I took a series of sunrise photos. Once the sun actually came above the horizon, the brighter the sun became the more apparent and brighter a green flare (glare?) appeared. How can I avoid that?
Notice the green flare to the left of the sun...
tl; dr. Blend a "panorama" from only slightly rotated exposures and make sure no flare is included in the final result.
It's not possible to optically remove this type of flare when shooting into the sun (though different lenses have different levels of flare resistance). However, there are other effective ways to get rid of it.
What you can do is take multiple exposures, with the camera slightly rotated between them. When you rotate the camera just a bit, the flare usually moves to an entirely different part of the picture. Then you can align the exposures on a computer and blend them together, as if you were making a panorama. Finally, make sure that only flare-free parts of each image are being used for the final result.
This technique can be very effective in creating a flare-free image, but there are caveats. It works well only if there are no objects in the picture close to the camera. Otherwise you'll get relative displacements in the image due to parallax. To minimize this, find the no-parallax point of your lens and try to rotate around it. If the subjects of your photo are not too close, this can work relatively well, even if taking photos handheld.
(I mixed up the top and bottom--the flare is on the bottom one--but I don't want to recreate the figure now.)
I have done three things in the past to deal with this.
Use lens hoods, paper, or your hand to block the light that is causing the flare. This works when the flare is coming from the side.
Focus on your subject, then point the camera away from your subject to reduce the flare, then crop the picture later to locate the subject where you originally wanted. I would have tried that for the scene in your example. Position the sun way off to the side, take a "bigger" picture than what you wanted, and crop.
Lens flare happens when light internally reflects within the lens itself. There are a few possible sources of internal reflection. You could get it from using a non-digital lens on a digital camera and getting reflection off the sensor (doesn't seem like the case here), you could get it off a filter placed on the front of the lens (light tends to bounce around between the front element and the filter) or, if the lens is dirty enough, it could be bouncing around off dirt or grime on the lens itself.
That said, as Henk rightfully pointed out, you do still have the possibility of internal reflections regardless. Often more expensive lenses may be less likely to have that problem, but that also doesn't always hold true.
Some lenses are more prone to this, those with a bulbous front element will flare easier and are more difficult to control. Some photographers that shoot a lot of sun/sunbursts buy lenses specifically for this purpose. The Canon 16-35mm f2.8 L II for example is known for well controlled flare and a beautiful sun star shape due to coating and the shape/number of aperture blades. Some people are reporting the new Canon 16-35 f4 IS is even better. Positively remove all filters when shooting the sun not only will the flare be more intense but it will also be unsightly. A lens hood may help too.
You really can't. It's unfortunately unavoidable given the construction of lenses, which have several elements. The light bounces around between the elements.
Lens flare is always somewhere between a possibility and a likelihood when the sun or some other bright light is included in the frame. It can be reduced by avoiding filters, keeping everything clean and using a lens that flares less but the only way to avoid it is to keep the bright light source out of the frame.
The best sunrise and sunset pictures are almost always the ones where the sun is just below the horizon. Even aside from flare, shooting with the sun above the horizon turns the area of the sky around the sun into an ugly whited-out blob. The huge dynamic range caused by including the sun in the frame produces all sorts of exposure problems: you're more or less forced to either over-expose the sky or under-expose the land. The colour of the sky is always more vibrant and impressive when the sun's below the horizon.