# Spectral invariant behavior of zenith radiance around cloud edges observed by ARM SWS

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2 merged sounding product) converts the observation time of 300 s into 900 m with a cloud diameter of roughly 360 m. Cloud top height was found at 2.1 km by lidar and radar, so the cloud was only 100 m thick. Four total sky images taken 30 s apart starting from 156 s indicate that the cloud moves toward the northeast. 3. Linear Mixture Hypothesis [9] Let t 0 be the time corresponding to the cloud edge. We choose t 0 = 150 s for our example (see Figure 1). Let t T denote the time of definitely clear observations: t T ¼ t 0 þ T: ð2þ Figure 1. (top) Time-wavelength color contour plot of ARM Short-Wave Spectrometer (SWS) spectra measured from 21:35:24 to 21:40:24 UTC on 18 May 2007 at ARM SGP site in Oklahoma. SZA = 45 [see Chiu et al., 2009]. SWS-observed zenith radiances have been normalized by cos(sza) and by the extraterrestrial solar spectrum (see equation (1)). (bottom) Four total-sky images taken at 21:38:00 (156 s), and 21:38:30 (186 s), 21:39:00 (216 s) and 21:39:30 (246 s) during the time when the small cloud at zenith was moving from inside to outside the field of view of the SWS. Panferov et al., 2001]. Finally, we discuss how spectral invariant characteristics can be used to study the transition zone. We will call T the length of the transition zone between cloudy and cloud-free regions, which we take as T = 100 s in our analysis. With a wind speed of 3 m/s, T corresponds to a 300 m spatial segment. Figure 2 illustrates the normalized zenith radiance spectrum plotted at 10 s time intervals from t 0 = 150 s to t T = 250 s. [10] Now we are ready to state our hypothesis, namely: spectra in the transition zone, such as those in Figure 2, are a linear combination of cloudy (time t 0 ) and clear sky (time t T ) spectra with a wavelength-independent weight a(t), It; ð lþ ¼ at ðþit ð 0 ; lþþ½1 at ðþšit ð T ; lþ; t 2 ðt 0 ; t T Þ; at ðþ2ð0; 1Þ; ð3þ where a(t) is a monotonically decreasing function with a(t 0 ) = 1 and a(t T )=0. [11] Dividing equation (3) by clear sky spectral radiance, I(t T,l), results in the following relationship between the transition-zone and cloudy sky observations: 2. A Case Study [7] We use the ARM SWS measurements of zenith radiance I m (t, l) at 1-s temporal resolution and 8 nm visible and 12 nm near-infrared spectral resolution. First, we normalize the SWS measurements to an extraterrestrial solar spectrum: It; ð lþ It ð T ; lþ ¼ at ðþit ð 0; lþ It ð T ; lþ þ bt ðþ; bt ðþ¼1 at ðþ: t 2 ð t 0; t T Þ; at ðþ2ð0; 1Þ; ð4þ It; ð l Þ ¼ pi mðt; lþ m 0 F TOA ðlþ ; ð1þ where m 0 is the cosine of solar zenith angle (SZA) and F TOA (l) is the solar irradiance at the top of the atmosphere. We will focus here on one case fully described by Chiu et al. [2009]. Other cases that we examined showed a similar behavior. [8] Figure 1 shows a 300 s segment of normalized spectral zenith radiances measured by SWS on 18 May 2007 at the ARM SGP site. The vertical axis shows wavelength from 350 to 2170 nm. Strong water vapor absorption bands are seen at wavelengths of 930, 1120, 1400, and 1900 nm. Based on the color palette, we can roughly identify the first 60 s as clear followed by 120 s of cloudy and then by 120 s of clear. The wind speed of 3 m/s at cloud-base height of 2.0 km (derived from the ARM Figure 2. Normalized SWS zenith radiance spectrum measured on 18 May 2007 from t 0 = 150 s (cloudy) to t T = 250 s (clear) with 10 s time interval. Same case as Figure 1. 2of5

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