Why and how did climate change affect the Mayan civilization?

Is climate change a "modern problem"?

No. Climate change is far from a modern problem, although some of what follows is disputed and is also simplified. The Late Antiquity Little Ice Age from around 536 to 660 AD is one example of climate change. An article in Nature Geoscience argues that, in Europe and Asia, this

coincides with rising and falling civilizations, pandemics, human migration and political turmoil

This was followed by the Medieval Warm Period (circa 950 to 1250) and then the Little Ice Age which lasted until around 1850. During the height of the Little Ice Age

...The Baltic Sea froze over, as did most of the rivers in Europe. Winters were bitterly cold and prolonged, reducing the growing season by several weeks. These conditions led to widespread crop failure, famine, and in some regions population decline.

Climate change and Maya civilization

The role played by climate change in the collapse of Maya civilization is a very complex issue and there is no overall consensus as to the extent of that role. However, droughts are generally believed to have played an important role at certain points. Further, these droughts may have been worsened by human activity - deforestation.

The article The Role of Climate in the Collapse of the Maya Civilization: A Bibliometric Analysis of the Scientific Discourse (pdf) looks at 433 research papers from between 1923 and 2016 and shows there is disagreement between paleoclimatologists on the one hand and archeologists on the other:

climate change seems to be a major factor for the downfall, and this is what the paleoclimatic methods (i.e., the analysis and dating of paleoclimatic records) illustrate.

However, many Maya archeologists still argue that the mega-drought theory doesn’t fit their findings, mainly due to the complexity of the process and inconsistencies between the water supplies of different centers and the timing of their collapse....For many archeologists, the collapse of the Maya civilization is not a resolved issue

Source, originally from Hodell, et al, 1995 Reconstruction of Caribbean climate change over the past 10,500 years.

This abstract of the article Impacts of Climate Change on the Collapse of Lowland Maya Civilization broadly reflects the views of both sides, conceding that droughts caused by climate change cannot wholly explain the collapse of Maya civilization. At the same time, though, droughts did contribute to the collapse and also hindered later recovery.

Comparison with recent archaeological evidence...indicates an earlier beginning for complex economic and political processes that led to the disintegration of states in the southern region of the Maya lowlands that precedes major droughts. Nonetheless, drought clearly contributed to the unusual severity of the Classic Maya collapse, and helped to inhibit the type of recovery seen in earlier periods of Maya prehistory. In the drier northern Maya Lowlands, a later political collapse at ca. 1000 ce appears to be related to ongoing extreme drought.

This NASA article points to deforestation as being a possible contributory factor to worsening (natural) droughts:

...Mayan activities may have deepened the dry conditions. In an effort to sustain one of the highest population densities in history, the Mayans transformed the land. They removed nearly all of the forest and replaced it with agricultural crops.

Although population density figures are disputed, it is generally accepted that they were high (see some of the links below). Thus, while current concerns about climate relate primarily to human activity, we cannot rule out the possibility that, even over a thousand years ago, human activity also affected the environment, albeit on a much smaller scale. Clearly, further research is required to establish a clearer picture as to the role that climate, and the effects of human activity on the environment, played in the decline of Maya civilization.

Note: Thanks to Marzipanherz for his comment.

In addition to the links above, you may find these articles to be of further interest:

Drought and the Ancient Maya Civilization. This article also has several links resources "related to drought and the collapse of the Mayan civilization".

Severity of drought during the Maya collapse (2018)

Why Did the Mayan Civilization Collapse? A New Study Points to Deforestation and Climate Change (Smithsonian Magazine)

Calculating Late Classic Lowland Maya Population for the Upper Belize River Area (pdf)

Cities of the ancient Maya