A hierarchical threshold modeling approach for understanding phenological responses to climate change: when did North American lilacs start to bloom earlier?

Prior to the recent upward climb, global average temperatures were relatively stable. This trend was described by Mann et al. [23] using a hockey-stick model consisting of two line segments (with the x-axis as time and temperature as the y-axis) meeting at a single changepoint. The line segment prior to the changepoint is flat (indicating a stable temperature), and the line after the changepoint has a positive slope (indicating increasing temperatures). Because the long-term average temperature change is a defining characteristic of climate change, researchers have shown that changes in many phenological variables over time can also be described by a hockey-stick model. For phenological variables, the changepoint and the slope of the line after the changepoint represent the timing of the onset and the effect of climate change. However, large annual variation often obscures the pattern when analyzed using data from a single location, whereas regional differences due to spatial variability of climate and weather patterns render pooling data from different locations impractical. We demonstrate that the Bayesian hierarchical modeling approach is effective in separating these two sources of variability by partially pooling data from multiple sites. Using the North American lilac first bloom dates, we show that the Bayesian approach can adequately separate the temporal and spatial variations, thereby quantify site-specific patterns of change as well as national/regional average trends. Our analysis, using the Bayesian hierarchical hockey-stick model, showed that the effects of climate change started as early as the 1970s and the lilacs in North America have been blooming on average one day earlier every three years since.