Changeset 3022 for branches/2011/dev_r2855_CMCC3_divd/DOC

Timestamp:

2011-10-28T12:20:17+02:00 (13 years ago)

Author:

dobricic

Message:

Applied the divergence damping for horizontal velocity increments.

Location:

branches/2011/dev_r2855_CMCC3_divd/DOC/TexFiles

Files:

• Biblio/Biblio.bib (modified) (2 diffs)
• Chapters/Chap_ASM.tex (modified) (1 diff)
• Namelist/namasm (modified) (1 diff)

branches/2011/dev_r2855_CMCC3_divd/DOC/TexFiles/Biblio/Biblio.bib

@@ -722 +722 @@
   year = {2000},
   pages = {237--313}
+}
+
+
+@ARTICLE{Dobricic_al_OS07,
+  author = {S. Dobricic and N. Pinardi and M. Adani and M. Tonani and 
+            C. Fratianni and A. Bonazzi and V. Fernandez},
+  title = {Daily oceanographic analysis by the Mediterranean basin scale 
+           assimilation system},
+  journal = OS,
+  year = {2007},
+  volume = {3},
+  pages = {149-157}
 }
 
@@ -2485 +2497 @@
   volume = {359},
   pages = {123--129}
+}
+
+@ARTICLE{Talagrand_JAS72,
+  author = {O. Talagrand},
+  title = {On the damping of high-frequency motions in four-dimensional 
+           assimilation of meteorological data},
+  journal = JAS,
+  year = {1972},
+  volume = {29},
+  pages = {1571-1574}
 }
 

branches/2011/dev_r2855_CMCC3_divd/DOC/TexFiles/Chapters/Chap_ASM.tex

@@ -86 +86 @@
 
 %==========================================================================
+% Divergence damping description %%%
+\section{Divergence damping initialisation}
+\label{ASM_details}
+
+The velocity increments may be initialized by the iterative application of 
+a divergence damping operator. In iteration step $n$ new estimates of 
+velocity increments $u^{n}_I$ and $v^{n}_I$ are updated by:
+\begin{equation} \label{eq:asm_dmp}
+\left\{ \begin{aligned}
+ u^{n}_I = u^{n-1}_I + \frac{1}{e_{1u} } \delta _{i+1/2} \left( {A_D
+\;\chi^{n-1}_I } \right) \\
+\\
+ v^{n}_I = v^{n-1}_I + \frac{1}{e_{2v} } \delta _{j+1/2} \left( {A_D
+\;\chi^{n-1}_I } \right) \\
+\end{aligned} \right,
+\end{equation}
+where
+\begin{equation} \label{eq:asm_div}
+\chi^{n-1}_I = \frac{1}{e_{1t}\,e_{2t}\,e_{3t} }
+                \left( {\delta _i \left[ {e_{2u}\,e_{3u}\,u^{n-1}_I} \right]
+                       +\delta _j \left[ {e_{1v}\,e_{3v}\,v^{n-1}_I} \right]} \right).
+\end{equation}
+By the application of \eqref{eq:asm_dmp} and \eqref{eq:asm_dmp} the divergence is filtered
+in each iteration, and the vorticity is left unchanged. In the presence of coastal boundaries
+with zero velocity increments perpendicular to the coast the divergence is strongly damped.
+This type of the initialisation reduces the vertical velocity magnitude  and alleviates the
+problem of the excessive unphysical vertical mixing in the first steps of the model 
+integration \citep{Talagrand_JAS72, Dobricic_al_OS07}. Diffusion coefficients are defined as 
+$A_D = \alpha e_{1t} e_{2t}$, where $\alpha = 0.2$. The divergence damping is activated by
+assigning to \textit{ndivdmp} in the \textit{nam\_asminc} namelist a value greater than zero. 
+By choosing this value to be of the order of 100 the increments in the vertical velocity will 
+be significantly reduced.
+
+
+%==========================================================================
 
 \section{Implementation details}

branches/2011/dev_r2855_CMCC3_divd/DOC/TexFiles/Namelist/namasm

@@ -17 +17 @@
     ln_salfix = .false.    !  Logical switch for ensuring that the sa > salfixmin
     salfixmin = -9999      !  Minimum salinity after applying the increments
+    ndivdmp   = 0          !  Number of iterations of divergence damping operator
 /