The first way paleocimatologists study the earth’s past climates is by pollen. Pollen is sometimes trapped in lakes and bogs preserving it for many years. So when the scientist’s exstract the pollen they can see what type of plant it comes from. For example if they got the pollen from a silk tree they would know that that previous climate was a warmer one. Because silk trees need warm weather to grow. Then they count the number of pollen grains from different plants in each layer. To then make a chart that can give the approximate climate of that time period.
The first thing a paleocimatologist does is they detect the annual layers of snow. The way they do that is by looking at the changes in dust content. After they figure out what time period the section is from paleocimatologists look at bubbles of air trapped in the ice, which contain samples of the atmosphere from that time period. Paleocimatologists observe the oxygen in the ice\water molecules. Most of the oxygen atoms are in two forms called isotopes the two different isotopes are 18o and 16o which stand for 18-oxygen and 16-oxygen. The proportions of these two are really similar but different 18o is slightly heavier than 16o. The proportions of these two isotopes depend on the average temperatures. Snow that falls during warmer climates cause a greater proportion of 18o and snow that is fallen during colder climates causes a smaller proportion of 18o.
Also they use the amount of carbon dioxide trapped inside the air bubble so the more carbon dioxide the warmer the climate was back during that time period
Sand size shells from single celled animal called foraminifera build up on the bottom of the ocean. So when it is a cold climate the foraminifera spiral one direction. But during warmer climates the foraminifera spiral the opposite direction.
Also the foraminifera contain calcium carbonate which has oxygen isotopes in it.