## 2 System Design
### PANTHYR Data Processing  
Each of the scans within a sub-cycle are converted from DCs to calibrated (ir)radiances, as described in Equations (1-3) of Reference [20], using the calibration files appropriate for the instrument serial number and date as follows:  
* The 16-bit DCs are normalized by dividing by 65,535. * A long-term dark current correction is performed taking into account the instrument factory characterization and the scan integration time. * A residual dark signal is subtracted using the mean average from the sensor dark pixels. * The signal is normalized by the integration time and divided by the calibration sensitivity to retrieve final calibrated (ir)radiances. Incomplete spectra are removed, as well as \(L_{d}\) and \(L_{u}\) scans with \(>\)25% difference between neighboring scans at 550 nm. \(E_{d}\) scans are removed using the same criterion after normalizing \(E_{d}\) by \(\mathit{Cos}(\theta_{0})\), where \(\theta_{0}\) is the sun zenith angle. The sub-cycle is further processed if sufficient scans pass the quality control: \(L_{u}\) 9/11, and \(E_{d}\) and \(L_{d}\) 5/6 each. The remaining \(E_{d}\) and \(L_{d}\) measurements are then grouped and mean averaged to \(\overline{E_{d}}\) and \(\overline{L_{d}}\). For each \(L_{u}\) scan, the water-leaving radiance, \(L_{w}\), is computed by removing skyglint radiance as follows:  
\[L_{w}=L_{u}-\rho_{F}\overline{L_{d}}, \tag{1}\]  
where \(\rho_{F}\) is the \"wind-roughened Fresnel\" coefficient that represents the fraction of incident skylight that is reflected back toward the water-viewing sensor at the air-water interface and is given by the look-up table (LUT) of Reference [25]. This LUT describes \(\rho_{F}\) as function of viewing and sun geometry and wind speed. Wind speed is retrieved from ancillary data files or set to a user-defined default value if wind speed data are unavailable. The data in the LUT are linearly interpolated to the current observation geometry and wind speed. The \(L_{w}\) scans are then converted into (\"uncorrected\") water-leaving radiance reflectance scans, \(\rho_{wu}\), as follows:  
\[\rho_{wu}=\pi\frac{L_{w}}{E_{d}}. \tag{2}\] \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Sub-Cycle** & **Instrument** & **Measurement** & **Zenith** & **Azimuth Relative** & **Replicate** \\
**Number** & & & **Angle (\({}^{\circ}\))** & **to Sun (\({}^{\circ}\))** & **Scans** \\ \hline
1 & Irradiance & \(E_{d}\) & 180 & 90 & 3 \\
2 & Radiance & \(L_{d}\) & 140 & 90 & 3 \\
3 & Camera & Sky photo & 140 & 90 & - \\
4 & Radiance & \(L_{u}\) & 40 & 90 & 11 \\
5 & Camera & Water photo & 40 & 90 & - \\
6 & Radiance & \(L_{d}\) & 140 & 90 & 3 \\
7 & Irradiance & \(E_{d}\) & 180 & 90 & 3 \\
8-14 & As 1–7 & As 1–7 & As 1–7 & 135 & As 1–7 \\
15-21 & As 1–7 & As 1–7 & As 1–7 & 225 & As 1–7 \\
22-28 & As 1–7 & As 1–7 & As 1–7 & 270 & As 1–7 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Pan-and-tilt hyperspectral radiometer system (PANTHYR) basic data acquisition cycle. Azimuth is measured clockwise with respect to sun with a relative azimuth of 0\({}^{\circ}\), meaning that the radiance sensor is pointing toward the sun, and a relative azimuth of 90\({}^{\circ}\), meaning that the radiance sensor is pointing to the right of sun. A zenith angle of 180\({}^{\circ}\) means that the instrument is pointing vertically upward and, hence, measuring downwelling (ir)radiance. Measurements within a predefined azimuth no-go zone will be skipped. A \"near infrared (NIR) similarity spectrum\" correction is then applied to remove any white error from inadequate skyglint correction as shown in Equation (3). A spectrally flat measurement error, \(\varepsilon\), is estimated using two wavelengths in the NIR [28], where \(\lambda_{1}=780\) nm and \(\lambda_{2}=870\) nm. \[\varepsilon=\frac{\alpha\rho_{wu}(\lambda_{2})-\rho_{wu}(\lambda_{1})}{\lambda _{2}-\lambda_{1}}, \tag{3}\]  
where \(\alpha\) is the similarity spectrum [26] ratio for the bands used; here, \(\alpha(780,\,870)=1/0.523=1.912\).