Simultaneous measurement of spectral sky radiance by a non-scanning multidirectional spectroradiometer (MUDIS)

The developed spectroradiometer is shown in figure 1. The main component of MUDIS is a hyperspectral imager consisting of a UV-sensitive CCD camera (PCO AG, Kelheim, Germany) and an Offner imaging spectrometer. This imager design is commonly used for so-called push broom measurements of two-dimensional sceneries. Instead of measuring each pixel of a scene sequentially, push broom instruments are capable of performing spectral measurements of a whole line of pixels at once (Davis et al 2002). However, instead of measuring line by line with a camera lens and an entrance slit, we attached a bundle of optical fibres to the imager consisting of 113 single fibres lined up to a slit. The other ends of the fibres are embedded in a hemispherical-shaped dome in which the 113 fibres are evenly distributed in zenith and azimuth directions (figure 1). The field of view (FOV) of the fibres is not additionally limited by any optical part. A characterization of the fibres showed a FOV of 10.6° at 600 nm increasing up to 18.4° for shorter wavelengths (figure 2). A single measurement (sky capture) performed with MUDIS therefore simultaneously performs 113 sky radiance measurements in different zenith and azimuth directions.

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MUDIS is capable of measuring spectra from 250 to 600 nm with a bandwidth of approximately 2 nm and a sampling interval of 0.4 nm. Figure 3 shows raw data captured with this setup under cloudless (a) and overcast (b) sky. Under cloudless sky, one fibre of the entrance optics is illuminated by direct sunlight. The corresponding area of the CCD sensor is oversaturated and several adjacent rows are affected by stray light. When measuring sky radiance during overcast sky, no saturation occurs and consequently stray light is less intense. In order to remove stray light in the UV, we apply a simple stray light correction method. Eight sensor rows that are not illuminated and thus only detect stray light during overcast sky (dashed lines in figure 3(b)) are averaged and the resulting average stray light spectrum is assumed to be sufficiently representative for the whole sensor area. Furthermore, illuminated sensor rows receive negligible radiation below 290 nm due to ozone absorption in the atmosphere. Each illuminated sensor row is now stray light corrected by a two-step method. First, the previously derived average stray light spectrum is scaled to the signal of the illuminated sensor row at 285 nm. Second, the scaled stray light is subtracted from the row. This method is similar to a stray light correction method developed by Jäkel et al (2007), where spectral filters are used to derive a reference stray light for a CCD array spectroradiometer. Nevertheless, we found that stray light originating from oversaturation differs in terms of intensity and spectrum from stray light observed without oversaturation. Rows affected by more than 20 counts of stray light at 285 nm are therefore discarded, since they cannot be corrected properly by this simple method.

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The SCCD system consists of a UV-VIS-sensitive CCD array spectrometer (StellarNet, Tampa, FL, USA) with a single radiance entrance optics attached to the instrument via a fibre bundle. The entrance optics has a FOV of 5° and is mounted on a positioning device that is able to scan a desired pattern of points in the hemisphere. A SCCD sky scan identical to the MUDIS entrance optics dome pattern takes about 12 min. The SCCD has been calibrated based on a 1000 W tungsten halogen lamp which has been calibrated by the Physikalisch-Technische Bundesanstalt. Details on the calibration process are described in Pissulla et al (2009). Kouremeti et al (2008) quantify the uncertainty of this calibration method with up to 5.55% in the UV. The measurements have been stray light corrected with an algorithm adopted from Kreuter and Blumthaler (2009). The SCCD is capable of measuring in a wavelength range of 270–900 nm with a bandwidth of approximately 1 nm and a sampling interval of 0.3 nm. Measurements performed with the SCCD are convoluted with a suitable slit function in order to achieve a 2 nm bandwidth for better spectral comparison with the MUDIS instrument.

MUDIS is calibrated relative to the SCCD because a direct calibration similar to the SCCD calibration is not feasible. By measuring the same sky radiance scenery simultaneously with a calibrated and an uncalibrated instrument, it is possible to perform a radiometric calibration of the uncalibrated instrument (Röder et al 2005). While cloudless sky might be the most suitable scenery for this, task channels with high signal strength like those pointing to the circumsolar region or those saturated by direct irradiance lead to severe stray light contamination of vast regions of the sensor area (see figure 3(a)). Therefore, the intercalibration has been performed during overcast sky. The intercalibration has been performed based on 20 SCCD sky radiance scans performed on 22 October 2012 from 8:52 to 12:55 UTC. The solar zenith angle (SZA) during that time was between 69.4° and 63.2°. However, clouds are the dominating factor for the variability of the spectral radiance in this situation, reducing the received radiance especially in the UV compared to the cloudless sky. Therefore, an average of the 20 measurements is used for the determination of the MUDIS sensitivity in order to reduce uncertainties arising from cloud movement and low signal strength in the UV. However, the resulting sensitivity is still uncertain for wavelengths shorter than 320 nm.

One possibility to quantify the difference between the two instruments is achieved by the integration of the measured spectral sky radiance over the hemisphere, which yields the spectral diffuse downward actinic irradiance (Seckmeyer et al 2010). Before integrating the spectral sky radiance, we remove faulty MUDIS measurements resulting from four broken fibres, oversaturation in the circumsolar region and measurements with high stray light (>20 counts at 285 nm). The remaining points are interpolated to a 5° grid using kriging interpolation (Isaaks and Srivastava 1989). The calculation of the spectral actinic irradiance F_DIFF(λ) is performed after Kylling et al (2003):

$$\begin{equation} F_{{\rm DIFF}} (\lambda ) = \int_0^{2\pi } {\int_0^{\pi /2} {L(\lambda ,\theta ,\phi )} } \sin\theta \, {\rm d}\theta \,{\rm d}\phi , \end{equation} \tag{ 1 }$$

where λ is the wavelength, θ the polar angle (90° zenith angle), ϕ the azimuth angle and L(λ, θ, ϕ) the spectral sky radiance.

Figure 4 shows the ratio of the spectral actinic irradiances measured with MUDIS and SCCD on 21 October (cloudless) and 25 October (overcast) 2012 at around 11 UTC. In order to remove fluctuations due to remaining differences in instrument bandwidth and wavelength shifts, a 10 nm median filter is applied. During cloudless sky, the ratio is decreasing from 1.04 to 1.00 in the wavelength range from 320 to 500 nm and increasing up to 1.02 from 500 to 600 nm. For overcast sky, the ratio is increasing from 0.96 to 1.00 from 320 to 600 nm. Based on this spectral comparison 320 and 500 nm are considered to be representative for the UV and VIS performance of MUDIS and therefore are used for the following temporal and spatial comparisons.

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The variation of the actinic irradiance ratios at 320 and 500 nm during a cloudless time period on 21 October and an overcast time period on 25 October is shown in figure 5. Measurements of spectral actinic irradiance smaller than 10 mW m^-2 nm^-1, which occur at sunrise and sunset, are not taken into account. The actinic irradiance measurements of MUDIS and SCCD show a deviation of 6% during cloudless sky and 8% during overcast sky. The ratios of the actinic irradiance measurements are higher at 320 nm compared to 500 nm under cloudless sky and, in contrast, lower at 320 nm compared to 500 nm for overcast sky. We assume that this behaviour is linked to the applied intercalibration method. A transmission change of the entrance optics can be excluded, since the effect occurs in the morning of 21 October as well. During this time, it was cloudy at first and the sky cleared up after 09:30 UTC. Broken clouds occurring on 25 October from 12:00 to 16:00 UTC lead to higher deviations of up to 12% caused by the differences in FOV of the instrument and acquisition time.

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In figure 6, the MUDIS and SCCD sky radiance measurements performed at noon under a cloudless sky are shown for two representative wavelengths (320 and 500 nm) as a function of zenith and azimuth angle as polar plots (further denoted as sky maps). The black dots in the SCCD sky map represent the measuring pattern. In the MUDIS sky maps, the difference of MUDIS to SCCD sky radiance measurements is given in per cent. The 23 missing numbers of the pattern are measurement points that have been removed due to broken fibres (4 points), high stray light (12 points) and oversaturation in the circumsolar region (7 points). At 500 nm, sky radiance measured near the zenith with MUDIS is lower compared to the SCCD, which seems to be a systematic difference for dark blue regions of the sky.

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Figure 7 shows the spectral sky radiance distribution of a sky covered with stratocumulus clouds at 320 and 500 nm measured with MUDIS and SCCD at noon time analogous to figure 6. Clouds lead to a higher spatial and temporal variation of sky radiance compared to cloudless sky. Due to the absence of direct sunlight, no points had to be removed due to oversaturation and stray light, leaving four points removed due to broken fibres. Despite the different FOVs and acquisition times, the measured sky radiance as a function of zenith and azimuth angle of both instruments agrees well.

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Histograms of MUDIS/SCCD sky radiance ratios at 320 and 500 nm of the cloudless time period on 21 October (09:30–16:00 UTC) and during overcast sky on 25 October (06:00–14:00 UTC) are shown in figure 8. MUDIS data points that are compromised by broken fibres, affected by high stray light, oversaturated in the circumsolar region or measured spectral radiance of less than 5 mW m⁻² nm⁻¹sr⁻¹ are removed from the dataset. Measurements performed at 84° zenith angle are partly obscured by obstacles like trees, thus leading to high deviations due to the different instrument FOVs. These points and outliers greater than four times the standard deviation (4σ) are also removed from the dataset. The bias between MUDIS and SCCD radiance under cloudless sky on 21 October is 1.7% with a 1σ standard deviation of 6.1% at 320 nm and −4.4% with a 1σ standard deviation of 8.7% at 500 nm. The 500 nm ratios show a minor maximum at 0.9 which is connected to low values of MUDIS measuring regions of dark blue sky as shown in figure 6. For overcast sky on 25 October the difference is −4.7% with a 1σ standard deviation of 9.9% at 320 nm and −1.6% with a 1σ standard deviation of 6.7% at 500 nm.

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An example of the rapid change of the spectral sky radiance with time is shown in figure 9. Two MUDIS sky captures performed at 11:04 and 11:16 UTC are plotted. It is the same time period in which the SCCD sky scan discussed in figure 8 was performed. Sky radiance at 500 nm increases in this time period by up to 103% while the actinic irradiance increased by up to 41%. Such rapid changes demonstrate the advantage of the MUDIS instrument, which is capable of measuring the spectral sky radiance as a function of zenith and azimuth angle within seconds, rather than in minutes, compared to CCD array-based scanning instruments.

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