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I'm trying to figure out a realistic mechanism to explain a global drought that only lasts for about a decade. Assume an earth-like planet.

My goal for this drought is not to have no rain and kill off everything, but create a significant food shortage because of crop failure. Assume farming technology around 1600s proficiency.

My best explanation currently is that there was a period of increased solar activity. During, say, northern hemisphere summers, this led to excessive heat and no rain, whereas the perspiration is being carried to the southern hemisphere where there's lots of rain in their winter, but it's too warm for snow and they get no snowpack.

Would something like that work?

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Your scenario could work. Increasing solar activity will make some areas drier but it will also make other places receive more precipitations because hot air means more evaporation and more precipitation. A lot of places including Europe, will receive more precipitation but it will be more concentrated. More rain but less rainy days = more flooding and more drought but it's probably not intense enough for your question.

Based on climate projections, we can expect that increasing the temperatures will reduce the precipitations in several regions including: North Africa, Spain, US/Mexico border, Iran and other places. The changes in Argentina could be pretty severe in the south as the country could become a desert.

This phenomenon is explained by the intensification of the Hadley cell. It's the name of the air circulation movement located roughly between the equator and the tropics. The hot air rises over the equator, moves toward the tropics and eventually get sucked back to sea level. At this point, (it's called the subtropical ridge) the air has lost all humidity. Thus, this is why we have most deserts near the tropics.

Increasing the temperature will increase the strength of the cell and will push the dryness toward the poles making the Mediterranean sea and other places at the same latitudes drier.

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