# longitude derivations

1. longitude from polygon

   See latitude from polygon

2. longitude from range

   symbol | description | unit | variable name
   --- | --- | --- | ---
   \(\lambda\) | longitude | \(degE\) | longitude {:}
   \(\lambda^{B}(l)\) | longitude boundaries (\(l \in \{1,2\}\)) | \(degE\) | longitude_bounds {:,2}

   The pattern : for the dimensions can represent {longitude}, or {time,longitude}.

   \[\lambda = \frac{\lambda^{B}(2) + \lambda^{B}(1)}{2}\]

3. longitude from vertical profile longitudes

   symbol | description | unit | variable name
   --- | --- | --- | ---
   \(\lambda\) | single longitude for the full profile | \(degE\) | longitude {:}
   \(\lambda(i)\) | longitude for each profile point | \(degE\) | longitude {:,vertical}
   \(N\) | number of profile points |  |

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

   \begin{eqnarray} N & = & max(i, \lambda(i) \neq NaN) \\ \lambda & = & \lambda(N/2) \end{eqnarray}

4. longitude from sensor longitude

   symbol | description | unit | variable name
   --- | --- | --- | ---
   \(\lambda\) | longitude | \(degE\) | longitude {:}
   \(\lambda_{instr}\) | longitude of the sensor | \(degE\) | sensor_longitude {:}

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

   \[\lambda = \lambda_{instr}\]