Rotational modulations of emission spectra in brown dwarf and exoplanet atmospheres show that clouds are often distributed non-uniformly in these ultracool atmospheres. The spatial heterogeneity in cloud distribution demonstrates the impact of atmospheric dynamics on cloud formation and evolution. In this study, we update the Hubble Space Telescope (HST) time-series data analysis of the previously reported rotational modulations of WISEP J004701+680352 -- an unusually red late-L brown dwarf with a spectrum similar to that of the directly imaged planet HR8799e. We construct a self-consistent spatially heterogeneous cloud model to explain the Hubble Space Telescope and the Spitzer time-series observations, as well as the time-averaged spectra of WISE0047. In the heterogeneous cloud model, a cloud thickness variation of around one pressure scale height explains the wavelength dependence in the HST near-IR spectral variability. By including disequilibrium CO/$CH_4$ chemistry, our models also reproduce the redder $J-K_{rm s}$ color of WISE0047 compared to that of field brown dwarfs. We discuss the impact of vertical cloud structure on atmospheric profile and estimate the minimum eddy diffusivity coefficient for other objects with redder colors. Our data analysis and forward modeling results demonstrate that time-series spectrophotometry with a broad wavelength coverage is a powerful tool for constraining heterogeneous atmospheric structure.
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