Multifractal modelling of liquid water clouds : cloud spatial structure and its effect on the solar radiation field

At any point in time a significant fraction of the globe is covered by liquid water clouds. Understanding the relationship between cloud and solar radiation is therefore of great importance for both climate modelling and remote sensing. Previous studies have found that cloud spatial structure has a significant effect on cloud albedo, with spatial inhomogeneities leading to less reflection of solar radiation than was predicted by the traditional homogeneous cloud model. This thesis investigates further the consequences of cloud spatial variability on atmospheric radiation, with the aim of developing methods to improve radiation modelling and remote sensing of cloud properties. The basis of this study is the quantification of the scaling and intermittency of liquid water fields using a multifractal model. The fractionally integrated flux (FIF) model is used to both describe and numerically simulate cloud fields, with model parameters being determined from aircraft measurements made during 98 flights over northern Tasmania, Australia. The aircraft data set is divided into three broad cloud types: stratocumulus, altostratus and low level cumulus. The horizontal fluctuations in all three cloud types are shown not only to be scale invariant and non-stationary, but also to have very similar statistics with only one out of three model parameters varying significantly between cloud types. Clouds with horizontal structure described by the FIF model but constant vertical profiles are then used in Monte Carlo radiative transfer calculations. The differences between the multifractal and homogeneous cloud results are larger than those previously reported for marine stratocumulus, due to the larger degree of inhomogeneity in the cloud types considered. The results of the Monte Carlo simulations are used to derive the \effective optical properties\" of the multifractal cloud fields defined as the optical properties of a homogeneous cloud producing the same radiative transfer results as the multifractal cloud. This allows the well-known and efficient radiative transfer techniques for homogeneous cloud to be applied to multifractal cloud. The effective optical properties were found to vary with the spatial scale under consideration and an empirical parameterisation for the effective optical properties is presented that is a function of spatial scale mean cloud optical depth and single-scattering albedo. The range of conditions under which the effective optical depth approximation can be used is then examined with vertical fluctuations in cloud liquid water radiance changes with viewing angle and differing single-scattering properties all considered. The approximation is found to be reasonable for most low-level cloud conditions with the greatest discrepancies occurring for absorbing clouds with vertical fluctuations and significant vertical extent. Finally the effective optical depth parameterisation is tested in the satellite remote sensing of cloud liquid water path with the results being compared to simultaneous aircraft measurements. The agreement between the data sets is significantly improved when the results are corrected for cloud inhomogeneity using the effective optical depth approximation with the remaining errors being shown to be of the level expected due to the discrepancies in measurement scales. These (root-mean-square) errors due to the mismatch of measurement scales when comparing satellite-based and in situ measurements are estimated using the spatial statistics of liquid water to be approximately 27%."