Can the weight of clouds and fog be calculated? When looking up at cumulus clouds I often wonder how much?

Question

water they contain. Surely knowing the visibility in fog would help determine its density and therefore water content, right?

Answer 1

Yes this value can easily be estimated. Actually it is the temperature and to a lesser degree the pressure that would be the most important factors in estimating the amount of water contained in a cloud or fog bank. It would be an estimate but would be reasonably close.

Radars do not estimate precipitable water. The precipitable water values are calculated from the radiosonde sounding data (weather balloons) and from forecast sounding data from the mathematical models.

Radars do estimate the amount of rainfall by algorithms using reflective data from the radars over each point after each volume scan. These estimate have proven very valuable in short term forecasting of flooding events. But since most of the precipitable water values are in the form of water vapor or the amount of water in a column of air, it has to be calculated only from something that can either measure humidity or dew point values. Radar can not do that since water vapor is transparent to radio waves.

Answer 2

It is possible to compute the quantity of liquid water in a cloud. Modern radar can give an assessment of the volume of precipitable water. Water that doesn't fall as rain , although it adds to the volume of water in the cloud, is not significant to people on the ground.