Can the model predict the thickness of the forecast snowfall?

At the weather station, when it snows, the condition (thickness) of the snow cover and the mass of water from the melted snow that has fallen into the rain gauge are measured. Thus, the increase in snow cover and the amount of precipitation in millimetres in terms of the thickness of the layer of water formed from this precipitation is measured.
The numerical model determines the phase state of the precipitation (snow, snow with rain, rain), but does not give the thickness (increment) of the snow cover, which it could do when it is only snowing. The reason is that the density of freshly fallen snow varies widely: from 10 kg/m3 to 150, or even, up to 170 kg/m3, according to meteorological literature.
The amount of precipitation, regardless of the phase state, is given by the model in kg/m2 and when it is only snowing, the user would like to know how many centimetres of this snow have fallen. This relationship can only be estimated.