--- manual/s_algorithm/text/shap.tex	2001/08/08 16:15:22	1.1
+++ manual/s_algorithm/text/shap.tex	2005/08/08 17:57:06	1.5
@@ -1,9 +1,10 @@
-% $Header: /home/ubuntu/mnt/e9_copy/manual/s_algorithm/text/shap.tex,v 1.1 2001/08/08 16:15:22 adcroft Exp $
+% $Header: /home/ubuntu/mnt/e9_copy/manual/s_algorithm/text/shap.tex,v 1.5 2005/08/08 17:57:06 jmc Exp $
 % $Name:  $
 
-\subsection{Shapiro Filter} 
+\section{Shapiro Filter} 
+\label{sect:shapiro-filter}
 
-The Shapiro filter (Shapiro 1970, 1975) is a high order horizontal 
+The Shapiro filter \cite{Shapiro_70} is a high order horizontal 
 filter that efficiently remove small scale grid noise 
 without affecting the physical structures of a field. 
 It is applied at the end of the time step %(the\_correction\_step),
@@ -21,7 +22,7 @@
 using pure numerical differences and ignoring 
 grid spacing. 
 This later form is stable whatever the grid is, and therefore
-specially useful for highly anisotrope grid such as spherical 
+specially useful for highly anisotropic grid such as spherical 
 coordinate grid.
 A damping time-scale parameter $\tau_{shap}$ 
 defines the strength of the filter damping.
@@ -46,7 +47,7 @@
 [1 - \frac{\Delta t}{\tau_{shap}} (\frac{1}{4}\delta_{jj})^n]
 $$
 
-In addition, the S2 operator can easly be extended to 
+In addition, the S2 operator can easily be extended to 
 a physical space filter: 
 $$
 \mathrm{S2g:}\hspace{2cm}
@@ -54,7 +55,7 @@
 \{ \frac{L_{shap}^2}{8} \overline{\nabla}^2 \}^n]
 $$
 
-with the Laplacien operator $\overline{\nabla}^2 $
+with the Laplacian operator $\overline{\nabla}^2 $
 and a length scale parameter $L_{shap}$.
 The stability of this S2g filter requires 
 $L_{shap} < \mathrm{Min}^{(Global)}(\Delta x,\Delta y)$.
