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Outdoors you can either choose to fight the natural lighting or supplement it.
If you place a group with back to the sun, get up on a ladder so their faces are up into the skylight, and expose at ISO 100 @ f/5.6 @ 1/100th you would find you had a very nice butterfly lighting pattern on the front of the faces which are normally exposed (Shady 5.6). The only problem would be the camera sensor couldn't handle the contrast with the exposure biased for the shady side an the sunny highlights would be blown.
If you took the same set-up and simply changed the exposure to ISO 100 @ f/16 @ 1/100th (Sunny 16) the natural skylight will still be creating the same flattering pattern on the faces. The change in exposure will keep the sunny highlights from clipping, but the faces, while well lit pattern-wise will be underexposed.
Next take the same set-up exposed for "Sunny 16" ambient and add flash. Put the flash up on a 12' stand directly behind your camera which because you are shooting from a ladder is up around 8' off the ground. So your flash will be about 4' above the camera and hitting the faces centered but at a 45° downward angle. The goal here is to match the angle of the flash with the 45° angle of the skylight that is already modeling the faces.
You'll need to change the exposure settings due to sync speed limit of the camera to 1/250th which will necessitate an aperture of around f/11 to keep the sunny parts below clipping. I just use the camera clipping warning in an ambient only shot to gauge the exposure.
SInce the raised flash is acting as modeling "key" light its power level needs to be based on the exposure of the highlights it creates on the faces OVER THE NATURAL PATTERN FROM THE SKYLIGHT. The skylight has two components, the brighter downward vector from the sky above and the 360° wrap around fill effect. What you will be doing with the raised flash is adding a second flash KEY light over the naturally soft key vector.
In terms of what is lighting the face any modifier you add to your flash, which is at the same angle as the skylight modeling the face in this scenario is a bit like taping a pistol to the barrel of a canon. The net effect of huge sky SB and smaller flash modifier is similar in cause and effect to the footprint of an umbrella which is more direct in the center where the umbrella shape is flatter and closer to the light source in the middle. The significant difference in the physics of the natural light vs. the flash will be the rate of the fall off front > back on foreground vs. background.
What you will notice in the flash assisted shot vs. the first hypothetical open shade 5.6 shot is the lighting on the faces has a higher ratio in the flash shot and the background will be darker (as dark as the Sunny 16) ambient shot. If you were to compare the three shots — ambient exposed for shady side, ambient exposed for sunny side, and ambient + flash exposed for facial highlights — you will find that the shadows on the face in the ambient + flash shot are as dark as in the Sunny 16 shot without flash. The reason is simple. No flash is reaching those shadows.
The thing to grasp here is that the flash is key light, not "fill flash" in this scenario. It is creating a highlight pattern on the faces and front of the bodies. The shadows the flash doesn't reach will remain dark and under filled by the skylight. But that's one of the reasons to use the centered butterfly pattern, vs placing the flash off to one side or the other. Butterfly winds up highlighting nearly the entire front of the face and bodies. There are very few shadows seen by the camera, except for places like under the chin or where the body of one person is shading the flash and natural skylight from another.
The decision at that point is a subjective one. Are the dark skylight only filled shadows objectionable or not? If not then you can get away with only using one flash outdoors. But if you want lighter shadows, or simply to have the option of adjusting them as necessary that's when you'd want to consider adding a second fill flash around chin level down below the ladder you are standing on.
In terms of keeping the equipment logistics simple, if you use a ladder for the elevated POV for the camera to get the faces up into the skylight (avoiding brow shaded eyes) you can attach the fill light directly to the ladder via a Super Clamp or baby pin attached to one of the legs. You could also attach the stand holding the overhead key light to the ladder giving you only one thing to worry about blowing over in the wind — the ladder with attached lights. An alternative to hauling sandbags is to use a corkscrew dog anchor or stakes and ropes to hold the ladder /stands to the ground.
With respect to modifier size in that scenario until you get very large the modifier will have very little effect if any on the shadows because the fill for the shadows is coming from the sky with single flash and near the camera axis and nearly shadowless in the two flash / chin level fill scenario. The difference you will see in the lighting if modifier size is increased is the specularity of the highlights. That's as much a function of skin of the subjects as the modifier. If the skin is damp or oily even a large modifier will create hot spots. Bigger is better, but how big is best in any situation is a compromise between results and logisitics — not only hauling the gear on site, but keeping it from blowing over in the wind.
The advantage of the above approach were the skylight does most of the work is that you should find with experimentation you can get by with smaller modifiers. The smaller modifiers may create specularity in the highlights but so does natural lighting outdoors. What makes those highlights look "fake" or not is where they wind up on the cheekbones and other parts of the face. The highlights from the raised "key" flash in the butterfly scenario wind up in the same place as the natural skylight highlights so they will seem more natural. More problematical in terms of aesthetics is the catchlights created by any chin level fill that is added.
While it might seem counter intuitive a smaller the fill source can work better for portraits, if you accept the fact that the secondary catchlights will require retouching. What is easier to retouch, the reflection of a point source fill light or a huge SB? That's why some outdoor portrait shooters use bare bulb flash for fill. It's a given that any fill source near the axis will create a secondary catchlight and the bare bulb makes it very easy to retouch away as part of the overall editing process. I use my 22" Buff dish as my fill source most of the time in the studio for that reason. I stumbled across that idea by accident when comparing the dish with a SB in a test. I switched the two as key / fill and found that the dish created a wide footprint with a very small easy to remove second catchlight in the middle of the pupil.