Stochastic Modeling for Velocity of Climate Change

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. Supplementary materials accompanying this paper appear on-line.

Duke Scholars

Author Alan E. Gelfand Statistical Science

Author James S. Clark Environmental Sciences and Policy