diff --git a/Convert_Matlab/Documentation_texfol/documentation.tex b/Convert_Matlab/Documentation_texfol/documentation.tex index 6f0e814d85f9c9003990e9afb6134a6c236bc2fb..55a0034b80aa87fefd46be7b0175e851555b6bed 100644 --- a/Convert_Matlab/Documentation_texfol/documentation.tex +++ b/Convert_Matlab/Documentation_texfol/documentation.tex @@ -55,6 +55,7 @@ for all $k$. That is, we guarantee that: \begin{equation*} \forall k, e_\mathrm{max}(k) \le E \end{equation*} +($E$ may not be the same for cyclones and anticyclones.) The eddy indices $e$ for eddies at date index $k$ start at 1 and increment 1 by 1, without any jump. So they go from 1 to @@ -174,24 +175,25 @@ the number of eddies at the date, in the field \verb+eddy_index+. The file \verb+ishape_last.txt+ in the directory \verb+SHPC_(anti|cyclo)+ is used to access directly any instantaneous -eddy at any date. Let $l(k)$ be the shape index in the shapefiles of -the last instantaneous eddy at date index $k$: +eddy at any date. Let $d_0$ be the first date in an SHPC. Let $l(d)$ +be the shape index in the SHPC of the last instantaneous eddy at date +$d$: \begin{equation*} - l(k) = \sum_{k' = 0} ^k e_\mathrm{max}(k') - 1 + l(d) = \sum_{d' = d_0} ^d e_\mathrm{max}(d') - 1 \end{equation*} -So the shape index $i$ of the eddy with eddy index $e$ at date index $k$ is: +So the shape index $i$ of the eddy with eddy index $e$ at date $d$ is: \begin{equation*} i = \begin{array}{|ll} - e - 1 & \mathrm{if}\ k = 0 \\ - l(k - 1) + e & \mathrm{if}\ k \ge 1 + e - 1 & \mathrm{if}\ d = d_0 \\ + l(d - 1) + e & \mathrm{if}\ d > d_0 \end{array} \end{equation*} -Also, note that, if $k \ge 1$ then: +Also, note that, if $d > d_0$ then: \begin{equation*} - e_\mathrm{max}(k) = l(k) - l(k - 1) + e_\mathrm{max}(d) = l(d) - l(d - 1) \end{equation*} -\verb+ishape_last.txt+ gives $l(k)$ for all $k$. +\verb+ishape_last.txt+ gives $l(d)$ for all $d$ in an SHPC. Finally, the file \verb+grid_nml.txt+ in the directory \verb+SHPC_(anti|cyclo)+ gives (in Fortran namelist format) the grid