Abstract
The velocity of climate change is defined as an instantaneous rate of change needed to maintain a constant climate. It is developed as the ratio of the temporal gradient of climate change over the spatial gradient of climate change. Ecologically, understanding these rates of climate change is critical since the range limits of plants and animals are changing in response to climate change. Additionally, species respond differently to changes in climate due to varying tolerances and adaptability. A fully stochastic hierarchical model is proposed that incorporates the inherent relationship between climate, time, and space. Space-time processes are employed to capture the spatial correlation in both the climate variable and the rate of change in climate over time. Directional derivative processes yield spatial and temporal gradients and, thus, the resulting velocities for a climate variable. The gradients and velocities can be obtained at any location in any direction and any time. In fact, maximum gradients and their directions can be obtained, hence minimum velocities. Explicit parametric forms for the directional derivative processes provide full inference on the gradients and velocities including estimates of uncertainty. The model is applied to annual average temperature across the eastern United States for the years 1963– 2012. Maps of the spatial and temporal gradients are produced as well as velocities of temperature change.
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Acknowledgments
The research of the authors was supported in part by NSF-EF-1137364. The authors thank Kai Zhu for help in obtaining PRISM annual average temperature data and Bailey Fosdick for insightful conversations in developing the MCMC sampling algorithms.
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Appendix
Appendix
(left) Observed elevation surface and (right) posterior mean elevation surface indicating that the model is capturing the main features of elevation across the large spatial region. Again, our goal is not to estimate “true” elevation but rather to create a differentiable surface for elevation to improve the estimation of the spatial gradients of temperature.
The upper and lower bounds of the middle 95 % of residuals by year where the residuals are computed as the observed minus the posterior mean of temperature conditional on the random effects. The model appears to underestimate annual average temperature in the years 1990, 1998, and 2012. In general, however, there does not appear to be a trend in over or under prediction through time indicating that the model adequately captures the variability in annual average temperature.
The percent of under predictions of annual average temperature for each location. Dark red (blue) locations indicate that the model tends to under (over) predict annual average temperature. Regions with the most consistent under and over prediction are predominantly in regions with highly variable elevation.
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Schliep, E.M., Gelfand, A.E. & Clark, J.S. Stochastic Modeling for Velocity of Climate Change. JABES 20, 323–342 (2015). https://doi.org/10.1007/s13253-015-0210-9
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DOI: https://doi.org/10.1007/s13253-015-0210-9