How does the temperature and humidity of air affect the water consumption of a humidifier?

We can model the water consumption $dot{m}_{w}$ of a simple humidifier using the following equations:

begin{align}
eta_{hum} & = {T_{db,i} – T_{db,o} over T_{db,i} – T_{wb,i}}
h_{o} & = h_{i}
dot{m}_{w} & = dot{m}_{a}(w_{o} – w_{i})
end{align}

where the subscripts $i$ and $o$ denote the entrance and exit of the humidifier respectively, $eta_{hum}$ is the efficiency of the humidifier, $T_{db}$ and $T_{wb}$ are the dry and wet bulb temperatures of the air respectively, $h$ and $w$ are the enthalpy and humidity ratio of the air respectively, and $dot{m}_{w}$ and $dot{m}_{a}$ are the mass flow rate of the water and air respectively.

We can fix $eta_{hum}$, $dot{m}_{a}$, and the atmospheric air pressure to study just the effects of the temperature and humidity of the entering air on the water consumption.

I created this psychometric chart with four different air conditions to see if I could pinpoint one thermodynamic property of the entering air that would be responsible for the water consumption, but the story seems to be a bit more complicated than that. The relative humidity $phi$ appears to be the property with the highest correlation with water consumption, but higher relative humidities don’t always result in lower water consumptions.

What is the full story?