update from Judith #47

Adding changes from Judith, including the figure showing the perturbation pattern.

stoch.tex

@@ -1,4 +1,4 @@
-\chapter{Stochastic Parameterization Schemes}
+\chapter{Stochastic Parameterization Suite}
 \label{stoch}
 
 Physical parameterization schemes represent averages over unresolved,
@@ -18,38 +18,53 @@ \chapter{Stochastic Parameterization Schemes}
 
 The stochastic parameterization suite in WRF comprises a number of
 stochastic parameterization schemes, targeted at representing different aspects 
-of uncertainty (see Table \ref{stoch_table}). Generally, one or more random
+of uncertainty (see Table \ref {stoch_table}). Generally, one or more random
 perturbation fields are generated and used to perturb tendencies or
-parameters in the physical parameterization schemes.  It important to understand 
-that the random perturbation fields are characterized by spatial and temporal
-correlations, which can be prescribed.  Figure 9.1 provides an example of 
-variations of perturbation patterns for different spatial scales.
-
-The benefits of stochastic parameterization schemes are most evident in ensemble 
-prediction systems, where the added ensemble diversity leads to more reliable 
-ensemble spread and improved probabilistic forecast skill \citep[e.g.][]{Be15}.
+parameters in the physical parameterization schemes.
+The random perturbation fields are characterized by spatial and temporal
+correlations as well as an overall perturbation amplitude, which can be
+prescribed by namelist parameters. Figure \ref{stoch_pattern}
+provides an example for perturbation patterns with different spatial length-scales.
 
 %--------------------------------------------------------------------------------------------
 \begin{table}[h!]
+\label{stoch_table}
 \begin{center}
 \caption{Stochastic parameterization suite}
 \begin{tabular}{ | l | l | l |}
 \hline
 Scheme          & Name & Perturbations to \\ 
 \hline
-SPPT  & Stochastically perturbed    &  u-,v-,$\theta$- and $q_v$-tendencies\\
-      & parameterization tendencies &  from PBL and convection\\ | \\
+SPPT  & Stochastically perturbed    &  u-,v-,$\theta$- and $q_v$-tendencies from PBL\\
+      & parameterization tendencies &  and convection scheme\\  \hline
+
 SKEBS & Stochastic kinetic-energy   &  Full ($=$ physics + dynamics) \\
-      & backscatter scheme          &  $u_{\rm rot}$-,$v_{\rm rot}$- and $\theta$- tendencies\\ | \\
-SPP & Stochastically perturbed      &  Select parameters from\\
-    & parameter scheme              &  PBL and convection \\ | \\
-RPF & Random perturbation           &  Interface must be \\
-    & field                         &  provided by user\\
+      & backscatter scheme          &  $u_{\rm rot}$-,$v_{\rm rot}$- and $\theta$- tendencies\\  \hline
+
+SPP & Stochastically perturbed      &  Select parameters from PBL \\
+    & parameterization scheme       &  and convective scheme\\  \hline
+
+RPF & Random perturbation field     &  Creates perturbation pattern only;  \\
+    &                               &  interface must be provided by user\\
 \hline
 \end{tabular}
 \end{center}
-\label{stoch_table}
 \end{table}
+%--------------------------------------------------------------------------------------------
+
+The benefits of stochastic parameterization schemes are most evident in ensemble 
+prediction systems, where the added ensemble diversity leads to more reliable 
+ensemble spread and improved probabilistic forecast skill \citep[e.g.][]{Be15}.
+
+%--------------------------------------------------------------------------------------------
+\begin{figure}[h!]
+  \includegraphics[width=6.5in]{figures/stoch_pattern.png}
+    \caption{Perturbation patterns for three different spatial scales: 
+     a) convection-scale, b) meso-scale, c) synoptic scale.}
+  \label{stoch_pattern}
+\end{figure}
+%--------------------------------------------------------------------------------------------
+
 
 %--------------------------------------------------------------------------------------------
 \section {Stochastically Perturbed Physics Tendencies (SPPT)}
@@ -68,39 +83,40 @@ \chapter{Stochastic Parameterization Schemes}
 $D$ is the tendency from the dynamical core, 
 $P_i$ the tendency from the i-th physics scheme, 
 and $r$ is a two-dimensional, Gaussian distributed zero-mean random
-perturbation field with spatial and temporal correlations. 
+perturbation field with spatial and temporal correlations (as in Fig.\ref{stoch_pattern}).
 Depending on
 the implementation, the SPPT scheme can use up to three patterns with
-different spatial and time scales, sa well as a vertical tapering function which 
+different spatial and time scales, as well as a vertical tapering function which 
 tapers perturbations near the surface and for the highest model levels.
 The WRF implementation by default uses only a single perturbation field \citep{Be15},
 and it perturbs the tendencies from the PBL and convection schemes, but not those from 
-the radiation or microphysics schemes.
+the radiation or microphysics schemes. For multiple domains, the perturbation pattern of the 
+parent domain is interpolated to the nested domains.
 
 %--------------------------------------------------------------------------------------------
 \section{Stochastic Kinetic-Energy Backscatter Scheme (SKEBS)}
 %--------------------------------------------------------------------------------------------
-The Stochastic Kinetic Energy Backscatter scheme (SKEB) aims to represent
+The Stochastic Kinetic Energy Backscatter scheme (SKEBS) aims to represent
 the interactions of turbulent eddies near or below the
 truncation level with the resolved state. Some of the eddy-eddy interactions
 will dissipate, but others will lead to a resolved-scale effect.
 Originally developed for large-eddy simulation applications, these ideas were 
 adapted for numerical weather prediction by
 \citet{Sh05} and \citet{Be09}.
-SKEBS generates streamfunction perturbations with spatio-temporal correlations. These
-can be weighted with the dissipation rate from numerical diffusion, 
-convection, and orographic wave drag. 
-
+SKEBS generates streamfunction perturbations with spatio-temporal
+correlations, which perturb the rotational wind. These can be weighted
+with the dissipation rate from numerical diffusion, convection, and
+orographic wave drag.
 In the WRF implementation, no dissipation weighting is used and the 
-perturbations can be extended to the potential temperature field \citep{Be11}.
+perturbations are extended to the potential temperature field \citep{Be11}.
 Wind component perturbations are proportional to the square
 root of the kinetic-energy backscatter rate, and temperature
 perturbations are proportional to the potential energy backscatter rate.
 
 A comparison of SKEBS and SPPT shows that SKEBS introduces the most model 
 diversity in the free atmosphere and for dynamical variables, 
 while SPPT is most active in regions with large tendencies (e.g., in areas with convection 
-and near the surface) (\citep{Be15}).
+and near the surface) \citep{Be15}.
 %--------------------------------------------------------------------------------------------
 \section {Stochastically Perturbed Parameterization Scheme (SPP)}
 %--------------------------------------------------------------------------------------------
@@ -120,44 +136,37 @@ \section{Stochastic Kinetic-Energy Backscatter Scheme (SKEBS)}
 Perturbations in the convection scheme (e.g., to the vertical mass flux 
 profile) or in the microphysics scheme (e.g., to the shape parameter of 
 the particle size distribution) in principle allow the representation of
-structural model error.  In the statistical sciences there is a fundamental 
-distinction between ``parameter error'' and 
-``structural model error ''. When some parameters in the physical schemes 
-are perturbed, however, this distinction is blurred, and the scheme is 
-called a ``Stochastically perturbed {\it parameterization} scheme''
-rather than ``Stochastically perturbed {\it parameter} scheme''. 
+structural model error.  The statistical sciences fundamentally 
+distinguish between ``parameter error'' and 
+``structural error''. This distinction is blurred when some parameters in 
+the physical schemes are perturbed, since parameter changes
+can change the structural model error. Hence the scheme is referred to as 
+``Stochastically perturbed \textit {parameterization} scheme'' rather than
+``Stochastically perturbed \textit {parameter} scheme''. 
 
 The SPP released in WRF has been designed in close collaboration with 
 developers of physical parameterization and is under active development. 
-Hence, it is only
-available for selected physics packages, namely the Grell-Freitas convection
-scheme and the MYNN PBL scheme \citep{jankov2017performance}.
+Hence, it is only available for selected physics packages, namely the 
+Grell-Freitas convection scheme and the MYNN PBL scheme \citep{jankov2017performance}.
 
-The member diversity introduced by SPP tends to be smaller than that of SKEBS and SPPT 
-and is in itself typically not enough to generate reliable ensemble spread 
-\citep{Be15}.  SPP, however, can be augmented by one of the other model-error schemes 
-or used in itself to study forecast sensitivity to a particular parameter setting.
+The perturbations introduced by SPP tend to be smaller than those
+introduced by SKEBS and SPPT and are by themselves typically not enough to
+generate reliable ensemble spread \citep{Be15}.  However, SPP can be used 
+to study forecast sensitivity to a particular parameter setting and/or
+can be augmented by one of the other model-error schemes.
 
 %--------------------------------------------------------------------------------------------
 \section {Random Perturbation field (RPT)}
 %--------------------------------------------------------------------------------------------
-WRF enables the user to generate a 3D Gaussian random perturbation field
+WRF enables the user to generate a 3-D Gaussian random perturbation field
 with prescribed spatial and temporal correlations and use to it perturb
-parameters of interest.  Since the interface has to be provided by the
-user, this option is not recommended for WRF novices.
+parameters or variables of interest. The interface to the perturbed quantity
+has to be provided by the user. 
 
 %--------------------------------------------------------------------------------------------
 \section {Stochastic Perturbations to the Lateral Boundary Conditions}
 %--------------------------------------------------------------------------------------------
 The stochastic tendencies in WRF are typically treated as physics tendencies, and 
 they change the perturbed fields at each time step within the WRF domain. However, since 
 the stochastic perturbation field is also generated on the boundary, it can be used to 
-perturb the lateral boundary specified and relaxation zones. The WRF Users' Guide 
-provides details on this.
-
-%--------------------------------------------------------------------------------------------
-\begin{figure}[h!]
-  \includegraphics[trim=0cm 15cm 0 10cm,scale=.80]{figures/stoch_pattern.png}
-    \caption{Perturbation patterns for three different length scales: a) convection-permitting scale, b) meso-scale, c) synoptic scale.}
-  \label{fig_stoch_pattern}
-\end{figure}
+perturb the lateral boundary specified and relaxation zones.