How global temperatures and CO₂ levels are determined.

Ice core data.

• 110,000 year record from Greenland in several locations and other locations in Antartica which agree.
  
• Hoarfrost layers can be used to count years.
• Hydrogen peroxide levels are higher in years that have more sunlight.
• Electrical conductivity varies according to acidity.
• Seasonal chemical changes affect acidity.
• Vocanic debris affects acidity.
• Borehole temperature varies. A warm climate sends a warm pulse into the ice from the top. These pulses remain as temperature variations in the ice and can be measured.
• Aerosols found in ice layers vary. Warm climate means more open water which yields more ocean spray and a larger proportion of aerosols in the ice.
• Isotopes found in ice layers vary. Atmospheric temperatures affect the relative abundance of various isotopes in ice, liquid and vapor phases.
  
• Heavier isotopes of oxygen (O₁₈ to O₁₆ ratio) indicate warmer temperatures (more evaporation of water and more winds, hence higher heavy isotope levels).
  
• Heavier H isotopes (deuterium) in water also indicate warmer temperatures.
  
• N₁₄ and N₁₅ ratios depend on the difference in temperature between the surface and the trapped nitrogen at the time the nitrogen was trapped. 
• More beryllium-10 (created in the upper atmosphere by cosmic rays) indicates more cosmic rays reaching the earth hence either weaker magnetic fields or more active (and possibly hotter) sun.
• Increased levels of trapped methane indicates a warmer climate.
• Trapped CO₂ can be measured directly.
  

Ocean sediment core data (varved sediment).

• Two main data sources are available one based on chemical analysis ther other on analysis of mircorfossil species.
  
• Surface sea temperatures affect the ratio of di- to tri- saturated alkenones in top feeding algae. The sediment layers record these variations which match ice core data in locations where sedimentation is heavy (so that there is enough detail).
• Isotopes vary.
• C₁₄ and thorium -230/uranimum -234 can be used to date layers.
• Heavier isotopes of oxygen (O₁₈ to O₁₆ ratio) found in shells of surface dwelling plankton indicate warmer temperatures (more evaporation of water and more winds, hence higher heavy isotope levels).
• Heavy metal uptake in corals is temperature influenced. Warmer temperatures mean faster growth which means larger amounts of strontium, uranium and magnesium in calcium compounds.
  
• Oxygen depletion (indicating slower ocean currents and hence a cooler climate) can be statistically determined by relative abundance of organisms adapted to low oxygen conditions.
• Marine bacteria adapted to low oxygen conditions preferentially use N₁₄. Changes in the N₁₅/N₁₄ ratio map ocean floor oxygen levels and therefore ocean circulation.
  
• Marine sediments show pollen grain variations which indicate climate changes (the ratio of cold adapted plant pollent to warm addapted plant pollen indicate seasonal variation in temperature).
  
• Ice from glaciers and polar ice caps has debris embedded on the underside. If there is an increase in ice break up due to a warmer climate the ice carries more debris into the ocean which shows up in ocean sediment layers. These can be measured in the sediment by measuring magnetic susceptibility.
  

Other data.

• Tree rings (living an petrified) corroborate (at least for the past few thousand years) temperature variation data coming from ice core and ocean sediment core samples.