  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.
