With the increasing number of directly imaged giant exoplanets, the current atmosphere models are often not capable of fully explaining the spectra and luminosity of the sources. A particularly challenging component of the atmosphere models is the formation and properties of condensate cloud layers, which fundamentally impact the energetics, opacity, and evolution of the planets. Here we present a suite of techniques that can be used to estimate the level of rotational modulations these planets may show. We propose that the time-resolved observations of such periodic photometric and spectroscopic variations of extrasolar planets due to their rotation can be used as a powerful tool to probe the heterogeneity of their optical surfaces. In this paper, we develop simulations to explore the capabilities of current and next-generation ground- and space-based instruments for this technique. We address and discuss the following questions: (1) what planet properties can be deduced from the light curve and/or spectra, and in particular can we determine rotation periods, spot coverage, spot colors, and spot spectra?; (2) what is the optimal configuration of instrument/wavelength/temporal sampling required for these measurements?; and (3) can principal component analysis be used to invert the light curve and deduce the surface map of the planet? Our simulations describe the expected spectral differences between homogeneous (clear or cloudy) and patchy atmospheres, outline the significance of the dominant absorption features of H2O, CH4, and CO, and provide a method to distinguish these two types of atmospheres. Assuming surfaces with and without clouds for most currently imaged planets the current models predict the largest variations in the J band. Simulated photometry from current and future instruments is used to estimate the level of detectable photometric variations. We conclude that future instruments will be able to recover not only the rotation periods, cloud cover, cloud colors, and spectra but even cloud evolution. We also show that a longitudinal map of the planet's atmosphere can be deduced from its disk-integrated light curves.
methods: analytical - planetary systems - planets and satellites: atmospheres - planets and satellites: composition - techniques: photometric - techniques: spectroscopic