I am not a smart person, but I do like performing a bit of science

Perhaps use make use of the QTouch feature of the AVR ?

Embedded World 2015: QTouch-Based Water Level Sensing
https://www.youtube.com/watch?v=MY33xg83gnM

Humidifiers are awesome! : ) 

The one I have works like Dave mentions, i.e. it only blows cold air through a material that wicks up water from the bottom, i.e. it's ok to run it dry. If your model doesn't have a wick material (the wick is usually replaceable to prevent using mouldy ones) then it could be using a different mechanism, but I'm not very knowledgeable on other methods.

Parts are getting hard to find, but if you can find a humidity sensor, that would be a good addition just attached to the side of the unit, since the amount of humidity will be easily picked up by the sensor (hopefully!), just for observing your room status and the impact of the humidifier. 

Regarding adding a bottle, that's a good idea (some mechanism may be needed to stop the water if the reservoir is full, the one I have uses mechanical means, like a float I think (not sure).

Tap water is quite conductive.

cstanton said:

I couldn't wait for looking up too much detail or ordering parts from an online store.

Guys, I think this is the key line: what can be done with what is to hand rather than buying sensors or such.  Obviously, we don't know what Chris has to hand but I'm assuming for this experiment, little more than resistors, capacitors, wires, battery, Arduino and the like.  I guess it's ok to assume standard household stuff as well: perhaps a cork, paperclip(!), plastic milk bottle cap, wire coat hanger etc.  Simple stuff.  It's an interesting problem.  So suggestions that don't require logging on to a parts store!

"....detect how much water is left" is a different proposition to "...is it about to get empty" as it implies either steady readings as the water level drops, or an indication of the water level at pre-specified points, e.g. 3/4, 1/2, 1/4, 1/8 full.

I suppose it will take a mechanical engineer to solve this :-)

Make a capacitor by twisting about 600mm of 26 AWG insulated wire together for use as the sensor.  Or whatever small diameter wire is at hand.  A hand drill works great for this.

Now coil it around something like a pencil to the right length so that it will all fit into the reservoir.

If you have an LCR meter it can be tested before setting up the Arduino.  Here the capacitance is shown to be 61pF with the sensor out of the water.

Sticking the sensor into the water results in a measured capacitance of 123 pF.  Note that the end of the sensor needs to either be insulated or turned up so as to be kept dry as shown here.

Recall that in an RC Low Pass Filter the time constant is given by Tc = R x C.  Using that relationship and the ability of the Arduino to measure voltage and time a simple Capacitance Meter can be created as described here: https://www.arduino.cc/en/Tutorial/Foundations/CapacitanceMeter

The Arduino code in the link above was modified by substituting micros() for millis() in the time measurement and the use of a 10M Ohm resistor since the DIY sensor has small capacitance and charges up fast.  The output to the serial monitor is shown below as the coil is inserted and removed from the water.

I didn't change the print statement so it says nanoFarads instead of picoFarads.  Note that it varies from 134 to 224 dry to wet which is more than what the LCR meter showed.  But it shows a clear and easily measured difference between dry and wet that could be calibrated.  Here it is plotted.

For those that require video, here you go:

1321.IMG_7301.MOV

This is the first thing that came to mind using the criteria that Andrew set out.  I've not tested repeatability or drift.  Another thing that might be done is just measure the temperature out as compared to the environment.  If it is cooler then presumably there is water evaporating and cooling the air if humidity is low enough. 

Nice one Frank.  Even as I wrote my last post I started wondering if the water would make a useful dielectric and if so could we take a capacitance measurement.  Clever.

That is a nice succinct description of how it works 

Also should mention (you probably already know, but to me it was non-intuitive initially) that you'll want to enable the humidity feature a bit intermittently once it starts getting hotter, to control it to a lower value (whereas originally I thought higher humidity as the temperature rises was better). Meaning, if you ordinarily like (say) 60% RH, then you might want it set to (say) 40% RH once the weather is hot, to keep the dew point value from going high, if we assume dew point to be a good indicator of personal comfort.

I've never understood why typical home temperature/humidity sensors often don't display the dew point, whereas they have all the information to compute that. 

The Mijia modules are pretty good (think I've mentioned them in the past), they use a nice Sensirion chip internally, and they are BLE-enabled, so a Pi etc can read off the temperature and humidity, compute the dew point and alert if it is out of the desired range.

beacon_dave said:

Some of the evaporative ones just blow air through a wicking filter or use ultrasonics or an impeller to create a mist that gets blown out by the fan.

Yes I believe this is closer to how it works

Dang, no stock there. Must keep searching.