I am running Invest carbon model. I understand the units of the carbon pools provided in the intermediate .tiff files are Mg C /pixel (which might explain the mismatch with the input carbon data which is given in MgC/ha). Is it possible to get the carbon stored in each LULC class (apart from the carbon stored in each pool)?
Yes, the model converts from Mg C/ha to Mg C/pixel. The model does not output the carbon total for each LULC class, but it should be easy to do as a post-processing step in your GIS software. For example, in QGIS you can use the Raster Calculator tool to create a layer which only has carbon values for pixels with a given LULC code, and all others are set to 0:
"tot_c_cur@1" * ("lulc_current_willamette@1" = 95) for a LULC code of 95.
Then you can take the sum, average, etc. of that raster using something like the Raster Layer Statistics tool in QGIS. I hope that helps!