Now r₀ is the density of saturated water vapour, h is a relative humidity, R is a gas constant. And this expression was again given by Mayhew and Rogers which related the r₀ to temperature.
So what we assume, that r₀ is only function of the temperature, and relative humidity is only a function of q₀. So, by substituting that, we can calculate the gradient of r_v and we get this equation.