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One of the more frequent problems I see in outdoor portraits taken under tress or on grass is an overall green bias to the photo which the person who took it didn't see when shooting or when editing on their perfectly calibrated monitor.
The problem isn't one of color management but of color perception by the brain of the photographer. A white shirt and face above are perceived as "normal" (i.e. neutral WB) in most lighting because our brains knowing the face and the fact the shirt is white adapt color perception to "normalize" it. So unless the photographer is experienced enough to know the light bouncing off foliage makes the light green they will not see it in person or in the playback of the camera. The image in the playback will have a green cast if the camera is set for Daylight WB, but the photographer's eyes already adjusted to the greenish ambient will see the playback image as perfectly neutral and not detect any problem.
Back on the computer when opening the file in the RAW editor the metadata in the RAW file will display it from the same "Daylight" baseline used at capture. The image will have an overall green bias on the calibrated screen. But the brain of the photographer will calibrate to what is seen on screen the same way as when shooting and his brain will tell him it looks neutral, but the lighting is dimensionally flat (lack of 3D modeling) on the subject.
The lighting looks "flat" like and overcast day because of how + green affects the skin tone which is dominant in the red channel in an RGB image. The net effect what looks like a gray veil over skin. Any red clothing will also look abnormally desaturated. But at the same time the +green bias will make all the green foliage even more vibrant than typically seen by eye. All that green around the face can further skew the color perception of the viewer and make it difficult to objectively judge the skin tone. It's not a color management / hardware problem it's a "meatware" problem.
When the color cast like that in an outdoor image will be noticed is when the face and white shirt are finally compared it with other photos which do have R=G=B neutrals and skin tones without the color cast. That's one of the quirks of human color perception. It adapts perception to whatever lighting is on known reference lighting and can't detect color casts, but even minor differences can be detected by direct comparison.
That situation illustrates why a gray card reference and Custom WB are helpful in a color workflow, even one that is perfectly color managed. The gray card allows the photographer to see, by comparison if there is a color cast in an image.
If the photographer had the subject hold the gray card in a test shot he still wouldn't see the color cast on the card in the playback because his color perception adapted to the + green light. But if when back at the computer his first action is to open the file with the card and click it with the white balance eyedropper that will cause the image to shift to neutral as the file values are adjusted to the degree needed to make the card R=G=B. In addition to changing the color of the image knowing how a gray card works also shifts what the photographer trusts as the "baseline" for when the color is accurate. Toggling between the SOOC version and the adjusted one the photographer will be able to see how much the SOOC capture deviated from the Daylight capture baseline. The adjusted version will look neutral and the SOOC green BY COMPARISON.
One of the workflow advantages of RAW is being able to copy adjustments made in one file to other files taken in the same lighting. So after correcting the file with the gray card, first by "snapping" it to a technically neutral evaluation baseline then tweeking to taste from there, the adjustments can be copy / based to the metadata of all the other files. It's a huge time saver.
Setting Custom WB before capture eliminates the need to click correct and copy/paste the settings when editing. The gray card, which would be in the test shot anyway for click correcting, is used to change the camera WB baseline.
Outdoors and indoors I set the camera WB to "Daylight" as a starting baseline before shooting the gray card to set Custom WB. That might seem odd when shooting in tungsten or fluorescent light indoors but by comparison with a shot of gray card target after setting Custom WB I can toggle back to the first shot and visualize how the ambient light deviates from the Daylight baseline. For example under trees in green bias light the before/after comparison in the playback would look like this because my brain would trust the second Custom WB frame as being neutral:
Here's a caveat regarding using flash under trees. The color temp of bare flash is about 500 K higher than Daylight. So in a Daylight WB shot anything filled with the flash looks cooler (+blue) compared to Daylight ambient. Under trees where the ambient is green and the camera is set to Daylight the flash lit highlights will look +blue and the shadows the flash doesn't hit look +green. It's a perceptual muddle and impossible to correct without separate masked color correction adjustment layers for what the ambient flash hits.
Performing Custom WB on the ambient as described above will eliminate the +green cast in the ambient shadows. But that shifts the overall balance of the camera +magenta so relative to that new baseline the flash will appear +magenta +blue in the highlights the flash creates over the ambient. It creates an even worse mixed lighting nightmare.
To get ambient neutral and flashed balanced to the new baseline would require adding green gell to the flash to match the ambient color cast. But it's difficult to judge how much green to add by eye because the eyes will be adapted to the green light. So all things considered the better solution is not to use flash when shooting under trees creating a green color cast. Instead set Custom WB to make the ambient neutral, then use reflectors to bounce light instead of flash. Or alternately, don't shoot portraits under trees if you can avoid it.
Some might be thinking, "Won't AWB solve most of those problems?" Only if the AWB is able to analyze the content in the scene accurately. Also because AWB evaluates and sets each shot individually based on content there will be no consistent baseline over all the files making it impossible to batch correct. AWB also doesn't work very well with mixed lighting conditions and flash.
All things considered I find using the gray card reference in a test shot with Custom WB the easiest overall.
Just shooting the card without setting Custom WB produces the same results after click correcting the card shot but requires the extra copy/paste step of the corrections in the other files and doesn't provide the on site before/after comparison of the card shot that helps me visualize where there is a color cast in the ambient. If I set Custom WB and see there is a green cast in the lighting I'll move location to where there isn't one.
In situations when I can't even get a card in a test shot I put the camera on the nearest pre-set: Daylight, Tungsten, Fluorescent to keep the capture WB the same in all files. Then I find a file with neutral content, use it instead of the gray card to click correct, then copy it's settings in to the other files in the same light. If some shots are in sun and others in shade the sunny shots usually look OK with Daylight WB and I only need to batch correct the shaded shots in the cooler skylight.
If I'm editing a file and not sure whether or not my perception of color is being skewed by the colors on the screen I've been staring at I'll create a 128.128.128 square on a new layer then toggle it on and off. The comparison of that known neutral square re-calibrates my brain and allows it to more objectively see the color on neutral objects and skin tones in the file on the calibrated monitor.
You may already do some or all of these things in your capture > edit RAW workflow. If not you might want to get a gray card try them. You need a card rather than over lens WB tool so you can also put it in the test shot as a visual reference. There's no need to spent a lot on a gray card. The current version of the Kodak R-27 card is made in collaboration with X-Rite and is Munsel 18% neutral gray cost under $16 and includes an 8 x 10 big enough for setting Custom WB and a 4x5 for use as an in-shot reference.
Also helpful as a reference is a MacBeth color checker. I use one on the target I have portrait subject hold after setting WB on the plain card:
My goal in using the target isn't to match it perfectly, it is simply a way to more easily see what the selective color adjustments are actually doing when I try different styles or move the sliders. If the neutrals are neutral SOOC with Custom WB you don't want to change skin with temperature or tint because that will also shift the neutrals. The screen shot shows the Camera Calibration tab in ACR. That where selective color correction can be made via style selection and sliders to tweek the color of a skin tone without changing the neutrals in the clothing.
You should find if you start with Custom WB in the camera when you want "normal" neutral WB you'll need to make very few color adjustments to correct for color biases like the under the trees green light situation. You'll also become more aware of when there are problems like that and avoid them.