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.
\[\phi = \phi_{instr}\]