<p><b>skamaroc</b> 2007-01-11 14:15:12 -0700 (Thu, 11 Jan 2007)</p><p>additions to errata<br>
</p><hr noshade><pre><font color="gray">Modified: trunk/wrf/technote/errata.tex
===================================================================
--- trunk/wrf/technote/errata.tex        2007-01-11 21:14:20 UTC (rev 25)
+++ trunk/wrf/technote/errata.tex        2007-01-11 21:15:12 UTC (rev 26)
@@ -55,13 +55,13 @@
\partial_t U + (</font>
<font color="red">abla \cdot {\bf V} u )
- \partial_x (p\phi_\eta)
+ \partial_\eta (p\phi_x) &= F_U
-</font>
<font color="blue">otag
+\tag{2.3}
\\
%
\partial_t V + (</font>
<font color="red">abla \cdot {\bf V} v )
- \partial_y (p\phi_\eta)
+ \partial_\eta (p\phi_y) &= F_V
-</font>
<font color="gray">otag
+\tag{2.4}
%
\end{align}
@@ -74,27 +74,44 @@
F_{V_{cor}} & = - \biggl(f + u {\partial m \over
\partial y} - v {\partial m \over \partial x}\biggr) U
+ e W \sin \alpha_r - {vW \over r_e}
-</font>
<font color="blue">otag
+\tag{2.33}
\end{align}
</font>
<font color="red">oindent
-In Chapter 3, Model Discretization, the correct equations (3.12) and (3.26) are:
+In Chapter 3, Model Discretization, the coefficient $C$ on page 12
+should be defined as
+$$C=c_s^2/\mu^{t^*}{\alpha^{t^*}_d}^2$$.
+
+</font>
<font color="blue">oindent
+The correct equation 3.11 is
\begin{align}
+ \delta_\tau W''
+- m^{-1} g\overline{\left[(\alpha/\alpha_d)^{t^*} \biggl[
+ \partial_\eta (C \partial_\eta \phi'')
+ + \partial_\eta\biggl({c_s^2\over\alpha^{t^*}}{\Theta''\over\Theta^{t^*}}\biggr)\biggr]
+- \mu_d''\right]}^\tau
+ &= {R_W}^{t^*}
+\tag{3.11}
+\end{align}
+
+
+</font>
<font color="red">oindent
+The correct equations (3.12) and (3.26) are:
+\begin{align}
\delta_\tau \phi'' + {1\over\mu_d^{t^*}}
[
-% m^2 (U''\phi_x^{t^*} + V''\phi_y^{t^*})^{\tau+\Delta \tau} +
-m \Omega''^{\tau+\Delta \tau}\phi_\eta - \overline{g W''}^\tau ]
+m \Omega''^{\tau+\Delta \tau}\phi_\eta^{t^*} - \overline{g W''}^\tau ]
&= {R_\phi}^{t^*}
-</font>
<font color="red">otag
+\tag{3.12}
\end{align}
\begin{align}
\delta_\tau \phi'' + {1\over\mu_d^{t^*}}
[
- m \Omega''^{\tau+\Delta \tau} \delta_\eta \phi - \overline{g W''}^\tau ]
+ m \Omega''^{\tau+\Delta \tau} \delta_\eta \phi^{t^*} - \overline{g W''}^\tau ]
&= {R_\phi}^{t^*}
-</font>
<font color="blue">otag
+\tag{3.26}
\end{align}
</font>
<font color="gray">oindent
@@ -110,7 +127,7 @@
& - (\alpha/\alpha_d) ( {\mu}_d \partial_x \phi'
- \partial_\eta p' \partial_x \phi
+ {\mu}_d' \partial_x \phi ) + F_U
-</font>
<font color="gray">otag
+\tag{3.13}
\\
%
R_V^{t^*} = &
@@ -121,12 +138,12 @@
& - (\alpha/\alpha_d) ( {\mu}_d \partial_y \phi'
- \partial_\eta p' \partial_y \phi
+ {\mu}_d' \partial_y \phi ) + F_V
-</font>
<font color="red">otag
+\tag{3.14}
\\
%
R_{\mu_d}^{t^*} = &
- m^2[\partial_x U + \partial_y V] - m \partial_\eta \Omega
-</font>
<font color="gray">otag
+\tag{3.15}
\\
%
R_W^{t^*} = &
@@ -136,11 +153,17 @@
& + m^{-1} g (\alpha/\alpha_d) [\partial_\eta p'
- {\bar{\mu}}_d (q_v + q_c +q_r)]
- m^{-1} {\mu}_d'g + F_W
-</font>
<font color="blue">otag
+\tag{3.17}
%
\end{align}
+\vfill\eject
</font>
<font color="blue">oindent
+At the top of page 14 in Chapter 3, we have corrected the statement
+concerning the lower boundary condition for the vertically-implicit
+solution for $W''$, the correct lower boundary condition being
+$\Omega = \Omega'' = 0$.
+
Also in Chapter 3, page 18, the correct equation for $V$ component of
the Coriolis and curvature term is
</font>
</pre>