Uncertainty assessment of unattended above-water radiometric data collection from research vessels with the Dynamic Above-water Radiance (L) and Irradiance (E) Collector (DALEC): supplement

We used above- and below-water radiometry measurements collected during a research voyage in the eastern Indian Ocean to assess uncertainties in deriving the remote sensing reflectance, Rrs, from unattended above-water radiometric data collection with the In-Situ Marine Optics Pty. Ltd. (IMO) Dynamic Above-water Radiance (L) and Irradiance (E) Collector (DALEC). To achieve this, the Rrs values derived from using the latest version of this hyperspectral radiometer were compared to values obtained from two in-water profiling radiometer systems of rather general use in the ocean optics research community, i.e., the Biospherical Instruments Inc. Compact Optical Profiling System (C-OPS) and the Seabird HyperPro II. Our results show that unattended, carefully quality-controlled, DALEC measurements provide Rrs for wavelengths < 600 nm that match those derived from the in-water systems with no bias and a dispersion of about 8%, provided that the appropriate technique is used to quantify the contribution of sky light reflection to the measured signal. The dispersion is larger (25-50%) for red bands, which is expected for clear oligotrophic waters as encountered during the voyage, where ∼2 10-5 < Rrs < ∼2 10-4 sr-1. For comparison, the two in-water systems provided Rrs in agreement within 4% for wavelengths < 600 nm.

Uncertainty assessment of unattended abovewater radiometric data collection from research vessels with the Dynamic Above-Water Radiance (L) and Irradiance (E) Collector (DALEC): supplemental document S1. DALEC radiometric characterization and calibration Each DALEC optical channel utilizes a collimating lens (350 nm -2000 nm) and a 350 nm Optical Density 4 (OD4) long-pass filter in front of the spectrometer's optic fiber input. Using this configuration, ultraviolet light is adequately attenuated in the first few detector pixels and these pixels are then used to correct for the dark offset response of each spectrum.
The E s channel incorporates a Polytetrafluoroethylene (PTFE) diffuser and achieves a typical cosine response error < 3% to 60° and < 10% to 87.5° (Fig. S1). Fused Silica windows are used for both L u and L s channels and the collimating optics provide a FOV of ~ 5° for each.
Temperature sensors are located on each of the Zeiss TM Monolithic Miniature Spectrometers (MMS1) arrays to assist in correcting for temperature drift of the spectrometers. The pitch and roll data are utilized to quality control spectra where excessive ship motion may interfere with the measurement geometry.
Each spectrometer is calibrated separately using a National Institute of Standards and Technology (NIST)-traceable 1000W FEL lamp and stable power supply. The E s channel is radiometrically calibrated with a direct view of the FEL lamp filament, and the L t and L s channels are calibrated whilst viewing a calibrated 99% reflectance Spectralon TM plaque at 45 degree incidence [1]. A full set of calibrations are performed over a wide range of detector temperatures ranging from ~16°C to ~40°C and at different integration times (1, 2, 4, 8, 16, 32, 64, 128, 256, 512 ms). During calibration, the DALEC continually iterates through the set of integration times while the DALEC detectors are warming up. From this data, each spectrometers integration-time non-linearity, responsivity, temperature effects and radiometric calibration coefficients are derived. Fig. S1. Experimental DALEC cosine response (blue curve) compared to a theoretical perfect cosine response (black). The percent difference between both is displayed as the red curve (values on the right axis).
Non-linearity with respect to integration time for Zeiss MMS1 spectrometers arise from the additional photoelectron signal generated during the readout phase of the pixel array during the integration [2]. The conversion of a raw spectrum, to a dark corrected count rate, which accounts for the readout time, ∆ (Fig. S2a), is calculated as, where, is the integration time in milliseconds and is the dark count corrected signal. The count rate (normalized to 1 @ 30,000 counts) versus dark corrected counts (Fig. S2b) shows the effect of integration time non-linearity. From this, the linearly corrected spectrum, , is calculated as, = + , (2) where, the coefficients d 0 , d i and Δt are derived separately for each spectrometer. The illuminated signal response of Zeiss MMS1 spectrometers is known to change with temperature [3]. This is largely explained by the temperature response of silicon photodiodes (wavelength dependent) and, to a lesser extent, the optical components and spectrometer electronics. The derived temperature coefficients, (normalized to 1 at 24 degrees) for each spectrometer show a small effect at blue wavelengths and increasing toward NIR wavelengths. (Fig. S3). The temperature corrected spectrum, Tcorr for pixel i is calculated as, Once the temperature effects are corrected, the radiometric responsivity calibration coefficients are used to convert the spectrometer data into engineering units, i.e., where, F e , Fl u and Fl s are responsivity coefficients for each channel, calculated at 24 degrees C and normalized by the linearity corrected count rate.

S2. Statistics of instrument-pair comparisons
Tables S1, S2 and S3 below provide the per-wavelength and global statistics for the comparisons displayed in Figs. 8, 9 and 10 of the paper.