latitude derivations
- latitude from polygon - symbol - description - unit - variable name - \(\lambda\) - longitude - \(degE\) - longitude {:} - \(\lambda^{B}(i)\) - longitude - \(degE\) - longitude_bounds {:,N} - \(\phi\) - latitude - \(degN\) - latitude {:} - \(\phi^{B}(i)\) - latitude - \(degN\) - latitude_bounds {:,N} - Convert all polygon corner coordinates defined by \(\phi^{B}(i)\) and \(\lambda^{B}(i)\) into unit sphere points \(\mathbf{p}(i) = [x_{i}, y_{i}, z_{i}]\) - \(x_{min} = min(x_{i}), y_{min} = min(y_{i}), z_{min} = min(z_{i})\) - \(x_{max} = max(x_{i}), y_{max} = max(y_{i}), z_{max} = max(z_{i})\) - \(\mathbf{p}_{center} = [\frac{x_{min} + x_{max}}{2}, \frac{y_{min} + y_{max}}{2}, \frac{z_{min} + z_{max}}{2}]\) - The vector \(\mathbf{p}_{center}\) is converted back to \(\phi\) and \(\lambda\) 
- latitude from range - symbol - description - unit - variable name - \(\phi\) - latitude - \(degN\) - latitude {:} - \(\phi^{B}(l)\) - latitude boundaries (\(l \in \{1,2\}\)) - \(degN\) - latitude_bounds {:,2} - The pattern : for the dimensions can represent {latitude}, or {time,latitude}. \[\phi = \frac{\phi^{B}(2) + \phi^{B}(1)}{2}\]
- latitude from vertical profile latitudes - symbol - description - unit - variable name - \(\phi\) - single latitude for the full profile - \(degN\) - latitude {:} - \(\phi(i)\) - latitude for each profile point - \(degN\) - latitude {:,vertical} - \(N\) - number of profile points - The pattern : for the dimensions can represent {time}, or no dimensions at all. \[\begin{split}\begin{eqnarray} N & = & max(i, \phi(i) \neq NaN) \\ \phi & = & \phi(N/2) \end{eqnarray}\end{split}\]
- latitude from sensor latitude - symbol - description - unit - variable name - \(\phi\) - latitude - \(degN\) - latitude {:} - \(\phi_{instr}\) - latitude of the sensor - \(degN\) - sensor_latitude {:} - The pattern : for the dimensions can represent {time}, or no dimensions at all. \[\phi = \phi_{instr}\]