Regarding surround microphone arrays which will be most appropriate for recording nature ambiences, consider setups such as IRT-Cross or ORTF-surround. These setups work well, are easy to understand and are compact enough to fit under an umbrella. They use 4 cardioids or supercardioids to form 4 channel 360 degree extensions of the common near-spaced 2-channel stereo microphone techniques DIN and ORTF, which are familiar to stereo recordists. In that way, they are similar extensions from 2 to 4 channels as Dual-M/S is a 360 degree extension of standard 2-channel Mid/Side or X/Y.
Since these setups introduce some spacing between microphones, the difference in surround playback listening experience is somewhat similar to that of switching from a 2-channel stereo coincident microphone configuration to a near-spaced one. But I find it a bit more compelling than that actually. Coincident techniques such as M/S and X/Y record only level difference information between channels. By introducing some spacing between the mics you'll also record time/phase difference information in addition to level difference information. That time/phase information helps create a much more enveloping "you are there" type playback experience which to me is the most compelling and fundamentally important aspect of surround playback. Coincident surround recordings can correctly portray individual sounds in the correct directions, sometimes a bit more precisely when listening from the sweet spot, but they do not convey that same sense of being fully surrounded and immersed within the recorded environment. Spaced techniques tend to create a much larger playback "sweet zone" rather than a tightly confined "sweet spot" and allow for free movement of the listener within that playback zone without the virtual space and imaging collapsing to the nearest speaker.
IRT-cross is four cardioids arranged in a cross formation. It's easy to setup with four mics forming a cross with a right angle between each 'leg'. Another way of thinking of it is two DIN arrays (DIN = a pair cardioids spaced 12" and angled 90 degrees apart) placed back-to-back. It's commonly used for surround ambience because although it's larger than a compact Dual-M/S array, it's still relatively compact and quite portable. It won't fit within one zeppelin, but you can simply use a good windscreen on each mic like the Shure A81WS which is popular around here, maybe with individual furry windscreens for really windy conditions.
ORTF-surround is somewhat similar to two standard ORTF stereo setups placed back to back (standard ORTF is two cardioids spaced 17cm and angled 110 degrees apart). In the case of ORTF-surround, supercardioids spaced 20cm and angled 120 degrees apart are specified. Two of those are placed back-to-back so that the second pair is 10cm behind the first and the angle between the adjacent microphones of each pair is 80 degrees. You could use regular cardioids instead of supercardioids with some adjustment to the spacing/angle between mics. You could probably do the same using a pair of cardioids and a pair of supercardioids. Schoeps promotes ORTF-surround for sports and location ambiences, and it can fit within a large custom (and probably expensive) zepplin.
Here's a link to the Schoeps webpage covering all these surround recording options-
http://www.schoeps.de/en/products/categories/menue-surround. Also on that page is information on OCT-surround which uses still more spacing between the microphones. Variations on OCT have become my prefered techniques for recording music in surround. But those arrays are larger, usually more complex to setup, and although they also record 360 degree surround sound, they favor one particular direction over the others, which makes them more appropriate for recording music. If interested, here's a link to a thread on the evolution of my techniques for surround music recording-
http://taperssection.com/index.php?topic=96009.msg1279052#msg1279052 The OCT varients are towards the latter end of the thread. For years I was primarily using four omnis spaced about a meter apart, which also records nature ambiences quite well.