (or
-grids) into the simulation. In the current implementation, only
-horizontal refinement is available: there is no vertical nesting option.
-The nested grids are rectangular
-and are aligned with the parent (coarser) grid within which they are
-nested.
-Additionally, the nested grids allow any integer spatial
-($\Delta x_{coarse}/\Delta x_{fine}$)
-and temporal refinements of the
-parent grid.
-This nesting implementation is in many ways similar to the
-implementations in other mesoscale and cloudscale models (e.g. MM5,
-ARPS, COAMPS). The major improvement in the ARW's nesting
-infrastruture compared with techniques used in other models is the ability to compute nested
-simulations efficiently on parallel distributed-memory computer systems,
-which includes support for moving nested grids.
-The WRF Software Framework, described in
-\citet{michalak04}, makes these advances possible. In this chapter we
-describe the various nesting options available in the ARW and the numerical
-coupling between the grids.
-
-\section {Overview}
-
-%
-% 1-way vs 2-way
-%
-\begin{figure}
- \centering
- \includegraphics *[width=4.5in]{figures/12way.pdf}
- \caption{\label{figure:12way} 1-way and 2-way nesting options in the ARW.}
-\end{figure}
-
-\subsubsection{1-Way and 2-Way Grid Nesting}
-
-Nested grid simulations can be produced using either 1-way
-nesting or 2-way nesting as outlined in Fig. \ref{figure:12way}. The
-1-way and 2-way nesting options refer to how a coarse grid and the
-fine grid interact. In both the 1-way and 2-way simulation modes, the
-fine grid boundary conditions (i.e., the lateral boundaries) are interpolated
-from the coarse grid forecast. In a 1-way nest, this is the only
-information exchange between the grids (from coarse grid to fine grid).
-Hence, the name {\em 1-way nesting}. In the 2-way nest integration, the
-fine grid solution replaces the coarse grid solution for coarse
-grid points that lie inside the fine grid. This information exchange
-between the grids is now in both directions (coarse-to-fine and
-fine-to-coarse). Hence, the name {\em 2-way nesting}.
-
-The 1-way nest option may be run in one of two different methods. One
-option is to produce the nested simulation as two separate ARW simulations
-as described in the leftmost box in Fig. \ref{figure:12way}. In this mode,
-the coarse grid is integrated first. Output from the coarse grid
-integration is then processed to provide boundary conditions for
-the nested run (usually at a much lower temporal frequency than the
-coarse grid time step), and this is followed by the complete time
-integration of fine (nested) grid. Hence, this 1-way option is equivalent
-to running two separate simulations with a processing step in between. Also with
-separate grid simulations, an intermediate re-analysis (such as
-via 3D-Var, see Section \ref{var_chap}) can be used.
-
-The second 1-way option (lockstep with no feedback), depicted in the
-middle box in Fig. \ref{figure:12way}, is run as a traditional
-simulation with two (or more) grids integrating concurrently, except with
-the feedback runtime option shut off. This option provides lateral boundary
-conditions to the fine grid at each coarse grid time step, which
-is an advantage of the concurrent 1-way method (no feedback).
-
-
-\subsubsection{Fine Grid Initialization Options}
-
-The ARW supports several strategies to refine a coarse-grid
-simulation with the introduction of a nested grid. When using 1-way and
-2-way nesting, several options for initializing the fine grid
-are provided.
-\begin{itemize}\setlength{\parskip}{-4pt}
-\item All of the fine grid variables can be interpolated from the coarse grid.
-\item All of the fine grid variables can be input from an external file
-which has high-resolution information for both the meteorological
-and the terrestrial fields.
-\item The fine grid can have some of the variables initialized with a
-high-resolution external data set, while other variables are
-interpolated from the coarse grid.
-\item For a moving nest, an external orography file may be used to update
-the fine grid terrain elevation. This option is not generally available
-in this release.
-\end{itemize}
-
-</font>
<font color="red">oindent These fine grid initialization settings are user specified at
-run-time, and the ARW allows nested grids to instantiate and cease during any
-time that the fine grid's parent is still integrating. (The
-system is currently constrained to starting nests at the beginning of
-the coarse grid simulations if runs require input of nest-resolution
-terrain or other lower boundary data. This limitation will be addressed
-in the near future.)
-%
-% nest grids, some OK, some illegal
-%
-\begin{figure}
- \centering
- \includegraphics *[width=6.0in]{figures/nest_domains.pdf}
- \caption{\label{figure:nest_domains}Various nest configurations for multiple grids. (a)
- Telescoping nests. (b) Nests at the same level with respect to a parent grid.
- (c) Overlapping grids: not allowed (d) Inner-most grid has more than one parent grid: not allowed}
-\end{figure}
-
-
-\subsubsection{Possible Grid Configurations}
-
-A simulation involves one outer grid and may contain multiple
-inner nested grids. In the ARW, each nested region is entirely
-contained within
-a single coarser grid, referred to as the {\em parent}
-grid. The finer, nested grids are referred to as {\em child} grids.
-Using this terminology, children are also parents when multiple levels
-of nesting are used. The fine grids may be telescoped to any depth (i.e.,
-a
-parent grid may contain one or more child grids, each of which in turn
-may successively contain one or more child grids; Fig.
-\ref{figure:nest_domains}a), and several fine grids may share the
-same parent at the same level of nesting (Fig.
-\ref{figure:nest_domains}b).
-Any valid fine grid may either be a static domain or it may be a moving nest
-with prescribed incremental shifts.
-The ARW does not permit overlapping
-grids, where a coarse grid point is contained within more than a
-single child grid (i.e., both of which are at the same nest level with respect
-to the parent; Fig. \ref{figure:nest_domains}c). In addition, no grid can have
-more than a single parent (Fig. \ref{figure:nest_domains}d).
-
-For 2-way nested grid simulations, the ratio of the
-parent horizontal grid distance to the child horizontal grid distance
-(the spatial refinement ratio) must be an integer. This is also true for
-the time steps (the temporal refinement ratio). The model does allow
-the time step refinement ratio to differ from the spatial refinement
-ratio. Also, nested grids on the same level (i.e., children who have the
-same parent) may have different spatial and temporal refinement ratios.
-
-\section{Nesting and Staggering}
-
-The ARW uses an Arakawa-C grid staggering. As shown in Fig.
-\ref{figure:cg_fg}, the $u$ and $v$ components
-of horizontal velocity are normal to the respective faces of the
-grid cell, and the mass/thermodynamic/scalar variables are located
-in the center of the cell.
-
-%
-% Figure colorful single-grid u,v,t stagger
-%
-\begin{figure}
- \centering
- \includegraphics[width=4in]{figures/cg_fg.pdf}
- \caption{\label{figure:cg_fg}
-Arakawa-C grid staggering for a portion of a parent domain and an
-imbedded nest domain with a 3:1 grid size ratio. The solid lines
-denote coarse grid cell boundaries, and the dashed lines are the
-boundaries for each fine grid cell. The horizontal components of
-velocity (``U'' and ``V'') are defined along the normal cell face, and
-the thermodynamic variables (``$\theta$'') are defined at the center of
-the grid cell (each square). The bold typeface variables along the
-interface between the coarse and the fine grid define the locations
-where the specified lateral boundaries for the nest are in
-effect. } \end{figure}
-
-The variable staggering has an additional column
-of $u$ in the x-direction and an additional row of $v$ in the y-direction
-because the normal velocity points define the grid boundaries.
-The horizontal momentum components reflect an average across each
-cell-face, while each mass/thermodynamic/scalar variable
-is the representative mean value throughout the cell.
-Feedback is handled to preserve these mean values: the mass/thermodynamic/scalar
-fields are fed back with an average from within the entire
-coarse grid point (Fig. \ref{figure:cg_fg}), and the horizontal momentum variables are
-averaged along their respective normal coarse grid cell faces.
-
-The horizontal interpolation (to instantiate a grid and to provide
-time-dependent lateral boundaries) does not conserve mass. The
-feedback mechanism, for most of the unmasked fields, uses cell
-averages (for mass/thermodynamic/scalar quantities) and cell-face
-averages for the horizontal momentum fields.
-
-
-The staggering defines the way that the fine grid is situated
-on top of the coarse grid. For all odd ratios there is a coincident
-point for each variable: a location that has the coarse grid
-and the fine grid at the same physical point. The location of
-this point depends on the variable.
-In each of the
-coarse-grid cells with an odd ratio, the middle fine-grid cell
-is the coincident point with the coarse grid for all of the
-mass-staggered fields (Fig. \ref{figure:cg_fg}).
-For the horizontal momentum variables
-the normal velocity has coincident points along the grid boundaries for odd ratios.
-
-For fields
-that are averaged back to the coarse grid in the feedback, the
-mean of the nine mass/thermodynamic/scalar (for example, due to the 3:1 grid-distance ratio
-in the example shown in Fig. \ref{figure:cg_fg}) fine grid
-points is fed back to the coarse grid. These fields include most
-3D and 2D arrays.
-For the horizontal momentum fields averaged back to the coarse grid in the
-feedback, the mean of three (for example, due to the 3:1 grid-distance ratio
-in the example shown in Fig. \ref{figure:cg_fg}) fine grid
-points is fed back to the coarse grid from along the coincident cell face.
-The fields that are masked due
-to the land/sea category are fed back directly from the coincident points
-for odd ratios. Only masked fields use the feedback method where a single
-point from the fine grid is assigned to the coarse grid.
-
-A difference between the odd and even grid-distance ratios
-is in the feedback from the fine grid to the coarse grid. No
-coincident points exist for the single point feedback mechanisms
-for even grid distance ratios
-(such as used for the land/sea masked 2D fields).
-For a 2:1 even grid distance ratio, Figure
-\ref{figure:cg_fg_x2} shows that each coarse
-grid point has four fine grid cells that are equally close,
-and therefore four equally eligible grid points for use as the
-single fine-grid point that feeds back to the coarse grid. The
-single-point feedback is arbitrarily chosen as the south-west
-corner of the four neighboring points.
-This arbitrary assignment to masked fields implies that even
-grid distance ratios are more suited for idealized simulations
-where masked fields are less important.
-
-
-
-%
-% Figure colorful 2 grid, even ratio
-%
-\begin{figure}
- \centering
- \includegraphics[width=4in]{figures/cg_fg_x2.pdf}
- \caption{\label{figure:cg_fg_x2}
-Similar to Fig. \ref{figure:cg_fg}, but with a 2:1 grid-distance ratio.
-}
-\end{figure}
-
-\section{Nested Lateral Boundary Conditions}
-\label{nest-lbc}
-
-For the fine grid with 2-way nesting or 1-way nesting
-(using a concurrent ARW simulation, see Fig. \ref{figure:12way}),
-the boundary conditions are specified by the parent grid
-at every coarse-grid time step. The nest lateral boundary condition behaves similarly to the
-specified boundary condition for real-data cases (see Section \ref{lbc_spec}), but
-the relaxation zone is not active. Prognostic variables are entirely specified in the outer row and column
-of the fine grid through spatial and temporal interpolation from the coarse grid (the coarse grid is
-stepped forward in time prior to advancement of any child grid of that parent).
-
-\section{Steps to Generate a Nest Grid}
-
-Only the concurrent 1-way nest option or the 2-way nest
-option are considered in this section. The 1-way nest option (using two
-consecutive ARW simulations, see Fig. \ref{figure:12way})
-is functionally similar to two separate,
-single-grid simulations and does not fit the following description. For
-a multiple grid simulation within a single model run, there are some
-additional infrastructure steps that are required (briefly described in
-Fig. \ref{nest_domain_integration_figure}). While the following text
-details a simulation with a single coarse-grid and a single fine-grid,
-this implies no lack of generality when handling multiple grid levels or
-multiple grids on the same level.
-
-</font>
<font color="red">oindent
-\begin{figure}[nest]
-\setlength{\fboxrule}{.75pt}
-\framebox[\columnwidth]{
-\parbox{6.5truein}{
-\vskip 5truept
-</font>
<font color="red">oindent
-{\bf Integrate Parent Grid One Time Step} \medskip \hfill \break
-%
-\hphantom{Begin} {\bf If Nest Grid Start Time} \smallskip \hfill \break
-\hphantom{BeginBegin}
-(1) Horizontally Interpolate Parent to Child Grid \hfill \break
-\hphantom{BeginBegin}
-(2) Optionally Input High-Resolution Child Data \hfill \break
-\hphantom{BeginBegin}
-(3) Compute Child Reference State \hfill \break
-\hphantom{BeginBegin}
-(4) Feedback Child Initial Data to Parent Grid \hfill \break
-\hphantom{BeginBegin}
-(5) Re-Compute Parent Reference State \hfill \break
-\hphantom{Begin} {\bf End If Nest Grid Start Time} \medskip \hfill \break
-%
-\hphantom{Begin} {\bf Solve Time Step for Parent Grid (see Fig. \ref{time_integration_figure})} \medskip \hfill \break
-%
-\hphantom{Begin} {\bf While Existing Nest Grids to Integrate} \smallskip \hfill \break
-\hphantom{BeginBegin}
-(1) Lateral Forcing from Parent Grid to Child \hfill \break
-\hphantom{BeginBegin}
-(2) Integrate Child Grid to Current Time of Parent Grid\hfill \break
-\hphantom{BeginBegin}
-(3) Feedback Child Grid Information to Parent Grid \hfill \break
-\hphantom{Begin} {\bf End While Existing Nest Grids to Integrate} \medskip \hfill \break
-%
-{\bf End Grid Integrate}
-\vskip 5truept
-}
-}
-\caption{Nest grid integration sequence.}
-\label{nest_domain_integration_figure}
-\end{figure}
-
-\subsubsection{Nest Instantiation}
-
-The fine grid is instantiated as a child
-of a parent grid at the requested start time.
-This initialization is within the integration step for the parent
-grid, so no child grid can begin if the parent is not active.
-To fill in the correct meteorological
-fields, an initialization routine is called to horizontally interpolate
-the coarse-grid data to the fine grid locations using a monotone
-interpolation scheme \citep[described in][]{smolargrell90} for most fields
-(i.e., the same scheme employed for generating the fine grid lateral
-boundary conditions)
-and a simple linear interpolation or averaging scheme for masked or
-categorical fields.
-For fields that are masked with the land/sea background (such
-as land only fields (e.g., snow), or water only fields (e.g., sea ice)), the
-interpolator needs to know what field defines the template for the masking
-(such as the land use category). Part of the automatic code generation handles
-calling each field with its associated interpolator.
-
-\subsubsection{Fine Grid Input}
-
-After the horizontal interpolation is completed, a few orographic-based variables
-are saved so that they may be used to blend the lateral boundaries
-along the coarse-grid/fine-grid interface.
-The terrain elevation,
-$\overline {\mu}_d$,
-and the reference geopotential ($\overline{\phi}$) are stored for later use.
-The fields selected as input from the fine grid input file (for the
-concurrent 1-way and 2-way forecast methods shown in Fig. \ref{figure:12way}) are ingested, and
-they overwrite the arrays that were horizontally interpolated from the
-coarse grid. No quality control for data consistency is performed
-for the fine grid input. All such masked checks are
-completed by the ARW real-data pre-processor {\it real}.
-
-\subsubsection{Interface Blended Orography}
-
-When the fine grid data has been input, the previously-saved orographic-based fields
-are blended across the four outer rows and columns of the
-fine grid. The blending is a simple linear weighting between
-the interpolated coarse-grid values (the saved data)
-and the fine grid values from the input file.
-The weighting scheme is given as:
-\begin{itemize}\setlength{\parskip}{-4pt}
-\item row/column 1: 100\% interpolated coarse grid, 0\% fine grid,
-\item row/column 2: 75\% interpolated coarse grid, 25\% fine grid,
-\item row/column 3: 50\% interpolated coarse grid, 50\% fine grid,
-\item row/column 4: 25\% interpolated coarse grid, 75\% fine grid, and
-\item row/column 5: 0\% interpolated coarse grid, 100\% fine grid,
-\end{itemize}
-</font>
<font color="red">oindent where the row or column nearest the outer edge takes precedence in ambiguous corner zones.
-The blended arrays are required to compute the reference state for the
-fine grid. The first row and column (100\% interpolated from the coarse grid)
-ensures that the reference state for the coarse grid and
-fine grid is consistent along the fine grid boundary interface.
-The blending along the inner rows and columns ramps the coarse grid reference state to the
-fine grid reference state for a smooth transition between the grids.
-
-\subsubsection{Feedback}
-So that the coarse grid and the fine grid are consistent at coincident points, the
-fine grid values are fed back to the coarse grid.
-There are two available
-options for feedback: either the mean of all fine grid cells contained
-within each coarse grid cell is fed back (or cell faces in the case of the
-horizontal momentum fields), or a single-point feedback
-is selected for the masked or categorical fields.
-
-Subsequent to the feedback step, the coarse grid may be optionally smoothed in the area
-of the fine grid. Two smoothers are available: a 5-point 1-2-1 smoother and a smoother-desmoother
-with a similar stencil size.
-Both the feedback and the smoothers are run one row and column in from the
-interface row and column of the coarse grid that provides
-the lateral boundary conditions to the fine grid.
-
-\subsubsection{Reference State}
-The initial feedback when the nest is instantiated ensures
-that the coarse grid is consistent with the fine grid, particularly
-with regards to elevation and the reference state fields inside the blended region, and for such
-terrestrial features as coasts, lakes, and islands. The adjustment
-of the elevation in the coarse grid forces a base state recalculation.
-The fine-grid needs an initial base state calculation, and after
-the terrain feedback, the coarse grid is also in need of a base state
-recalculation.
-
-Note that with the horizontal interpolation of the coarse grid
-to the fine grid and the feedback of the fine grid to the coarse
-grid,
-the coarse grid base state is recomputed
-even without a separate fine-grid initial data file,
-since the coarse grid topography is adjusted.
-
-With the completed base state computations, the routines return
-back to the integration step for the coarse and fine grids.
-The fine grid data is now properly initialized for integration and
-can be advanced forward a time step.
-
-\subsubsection{Integration}
-
-The integration by grid is recursive. At the end of each grid's time step, a check
-is made to determine if a child grid exists for that parent and if the
-current time is bracketed by the child's start/end time.
-This is shown in Fig. \ref{nest_domain_integration_figure}. The integration process for the nest (step 2 under the
-while loop) is recursively calling the top step in the overall sequence as a coarse grid itself.
-This is a ``depth first''
-traversal of the tree of grids.
-If a child grid does exist, that child grid is integrated up through the current time of
-the parent grid.
+\chapter{Nesting}
+\label{nesting_chap}
+
+The ARW supports horizontal nesting that allows resolution to be
+focused over a region of interest by introducing an additional grid (or
+grids) into the simulation. In the current implementation, only
+horizontal refinement is available: there is no vertical nesting option.
+The nested grids are rectangular
+and are aligned with the parent (coarser) grid within which they are
+nested.
+Additionally, the nested grids allow any integer spatial
+($\Delta x_{coarse}/\Delta x_{fine}$)
+and temporal refinements of the
+parent grid (the spatial and temporal refinements are usually,
+but not necessarily the same).
+This nesting implementation is in many ways similar to the
+implementations in other mesoscale and cloudscale models (e.g. MM5,
+ARPS, COAMPS). The major improvement in the ARW's nesting
+infrastruture compared with techniques used in other models is the ability to compute nested
+simulations efficiently on parallel distributed-memory computer systems,
+which includes support for moving nested grids.
+The WRF Software Framework, described in
+\citet{michalak04}, makes these advances possible. In this chapter we
+describe the various nesting options available in the ARW and the numerical
+coupling between the grids.
+
+\section {Overview}
+
+%
+% 1-way vs 2-way
+%
+\begin{figure}
+ \centering
+ \includegraphics *[width=4.5in]{figures/12way.pdf}
+ \caption{\label{figure:12way} 1-way and 2-way nesting options in the ARW.}
+\end{figure}
+
+\subsubsection{1-Way and 2-Way Grid Nesting}
+
+Nested grid simulations can be produced using either 1-way
+nesting or 2-way nesting as outlined in Fig. \ref{figure:12way}. The
+1-way and 2-way nesting options refer to how a coarse grid and the
+fine grid interact. In both the 1-way and 2-way simulation modes, the
+fine grid boundary conditions (i.e., the lateral boundaries) are interpolated
+from the coarse grid forecast. In a 1-way nest, this is the only
+information exchange between the grids (from the coarse grid to the fine grid).
+Hence, the name {\em 1-way nesting}. In the 2-way nest integration, the
+fine grid solution replaces the coarse grid solution for coarse
+grid points that lie inside the fine grid. This information exchange
+between the grids is now in both directions (coarse-to-fine for the
+fine-grid lateral boundary computation and
+fine-to-coarse during the feedback at each coarse-grid time step).
+Hence, the name {\em 2-way nesting}.
+
+The 1-way nest set-up may be run in one of two different methods. One
+option is to produce the nested simulation as two separate ARW simulations
+as described in the leftmost box in Fig. \ref{figure:12way}. In this mode,
+the coarse grid is integrated first and the coarse grid forecast is completed.
+Output from the coarse grid
+integration is then processed to provide boundary conditions for
+the nested run (usually at a much lower temporal frequency than the
+coarse grid time step), and this is followed by the complete time
+integration of fine (nested) grid. Hence, this 1-way option is equivalent
+to running two separate simulations with a processing step in between. Also with
+separate grid simulations, an intermediate re-analysis (such as
+via 3D-Var, see Section \ref{var_chap}) can be included.
+
+The second 1-way option (lockstep with no feedback), depicted in the
+middle box in Fig. \ref{figure:12way}, is run as a traditional
+simulation with two (or more) grids integrating concurrently, except with
+the feedback runtime option shut off. This option provides lateral boundary
+conditions to the fine grid at each coarse grid time step, which
+is an advantage of the concurrent 1-way method (no feedback).
+
+
+\subsubsection{Fine Grid Initialization Options}
+
+The ARW supports several strategies to refine a coarse-grid
+simulation with the introduction of a nested grid. When using concurrent 1-way and
+2-way nesting, several options for initializing the fine grid
+are provided.
+\begin{itemize}\setlength{\parskip}{-4pt}
+\item All of the fine grid variables can be interpolated from the coarse grid (useful
+when a fine grid starts later in the coarse grid forecast).
+\item All of the fine grid variables can be input from an external file
+which has high-resolution information for both the meteorological
+and the terrestrial fields (a standard set-up when the fine-grid topography
+is expected to impact the forecast).
+\item The fine grid can have some of the variables initialized with a
+high-resolution external data set, while other variables are
+interpolated from the coarse grid (permits an improved 3D-Var initialization of the
+coarse grid's metoerological fields to be consistent with the fine grid).
+\item For a moving nest, an external orography file may be used to update
+the fine grid terrain elevation.
+\end{itemize}
+
+</font>
<font color="blue">oindent These fine grid initialization settings are user specified at
+run-time, and the ARW allows nested grids to instantiate and cease during any
+time that the fine grid's parent is still integrating.
+%
+% nest grids, some OK, some illegal
+%
+\begin{figure}
+ \centering
+ \includegraphics *[width=6.0in]{figures/nest_domains.pdf}
+ \caption{\label{figure:nest_domains}Various nest configurations for multiple grids. (a)
+ Telescoping nests. (b) Nests at the same level with respect to a parent grid.
+ (c) Overlapping grids: not allowed (d) Inner-most grid has more than one parent grid: not allowed}
+\end{figure}
+
+
+\subsubsection{Possible Grid Configurations}
+
+A simulation involves one outer grid and may contain multiple
+inner nested grids. In the ARW, each nested region is entirely
+contained within
+a single coarser grid, referred to as the {\em parent}
+grid. The finer, nested grids are referred to as {\em child} grids.
+Using this terminology, children are also parents when multiple levels
+of nesting are used. The fine grids may be telescoped to any depth (i.e.,
+a
+parent grid may contain one or more child grids, each of which in turn
+may successively contain one or more child grids; Fig.
+\ref{figure:nest_domains}a), and several fine grids may share the
+same parent at the same level of nesting (Fig.
+\ref{figure:nest_domains}b).
+Any valid fine grid may either be a static domain or it may be a moving nest
+(with either prescribed incremental shifts or with automatic moves
+via the 500 mb height vortex following algorithm).
+The ARW does not permit overlapping
+grids, where a coarse grid point is contained within more than a
+single child grid (i.e., both of which are at the same nest level with respect
+to the parent; Fig. \ref{figure:nest_domains}c). In addition, no grid can have
+more than a single parent (Fig. \ref{figure:nest_domains}d). For global domains, a
+fine grid domain cannot cross the periodic lateral boundary of the parent domain.
+
+For both 1-way and 2-way nested grid simulations, the ratio of the
+parent horizontal grid distance to the child horizontal grid distance
+(the spatial refinement ratio) must be an integer. For 2-way and concurrent 1-way
+nesting, this is also true for
+the time steps (the temporal refinement ratio). The model does allow
+the time step refinement ratio to differ from the spatial refinement
+ratio. Also, nested grids on the same level (i.e., children who have the
+same parent) may have different spatial and temporal refinement ratios. For example,
+in Fig. \ref{figure:nest_domains}b, the horizontal grid resolution for
+domain 1 could be 90 km, for
+domain 2 could be 45 km, and for domain 3 could be 30 km.
+
+\section{Nesting and Staggering}
+
+The ARW uses an Arakawa-C grid staggering. As shown in Fig.
+\ref{figure:cg_fg}, the $u$ and $v$ components
+of horizontal velocity are normal to the respective faces of the
+grid cell, and the mass/thermodynamic/scalar/chemistry variables are located
+in the center of the cell.
+
+%
+% Figure colorful single-grid u,v,t stagger
+%
+\begin{figure}
+ \centering
+ \includegraphics[width=4in]{figures/cg_fg.pdf}
+ \caption{\label{figure:cg_fg}
+Arakawa-C grid staggering for a portion of a parent domain and an
+imbedded nest domain with a 3:1 grid size ratio. The solid lines
+denote coarse grid cell boundaries, and the dashed lines are the
+boundaries for each fine grid cell. The horizontal components of
+velocity (``U'' and ``V'') are defined along the normal cell face, and
+the thermodynamic variables (``$\theta$'') are defined at the center of
+the grid cell (each square). The bold typeface variables along the
+interface between the coarse and the fine grid define the locations
+where the specified lateral boundaries for the nest are in
+effect. } \end{figure}
+
+The variable staggering has an additional column
+of $u$ in the x-direction and an additional row of $v$ in the y-direction
+because the normal velocity points define the grid boundaries.
+The horizontal momentum components reflect an average across each
+cell-face, while each mass/thermodynamic/scalar/chemistry variable
+is the representative mean value throughout the cell.
+Feedback is handled to preserve these mean values: the mass/thermodynamic/scalar/chemistry
+fields are fed back with an average from within the entire
+coarse grid point (Fig. \ref{figure:cg_fg}), and the horizontal momentum variables are
+averaged along their respective normal coarse grid cell faces.
+
+The horizontal interpolation (to instantiate a grid and to provide
+time-dependent lateral boundaries) does not conserve mass. The
+feedback mechanism, for most of the unmasked fields, uses cell
+averages (for mass/thermodynamic/scalar/chemistry quantities) and cell-face
+averages for the horizontal momentum fields.
+
+
+The staggering defines the way that the fine grid is situated
+on top of the coarse grid. For all odd ratios there is a coincident
+point for each variable: a location that has the coarse grid
+and the fine grid at the same physical point. The location of
+this point depends on the variable.
+In each of the
+coarse-grid cells with an odd ratio, the middle fine-grid cell
+is the coincident point with the coarse grid for all of the
+mass-staggered fields (Fig. \ref{figure:cg_fg}).
+For the horizontal momentum variables
+the normal velocity has coincident points along the grid boundaries for odd ratios.
+
+For fields
+that are averaged back to the coarse grid in the feedback, the
+mean of the nine mass/thermodynamic/scalar/chemistry (for example, due to the 3:1 grid-distance ratio
+in the example shown in Fig. \ref{figure:cg_fg}) fine grid
+points is fed back to the coarse grid. These fields include most
+3-dimensional and 2-dimensional arrays.
+For the horizontal momentum fields averaged back to the coarse grid in the
+feedback, the mean of three (for example, due to the 3:1 grid-distance ratio
+in the example shown in Fig. \ref{figure:cg_fg}) fine grid
+points is fed back to the coarse grid from along the coincident cell face.
+The fields that are masked due
+to the land/sea category are fed back directly from the coincident points
+for odd ratios. Masked fields include soil temperature and sea ice. It does not make
+sense to average neighboring locations of soil temperature on the fine grid
+if the coarse grid point being fedback to is a water value. Similarly, averaging
+several sea ice values on the fine grid does not make sense if some of the neighboring
+points included in the mean are fine grid land points.
+Only masked fields use the feedback method where a single
+point from the fine grid is assigned to the coarse grid.
+
+A difference between the odd and even grid-distance ratios
+is in the feedback from the fine grid to the coarse grid. No
+coincident points exist for the single point feedback mechanisms
+for even grid distance ratios
+(such as used for the land/sea masked 2D fields).
+For a 2:1 even grid distance ratio, Figure
+\ref{figure:cg_fg_x2} shows that each coarse
+grid point has four fine grid cells that are equally close,
+and therefore four equally eligible grid points for use as the
+single fine-grid point that feeds back to the coarse grid. The
+single-point feedback is arbitrarily chosen as the south-west
+corner of the four neighboring points.
+This arbitrary assignment to masked fields implies that even
+grid distance ratios are more suited for idealized simulations
+where masked fields are less important.
+
+
+
+%
+% Figure colorful 2 grid, even ratio
+%
+\begin{figure}
+ \centering
+ \includegraphics[width=4in]{figures/cg_fg_x2.pdf}
+ \caption{\label{figure:cg_fg_x2}
+Similar to Fig. \ref{figure:cg_fg}, but with a 2:1 grid-distance ratio.
+}
+\end{figure}
+
+\section{Nested Lateral Boundary Conditions}
+\label{nest-lbc}
+
+For the fine grid with 2-way nesting or 1-way nesting
+(using a concurrent ARW simulation, see
+Fig. \ref{figure:12way}),
+the boundary conditions are specified by the parent grid
+at every coarse-grid time step. The nest lateral boundary condition behaves similarly to the
+specified boundary condition for real-data cases (see Section \ref{lbc_spec}), but
+the relaxation zone is not active. Prognostic variables are entirely specified in the outer row and column
+of the fine grid through spatial and temporal interpolation from the coarse grid (the coarse grid is
+stepped forward in time prior to advancement of any child grid of that parent).
+
+\section{Steps to Generate a Nest Grid}
+
+Only the concurrent 1-way nest option or the 2-way nest
+option are considered in this section. The 1-way nest option (using two
+consecutive ARW simulations, see Fig. \ref{figure:12way})
+is functionally similar to two separate,
+single-grid simulations and does not fit the following description. For
+a multiple grid simulation within a single model run, there are some
+additional infrastructure steps that are required (briefly described in
+Fig. \ref{nest_domain_integration_figure}). While the following text
+details a simulation with a single coarse-grid and a single fine-grid,
+this implies no lack of generality when handling multiple grid levels or
+multiple grids on the same level.
+
+</font>
<font color="blue">oindent
+\begin{figure}[nest]
+\setlength{\fboxrule}{.75pt}
+\framebox[\columnwidth]{
+\parbox{6.5truein}{
+\vskip 5truept
+</font>
<font color="blue">oindent
+{\bf Integrate Parent Grid One Time Step} \medskip \hfill \break
+%
+\hphantom{Begin} {\bf If Nest Grid Start Time} \smallskip \hfill \break
+\hphantom{BeginBegin}
+(1) Horizontally Interpolate Parent to Child Grid \hfill \break
+\hphantom{BeginBegin}
+(2) Optionally Input High-Resolution Child Data \hfill \break
+\hphantom{BeginBegin}
+(3) Compute Child Reference State \hfill \break
+\hphantom{BeginBegin}
+(4) Feedback Child Initial Data to Parent Grid \hfill \break
+\hphantom{BeginBegin}
+(5) Re-Compute Parent Reference State \hfill \break
+\hphantom{Begin} {\bf End If Nest Grid Start Time} \medskip \hfill \break
+%
+\hphantom{Begin} {\bf Solve Time Step for Parent Grid (see Fig. \ref{time_integration_figure})} \medskip \hfill \break
+%
+\hphantom{Begin} {\bf If Nest Grid Move Time} \smallskip \hfill \break
+\hphantom{BeginBegin}
+(1) Move Nest Grid (Vortex Following or Prescribed)\hfill \break
+\hphantom{BeginBegin}
+(2) Horizontally Interpolate Parent to Child Grid (Along New Boundary) \hfill \break
+\hphantom{BeginBegin}
+(3) Optionally Input High-Resolution Child Topo Data \hfill \break
+\hphantom{BeginBegin}
+(4) Compute Child Reference State \hfill \break
+\hphantom{BeginBegin}
+(5) Feedback Child Initial Data to Parent Grid \hfill \break
+\hphantom{BeginBegin}
+(6) Re-Compute Parent Reference State \hfill \break
+\hphantom{Begin} {\bf End If Nest Grid Move Time} \medskip \hfill \break
+%
+\hphantom{Begin} {\bf While Existing Nest Grids to Integrate} \smallskip \hfill \break
+\hphantom{BeginBegin}
+(1) Lateral Forcing from Parent Grid to Child \hfill \break
+\hphantom{BeginBegin}
+(2) Integrate Child Grid to Current Time of Parent Grid\hfill \break
+\hphantom{BeginBegin}
+(3) Feedback Child Grid Information to Parent Grid \hfill \break
+\hphantom{Begin} {\bf End While Existing Nest Grids to Integrate} \medskip \hfill \break
+%
+{\bf End Grid Integrate}
+\vskip 5truept
+}
+}
+\caption{Nest grid integration sequence.}
+\label{nest_domain_integration_figure}
+\end{figure}
+
+\subsubsection{Nest Instantiation}
+
+The fine grid is instantiated as a child
+of a parent grid at the requested start time.
+This initialization is within the integration step for the parent
+grid, so no child grid can begin if the parent is not active.
+To fill in the correct meteorological
+fields, an initialization routine is called to horizontally interpolate
+the coarse-grid data to the fine grid locations using a monotone
+interpolation scheme \citep[described in][]{smolargrell90} for most fields
+(i.e., the same scheme employed for generating the fine grid lateral
+boundary conditions)
+and a simple linear interpolation or averaging scheme for masked or
+categorical fields.
+For fields that are masked with the land/sea background (such
+as land only fields (e.g., snow), or water only fields (e.g., sea ice)), the
+interpolator needs to know what field defines the template for the masking
+(such as the land use category). Part of the automatic code generation handles
+calling each field with its associated interpolator.
+
+\subsubsection{Fine Grid Input}
+
+After the horizontal interpolation is completed, a few orographic-based variables
+are saved so that they may be used to blend the lateral boundaries
+along the coarse-grid/fine-grid interface.
+The terrain elevation,
+$\overline {\mu}_d$,
+and the reference geopotential ($\overline{\phi}$) are stored for later use.
+The fields selected as input from the fine grid input file (for the
+concurrent 1-way and 2-way forecast methods shown in Fig. \ref{figure:12way}) are ingested, and
+they overwrite the arrays that were horizontally interpolated from the
+coarse grid. No quality control for data consistency is performed
+for the fine grid input. All such masked checks are
+completed by the ARW real-data pre-processor {\it real}.
+
+\subsubsection{Interface Blended Orography}
+
+To reduce lateral boundary noise entering the fine grid, the fine grid topography has two
+zones of smoothing, as seen in Fig. \ref{figure:12way}.
+The first zone is along the outer edge of the fine domain and
+extends into the nest, with a width defined the same as the number of coarse grid points
+in the width of the lateral boundary file. In this first zone, the topography is horizontally
+interpolated from the coarse grid. The second zone extends inward from the first zone, with a
+user-defined width. The topography is linearly weighted between the interpolated coarse-grid
+topography and the fine-grid topography, and it ramps from 100\% coarse-grid
+topography (at the interface between
+first and second zones) to 100\%
+fine-grid topography interior to second zone.
+</font>
<font color="blue">oindent
+The weighting scheme in the second zone (assuming a width of 5 fine-grid cells) is given as:
+\begin{itemize}\setlength{\parskip}{-4pt}
+\item row/column 1: 100\% interpolated coarse grid, 0\% fine grid,
+\item row/column 2: 75\% interpolated coarse grid, 25\% fine grid,
+\item row/column 3: 50\% interpolated coarse grid, 50\% fine grid,
+\item row/column 4: 25\% interpolated coarse grid, 75\% fine grid, and
+\item row/column 5: 0\% interpolated coarse grid, 100\% fine grid,
+\end{itemize}
+</font>
<font color="blue">oindent
+where row=1 is the first row in the second zone, and where the row or column
+nearest the outer edge takes precedence in ambiguous corner zones.
+The reference variables computed from the topography,
+$\overline{\mu}_d$ and $\overline{\phi}$, are similarly treated.
+The blended arrays are required to compute the reference state for the
+fine grid. The blending along the inner rows and columns ramps the
+coarse grid reference state to the
+fine grid reference state for a smooth transition between the grids.
+
+%
+% zones of topo smoothing
+%
+\begin{figure}
+ \centering
+ \includegraphics *[width=4.5in]{figures/zone12.pdf}
+ \caption{\label{figure:zone12} Zones of topographic blending
+for a fine grid. In the fine grid, the first zone is
+entirely interpolated from the coarse grid topography. In
+the second zone, the topography is linearly weighted between
+the coarse grid and the fine grid.}
+\end{figure}
+
+\subsubsection{Feedback}
+So that the coarse grid and the fine grid are consistent at coincident points, the
+fine grid values are fed back to the coarse grid.
+There are two available
+options for feedback: either the mean of all fine grid cells contained
+within each coarse grid cell is fed back (or cell faces in the case of the
+horizontal momentum fields), or a single-point feedback
+is selected for the masked or categorical fields.
+
+Subsequent to the feedback step, the coarse grid may be optionally smoothed in the area
+of the fine grid. Two smoothers are available: a 5-point 1-2-1 smoother and a smoother-desmoother
+with a similar stencil size.
+Both the feedback and the smoothers are run one row and column in from the
+interface row and column of the coarse grid that provides
+the lateral boundary conditions to the fine grid.
+
+\subsubsection{Reference State}
+The initial feedback when the nest is instantiated ensures
+that the coarse grid is consistent with the fine grid, particularly
+with regards to elevation and the reference state fields inside the blended region, and for such
+terrestrial features as coasts, lakes, and islands. The adjustment
+of the elevation in the coarse grid forces a base state recalculation.
+The fine-grid needs an initial base state calculation, and after
+the terrain feedback, the coarse grid is also in need of a base state
+recalculation.
+
+Note that with the horizontal interpolation of the coarse grid
+to the fine grid and the feedback of the fine grid to the coarse
+grid,
+the coarse grid base state is recomputed
+even without a separate fine-grid initial data file,
+since the coarse grid topography is adjusted.
+
+With the completed base state computations, which follow similarly to
+that described for the real-data initialization in section
+\ref{initialization_real_base_section},
+the routines return
+back to the integration step for the coarse and fine grids.
+The fine grid data is now properly initialized for integration and
+can be advanced forward a time step.
+
+\subsubsection{Integration}
+
+The integration by grid is recursive. At the end of each grid's time step, a check
+is made to determine if a child grid exists for that parent and if the
+current time is bracketed by the child's start/end time.
+This is shown in Fig. \ref{nest_domain_integration_figure}. The integration process for the nest (step 2 under the
+while loop) is recursively calling the top step in the overall sequence as a coarse grid itself.
+This is a ``depth first''
+traversal of the tree of grids.
+If a child grid does exist, that child grid is integrated up through the current time of
+the parent grid.
</font>
</pre>