An earth-sized planet has been cut in half along a meridian by higher beings. The gravity is experienced the same as if the other half was still there. Let's say there's a big magic wall that prevents any matter from spilling into the missing half. This wall would hold back wind and water from flowing all the way around.
How would the climate be different as a result of the change in wind circulation?
Currently the Earth's water and air follow paths where they move in long, slow circular currents. While these currents are not very fast. They carry incredible amounts of mass and help regulate the temperatures of various parts of the world. They also help maintain a sort of tidal equilibrium making sure than any water that leaves one place already has water flowing in to replace it.
So, should they be suddenly disrupted they would create a massive tidal shift with the Oceans accumulating on the West side of the cut and tides dropping dramatically in the East since the water would crash into the barrier with suddenly nowhere "forward" to move but all the momentum of the water moving in that direction is preserved. This tidal shift will likely ripple back and forth across the hemisphere until the tides and currents can find a new equilibrium, but it could result in a pattern of tsunamis that batter all of the world's coastal regions for what would likely be a matter of years. During this time, rivers and bays will also have issues flowing upstream causing flooding and then completely empty out.
Disrupting these currents will also cause dramatic changes in the temperatures of water because you will interrupt the flow of water and air in the north/south directions. This will cause massive die-offs of marine life, but terrestrial life will be less affected as we tend to already be more resistant to rapid changes of temperature. Marine life will be further effected as many freshwater sources will be infringed on by salt water and vice versa.
Depending on how "clean" the cut is, the very act of slicing and separating the world would likely be the biggest hazard of all. The global earthquakes it would cause would break the Richter scale. Compared to the Earth, humans are small. We are very very small. So anything energetic enough to slice it in half will be very very big compared to us. The reverberations caused by the slice itself will likely level cities and topple mountains.
Given enough time for all the bad stuff to settle out thought, new oceans currents will eventually form and the environment should return to a fairly stable condition. The cut lines would just act similar to how the currents currently interact with a land mass.
Coriolis pushes weather systems around the globe and away from the equator, with continued rotation, gravity, air density, etc... this will try to continue, but now the wind flow goes halfway and then hits a wall. This will set up a very powerful new wind system along the wall moving away from the equator at the western edge and flooding back directly from the poles along the eastern edge. Hadley Cell circulation will be overridden by these winds over at least a quarter of the remaining hemisphere. I expect it would be more like only the equatorial cells would survive and only over about half the remaining length of the equator.
The western boundary winds are going to bring tropical moisture to any and all land areas along that margin, creating extensive high rainfall biomes. The air coming from the poles along the other edge will be cold and dry extending tundra and desert along that edge, possibly as far south as the equator.
The effect this would have on ocean currents is probably going to be truly catastrophic, and completely unsurvivable, but that is a question and answer for another day.
