Developing a Spatial Model to Examine Rainfall Extremes in Colorado's Front Range

Between 9-16 September 2013, northeast Colorado received some of its most extreme precipitation. The event affected 6 major rivers and their tributaries and 14 counties, breaking observed records for all accumulations from sub-daily through to annual total. NOAA's precipitation atlases indicated that this event had an anticipated return period of 1000 years. But how statistically robust is this estimate given the data scarcity and observation record length? And how should decision makers account for this event when rebuilding within the flood damaged area.

We employ daily precipitation observations, with at least 30 years of data, from stations across the Front Range of the Rocky Mountains to develop a spatial statistical model for annual maximum daily precipitation. Our aim is to have an easily-implemented statistical approach which borrows strength across locations via a spatial model. We use a spatial hierarchical model and employ a two-stage approach for inference. In the first inference stage we obtain individual Generalized Extreme Value (GEV) parameter estimates at each station, and the associated uncertainty covariance matrices; the second stage applies Bayesian methods to determine the true parameter estimates, and the residual spatial dependence. Finally, universal kriging allows us to interpolate spatially and estimate the GEV parameters at unobserved locations. A further development of the model makes use of the climate space, rather than geographical space, to improve the parameter estimates (Cooley et al. 2007).

We then use this statistical model to examine the relative influence of a single anomalous extreme (September 2013) on return period estimates for daily precipitation extremes at Boulder and other locations along the Front Range and the consequences that this sensitivity could have on engineered structures lying within the floodplain.

Cooley, D., Nychka, D., & Naveau, P. (2007). Bayesian Spatial Modeling of Extreme Precipitation Return Levels. Journal of the American Statistical Association, 102(479), 824–840. doi:10.1198/016214506000000780