Man, there is a LOT of info out there regarding this topic but NONE of the ones that I found actually described an easy way to do it

..I've never done that effect before, so I might make this
one of my near-future video tutorials here at SM

My first gut response is if you have Maya 5, (might be in 4.5 too.. not sure)
there is the Height Feild utility.

Check the docs for correct usage, but this node was designed to "displace" ocean geometry for waves with the ocean shader with fluids, and it has a great built-in feature of letting you use images and image sequences as the rgb displacement value.

So, my idea is that you could attach this utility to your particles,
and attach your 2d "depth" image sequence to the color of the field node, and then attach the outAlpha and/or outRGB (whichever works... just use what the docs say hehe..)
of that to the input of the heightField node and then simply adjust the displacement magnitude via the heightFields' attribute ed.


Here are a few other things to try from folks around the web:

Klaus Stangl at www.worldofmaya.com wrote one of the only ParticleDisplacement melscripts that I know of, so it might be worth it to check out his site, as his documentation is hard to understand at first read, it makes sense in the end. hehe.. Nice guy tho!

Also at the Actro Media Agency, the have written a Maya PLUGIN that does this as well with pre-rendered .iff files as your heightField map.
The demo only supports a still image, while the full version ($395.00 US) supports image sequences.. BUMMER
Here is the link to that anyway: https://www.actro.com/ama_technology_pkg_i2u.php

Some guy named "Slooper" on the Highend list had this idea:
First of all, you have to animate your Sandstorm (e.g. for tests it will be sufficend to use a moving curve emitter, emitting upwards with some gravity (you will need really lot of particles). After that render a depth map of your object (be carefully with your camera clipping plane! This NEEDS to be exact) Put that as displacement map on a lambert-shader for the particles (don´t use Projection map) with enough bump value. That´s all. The rest is up to you, for getting a good look.

And if nothing else works for you, you could always make some geomtery and displace it with your 2D image maps.
Get it to look right for the degree of displacement, position, etc.
Then emit from that, but turn off the primary visibility of the emitting geometry, so you only see it's shape in the particles.
Sometimes it helps to emit in the negative direction, i.e. inward if the source object is a face.

Good luck! ..and if you find a way hat works, let me know, and I'll credit you in the tutorial!