The high-contrast imaging technique is meant to provide insight into those planets orbiting several astronomical units from their host star. Space missions such as WFIRST, HabEx, and LUVOIR will measure reflected light spectra of cold gaseous and rocky planets. To interpret these observations we introduce ExoReL$^Re$ (Exoplanetary Reflected Light Retrieval), a novel Bayesian retrieval framework to retrieve cloud properties and atmospheric structures from exoplanetary reflected light spectra. As a unique feature, it assumes a vertically non-uniform volume mixing ratio profile of water and ammonia, and use it to construct cloud densities. In this way, clouds and molecular mixture ratios are consistent. We apply ExoReL$^Re$ on three test cases: two exoplanets ($upsilon$ And e and 47 Uma b) and Jupiter. We show that we are able to retrieve the concentration of methane in the atmosphere, and estimate the position of clouds when the S/N of the spectrum is higher than 15, in line with previous works. Moreover, we described the ability of our model of giving a chemical identity to clouds, and we discussed whether or not we can observe this difference in the planetary reflection spectrum. Finally, we demonstrate how it could be possible to retrieve molecular concentrations (water and ammonia in this work) below the clouds by linking the non-uniform volume mixing ratio profile to the cloud presence. This will help to constrain the concentration of water and ammonia unseen in direct measurements.
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