Changeset 2483 for branches/nemo_v3_3_beta/DOC/TexFiles/Chapters/Chap_ASM.tex

Timestamp:

2010-12-18T13:36:55+01:00 (13 years ago)

Author:

djlea

Message:

Documentation fixes for OBS and ASM

File:

• branches/nemo_v3_3_beta/DOC/TexFiles/Chapters/Chap_ASM.tex (modified) (4 diffs)

branches/nemo_v3_3_beta/DOC/TexFiles/Chapters/Chap_ASM.tex

@@ -13 +13 @@
 $\ $\newline    % force a new line
 
-The ASM code adds the functionality to apply increments to model variables, 
+The ASM code adds the functionality to apply increments to the model variables: 
 temperature, salinity, sea surface height, velocity and sea ice concentration. 
 These are read into the model from a NetCDF file which may be produced by data
@@ -40 +40 @@
 IAU is used when \np{ln\_asmiau} is set to true.
 
-With IAU, the model state trajectory in the assimilation window 
+With IAU, the model state trajectory ${\bf x}$ in the assimilation window 
 ($t_{0} \leq t_{i} \leq t_{N}$)
-is corrected by adding the analysis increments for 
-for temperature, salinity, horizontal velocity and SSH
+is corrected by adding the analysis increments for temperature, salinity, horizontal velocity and SSH
 as additional tendency terms to the prognostic equations:
 \begin{eqnarray}     \label{eq:wa_traj_iau}
@@ -49 +48 @@
 \; + \; F_{i} \delta \tilde{\bf x}^{a} 
 \end{eqnarray}
-where $F_{i}$ is a weighting function defined such that $\sum_{i=1}^{N} F_{i}=1$. 
+where $F_{i}$ is a weighting function for applying the increments $\delta
+\tilde{\bf x}^{a}$ defined such that $\sum_{i=1}^{N} F_{i}=1$.
+${\bf x}^b$ denotes the model initial state and ${\bf x}^a$ is the model state
+after the increments are applied. 
 To control the adjustment time of the model to the increment,
 the increment can be applied over an arbitrary sub-window,
@@ -68 +70 @@
 The second function employs peaked hat-like weights in order to give maximum 
 weight in the centre of the sub-window, with the weighting reduced 
-linearly to a small value at the window end-points.
+linearly to a small value at the window end-points:
 \begin{eqnarray}     \label{eq:F2_i}
 F^{(2)}_{i}