Abstract
Abstract. This paper addresses the statistics underlying cloudy sky radiative transfer (RT) by inspection of the distribution of the path lengths of solar photons. Recent studies indicate that this approach is promising, since it might reveal characteristics about the diffusion process underlying atmospheric radiative transfer (Pfeilsticker, 1999). Moreover, it uses an observable that is directly related to the atmospheric absorption and, therefore, of climatic relevance. However, these studies are based largely on the accuracy of the measurement of the photon path length distribution (PPD). This paper presents a refined analysis method based on high resolution spectroscopy of the oxygen A-band. The method is validated by Monte Carlo simulation atmospheric spectra. Additionally, a new method to measure the effective optical thickness of cloud layers, based on fitting the measured differential transmissions with a 1-dimensional (discrete ordinate) RT model, is presented. These methods are applied to measurements conducted during the cloud radar inter-comparison campaign CLARE’98, which supplied detailed cloud structure information, required for the further analysis. For some exemplary cases, measured path length distributions and optical thicknesses are presented and backed by detailed RT model calculations. For all cases, reasonable PPDs can be retrieved and the effects of the vertical cloud structure are found. The inferred cloud optical thicknesses are in agreement with liquid water path measurements. Key words. Meteorology and atmospheric dynamics (radiative processes; instruments and techniques)
Highlights
Introduction1990; Wild et al, 1995, 1996, and others). Despite its important role for the terrestrial climate, the amount of SW radiation absorbed in the clear and cloudy atmosphere is still poorly understood
The deposition of the solar shortwave (SW) radiation is the driving force of many atmospheric processes, such as atmospheric dynamics or photochemistry
The present paper explores in more detail possibility (b) by presenting joint cloudy sky photon path length distribution and cloud optical thickness measurements, cloud structure data, and model calculations
Summary
1990; Wild et al, 1995, 1996, and others). Despite its important role for the terrestrial climate, the amount of SW radiation absorbed in the clear and cloudy atmosphere is still poorly understood. Real atmospheres do not fulfill this assumption, while theoretically they are more likely to support scattering statistics with individual step size distributions which allow for more frequent extreme step sizes This lack of theoretical correctness in classical cloudy sky RT modelling led Davis and Marshak. The probability that a photon has travelled a total path length l is given by the probability density function (PDF) of the geometrical path lengths p(l) (short PPD) This distribution is only valid in absence of absorption, i.e. for the scattering processes only. It is a consequence of the exponential form of Beer’s law that T (α) is the Laplace transform of the PPD This relationship implies that the explicitly unmeasurable path length distribution can be derived by measuring the transmissions for different absorption strengths and inverting the Laplace transformation. This approximation introduces a systematic error, but its approximated validity can be tested by a Monte Carlo simulation of the photon paths in a non-isotropic atmosphere (see Sect. 4)
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