degrees of freedom for signal

1. degrees of freedom for signal profile from avk

   symbol	description	unit	variable name
   \(d^{x}_{s}(i)\)	degrees of freedom for signal per level		<x>_dfs {:,vertical}
   \(A^{x}(i,j)\)	AVK of a profile x		<x>_avk {:,vertical,vertical}

   The pattern : for the first dimensions can represent {latitude,longitude}, {time}, {time,latitude,longitude}, or no dimensions at all.

   \[d^{x}_{s}(i) = A^{x}(i,i)\]

2. degrees of freedom for signal from degrees of freedom for signal profile

   symbol	description	unit	variable name
   \(d^{x}_{s}\)	degrees of freedom for signal		<x>_dfs {:}
   \(d^{x}_{s}(i)\)	degrees of freedom for signal per level		<x>_dfs {:,vertical}

   The pattern : for the first dimensions can represent {latitude,longitude}, {time}, {time,latitude,longitude}, or no dimensions at all.

   \[d^{x}_{s} = \sum_{i}{d^{x}_{s}(i)}\]