From Proxy to Temperature
Tree rings do not directly record temperature — they record growth, which is influenced by temperature among other factors. The bridge between ring width and temperature is the transfer function: a statistical model calibrated during the period when both tree-ring and instrumental data overlap (typically 1850-present). If ring-width index correlates strongly with summer temperature during calibration, we assume this relationship held in the past.
The Transfer Function
The simplest transfer function is linear regression: T = β₀ + β₁ × RWI, where β₀ is the intercept and β₁ is the slope. The explained variance R² quantifies how much temperature variation the ring-width index captures. For temperature-sensitive treeline conifers, R² values of 0.4-0.7 are typical. More complex approaches use principal components of multi-site networks.
Verification & Skill
A reconstruction is only as good as its verification. The reduction of error (RE) statistic compares reconstruction accuracy against the naive prediction of using the calibration-period mean. RE > 0 indicates skill. The coefficient of efficiency (CE) uses the verification-period mean and is a stricter test. Both must be positive for the reconstruction to be considered reliable.
Uncertainty & the Divergence Problem
Every reconstruction carries uncertainty from measurement error, calibration statistics, and the assumption of temporal stability in the growth-climate relationship. The 'divergence problem' — where some northern hemisphere trees stopped tracking temperature after ~1960, possibly due to pollution or threshold responses — challenges this assumption and remains actively debated in paleoclimatology.