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Land mobile satellite (LMS) channels at the L (1/2 GHz) and S (2/4 GHz) frequency bands are mainly affected by propagation effects due to the local environment of a mobile terminal, such as multipath, shadowing, and blockage. Future systems for mobile satellite services (MSS) will operate at higher frequency bands, such as Ku (12/14 GHz) and Ka (20/30 GHz), where the tropospheric propagation effects also play an important role. Experimental campaigns conducted so far for Ku/Ka-band LMS channels have not considered any possible correlation between the tropospheric and local environment propagation effects. However, recent experimental work has indicated that these fading effects are not independent. As a first analytical approach to this open problem, a novel statistical analysis is presented in this paper. Emphasis is put on Ku/Ka-band LMS channels whose fading events can be modeled by the Ricean distribution with a relatively high K-factor. A novel analytical relationship between the Ricean K-factor and the rain attenuation effects is derived, and based on them, an analytical statistical prediction model for the distribution of the Ricean K-factor is derived. Particular attention is paid to the rainfall spatial inhomogeneity, as well as to the different effects of the climatic area of interest (temperate versus tropical) on the Ricean K-factor statistics. Thus, the presented analysis considers both spatially correlated bivariate lognormal and gamma statistics for the accurate characterization of rain attenuation. The proposed models are flexible and incorporate the impact of several critical operational, climatic, and geometrical parameters of an LMS channel on its multipath behavior under rainfall conditions. Useful numerical results are provided, specific future planned work is outlined, and the need for further experimental verification data is also pointed out.