Flotech has a guide on their site for sizing fountain pumps, which mentions :
Step Two - Look for the maximum head height rating
This is how high (vertically) the pump can lift the water. Water pumped to its maximum height by a given pump doesn't necessarily mean the flow will be very strong at that maximum height. In fact, it might be only a trickle. Therefore, choose a pump whose maximum height is higher than the height at which the water emerges from your fountain feature to ensure a strong stream of water. A discharge flow reducer (valve) can be used to adjust the flow to your needs.
The flow rate is inversely related to how high you're attempting to lift the water -- so you'll end up with the rated GPH (gallons per hour) when there's almost no lift (I think they measure it at 1' lift, typically), and nothing at the full height rating. If you lift for 3/4 of the max height, you'll get around 1/4 of the max flow.
But that still doesn't mean that you need to go out and get some $200+ pump ... You just have to lift it in two stages, which you can do with a bucket, some rope, tubing, and two pumps rated for around 8' of lift:
- Place a submersible pump in a bucket, and run the pump's hose to the area you want watered.
- Take a second piece of tubing, and attach it (without crushing it) onto the side of the bucket (exiting inside the bucket)
- Hang the bucket about mid-way between your balcony height and the ground level.
- Connect the piece of tubing attached to the bucket to the second pump, and lower it into the rain barrel.
- Turn on both pumps.
The main thing that I'd be concerned with is that you'd have to make a hole in the rain barrel such that you could put in the pump ... which means the possibilities for mosquitos to come in to breed. You may need to treat the barrel with a larvacide, or find a way so that you can secure a screen over the hole that you'll be using.