The most pronounced association between climate change and migration involves the Sahel region of Africa (go here.) Now there is some evidence from Central America.
It has to do with drier weather adversely affecting those areas of Central America with a traditional dependence on agriculture for household income. The regions most affected by drier climate and out migration were southeastern and eastern Honduras, and most of El Salvador. There is not a complete and tight association between dryness and migration; however, the match overall is pretty good.
The Economist wrote: Using border-apprehension data from 2012 to 2018, researchers from the universities of Texas and Utah show that more people journey north when there is drier-than-usual weather during a growing season
Researchers found data on temperature and rainfall for Central American countries. By mapping the two they saw how drier-than-normal weather during growing seasons predicted emigration. Areas suffering from a particularly arid growing season saw 1.7 times more people travel to the United States than those with typical weather.
The impact of climate change on livelihoods is particularly acute in the Northern Triangle because large shares of the population are dependent on farming. According to data from the ILO, , 37% of Hondurans, 32% of Guatemalans and 30% of Salvadoreans of working age laboured in agriculture in 2012. Many other jobs also depend on the sector. Although by 2019 the share of people working in agriculture had fallen in all three countries, this drop is unlikely to cause migration to fall, since extreme weather events are becoming more common.