How to convert the units of specific cloud liquid water from ERA5 (kg/kg) to kg/m2?

Question

I am trying to initialize my model with the cloud liquid water data from ERA5. My model IITM-ESM which evolved from CFSv2 takes in the cloud liquid water information in $\small\mathsf{kg/m^2}$. However the ERA5 specific cloud liquid water data is in kg/kg. I have the following questions

1. Am I right in trying to derive cloud liquid water in $\small\mathsf{kg/m^2}$ for specific cloud liquid water in kg/kg
2. How do I go about this ? I found a way to convert kg/kg cloud liquid water content to $\small\mathsf{g/m^3}$ in the link https://www.nwpsaf.eu/site/download/documentation/rtm/docs_rttov12/rttov_gas_cloud_aerosol_units.pdf After getting the cloud liquid water in $\small\mathsf{g/m^3}$, will multiplying by layer thickness (data is 3D with lat, lon, levels and the level information is in pressure levels i.e. Pascals) and $\small\mathsf{10^{-3}}$ be okay to convert it to $\small\mathsf{kg/m^2}$

Answer 1

I got the solution https://www.researchgate.net/post/How_to_convert_the_units_of_specific_cloud_liquid_water_from_ERA5_kg_kg_to_kg_m2

and

https://www.nwpsaf.eu/site/download/documentation/rtm/docs_rttov12/rttov_gas_cloud_aerosol_units.pdf

In the above link the conversions between $\small\mathsf{kg/kg}$ , $\small\mathsf{g/m^3}$ , $\small\mathsf{kg/m^2}$ can be explicitly derived

EDIT The summary of the first hyperlink is:

$\small\mathsf{kg/kg}$ stands usually for kg liquid water per kg air. Multiplying the term with the calculated air density within the field will result into $\small\mathsf{kg/m^3}$, which means kg liquid water per $\small\mathsf{m^3}$ air. Then you have to multiply with the thickness of the liquid cloud, which will result into $\small\mathsf{kg/m^2}$."