For the die hard atheists that don't know what to think, the theory is simple enough, our brains take in everything regardless of whether our conscious mind knowledges it. When you sleep you take all the events that are stored into your memory and from those events, your brain tries to anticipate what will happen next, sometimes a dream is just well a dream, sometimes they are similar to a real event, and sometime, although rare, actually happen word for word, detail by detail. Everything we do now effects tomorrow and our brain when we can't drown it out will connect the dots and get and idea of what is to happen.
The other possible theory which can go hand in hand is that we are 3 dimensional entities but we exist all the way to the 6th dimension. The relationship of our energy in this location of space along the fourth dimension to other spaces in the fourth dimension can communicate and travel in either direction (we are talking about energy, which is believed to be able to jump to anywhere in 6 dimensions) although our conscious minds are alway moving in one direction along the line, we exist in a long string across the fourth as well. There is a possibility that ourselves in both future and past can communicate through wormhole that allow energy to move to any location on the fourth dimension, which in simple terms would allow us to get a glimpse of what will happen in the future.
As for the earthquakes and tsunamis, its how animals can detect danger, such as earthquakes, it has been suggested that the changes in the earth's magnetic field changes shortly before events like earthquake and solar flare and that change effects our brains, again being able to anticipate that events will take place based on those changes.
I have said the same thing about ghosts to. Notice how there have been no solid pictures or videos of full apparition like people see. As a studying Electrical Engineer, magnetic fields in high amounts can cause aural, visual and sensory hallucinations and interference/noise by electronics. Electronics pickup exactly what they see, but our brains try to find familiar shapes out of unfamiliar things. That is why you can see faces in grains of wood or in clouds/smoke and hear voices when you feel like someone is watching you in a creepy place. This can be caused by being near an area with poor electrical work and in areas where the ground is high in iron.