Five megatons of black carbon enter the atmosphere immediately. Black carbon comes from burned stuff and it absorbs heat from the sun before it can reach the Earth. Some black carbon does eventually falls back to Earth in rain.
After one year, the average surface temperature of the Earth falls by 1.1 kelvin, or about two degrees Fahrenheit. After five years, the Earth is, on average, three degrees colder than it used to be. Twenty years on, our home planet warms again to about one degree cooler than the average before the nuclear war.
Earth's falling temperatures reduces the amount of rain the planet receives. Year five after the war, Earth will have 9 percent less rain than usual. Year 26 after the war, Earth gets 4.5 percent less rain than before the war.
In years 2-6 after the war, the frost-free growing season for crops is shortened by 10 to 40 days, depending on the region.
Chemical reactions in the atmosphere eat away Earth's ozone layer, which protects Earth's inhabitants from ultraviolet radiation. In the five years after the war, the ozone is 20 to 25 percent thinner, on average. Ten years on, the ozone layer has recovered so that it's now 8 percent thinner.
In a separate study, published in 2013, International Physicians for the Prevention of Nuclear War estimated 2 billion people would starve in the wake of a 100-A-bomb war.