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

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 $$\small\mathsf{kg/m^2}$$

and

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
$$\small\mathsf{kg/kg}$$ 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 $$\small\mathsf{kg/m^2}$$."