the past 1000 years). Fossil leaves Paleoclimatologists often use leaf teeth to reconstruct mean annual temperature in past climates, and they use leaf size as a proxy for mean annual precipitation. In the case of mean annual precipitation reconstructions, some researchers believe taphonomic processes cause smaller leaves to be overrepresented in the fossil record, which can bias reconstructions. However, recent research suggests that the leaf fossil record may not be significantly biased toward small leaves. New approaches retrieve data such as content of past atmospheres from fossil leaf stomata and isotope composition, measuring cellular CO2 concentrations. A 2014 study was able to use the carbon-13 isotope ratios to estimate the CO2 amounts of the past 400 million years, the findings hint at a higher climate sensitivity to CO2 concentrations. Boreholes Borehole temperatures are used as temperature proxies. Since heat transfer through the ground is slow, temperature measurements at a series of different depths down the borehole, adjusted for the effect of rising heat from inside the Earth, can be "inverted" (a mathematical formula to solve matrix equations) to produce a non-unique series of surface temperature values. The solution is "non-unique" because there are multiple possible surface temperature reconstructions that can produce the same borehole temperature profile. In addition, due to physical limitations, the reconstructions are inevitably "smeared", and become more smeared further back in time. When reconstructing temperatures around 1500 AD, boreholes have a temporal resolution of a few centuries. At the start of the 20th century, their resolution is a few decades; hence they do not provide a useful check on the instrumental temperature record. However, they are broadly comparable. These confirmations have given paleoclimatologists the confidence that they can measure the temperature of 500 years ago. This is concluded by a depth scale of about to measure the temperatures from 100 years ago and to measure the temperatures from 1,000 years ago. Boreholes have a great advantage over many other proxies in that no calibration is required: they are actual temperatures. However, they record surface temperature not the near-surface temperature (1.5 meter) used for most "surface" weather observations. These can differ substantially under extreme conditions or when there is surface snow. In practice the effect on borehole temperature is believed to be generally small. A second source of error is contamination of the well by groundwater may affect the temperatures, since the water "carries" more modern temperatures with