Statistics and Its Interface

Volume 5 (2012)

Number 2

Dynamical random-set modeling of concentrated precipitation in North America

Pages: 169 – 181



Renato Assunção (Departmento de Ciência da Computação, Universidade Federal de Minas Gerais Belo Horizonte, Minas Gerais, Brazil)

Noel Cressie (Department of Statistics, The Ohio State University, Columbus, Ohio, U.S.A.)

Scott H. Holan (Department of Statistics, University of Missouri, Columbia, Mo., U.S.A.)

Michael Levine (Department of Statistics, Purdue University, West Lafayette, Indiana, U.S.A.)

Orietta Nicolis (University of Bergamo, Dalmine, Italy)

Jun Zhang (Statistical and Applied Mathematical Science Institute (SAMSI), Research Triangle Park, North Carolina, U.S.A.)

Jian Zou (Indiana University–Purdue University Indianapolis, Indianapolis, In., U.S.A.)


In order to study climate at scales where policy decisions can be made, regional climate models (RCMs) have been developed with much finer resolution (~50 km) than the ~500 km resolution of atmosphere-ocean general circulation models (AOGCMs). The North American Regional Climate Change Assessment Program (NARCCAP) is an international program that provides 50-km resolution climate output for the United States, Canada, and northern Mexico. In Phase I, there are six RCMs, from which we choose one to illustrate our methodology. The RCMs are updated every 3 hours and contain a number of variables, including temperature, precipitation, wind speed, wind direction, and air pressure; output is available from the years 1968–2000 and from the years 2038–2070. Precipitation is of particular interest to climate scientists, but it can be difficult to study because of its patchy nature: At hourly-up-to-monthly time scales, there are generally many zeroes over the precipitation field. In this research, we study sets of concentrated precipitation (i.e., the union of RCM pixels whose precipitation is above a given threshold), where we are interested in the way these sets evolve from one 3-hour period to the next. Assuming the sets are a realization of a time series of random sets, we are able to build dynamical models for the passage of rainfall fronts over 1–2 days. The dynamics are characterized by a growth/recession model for a time series of random sets, with several parameters that control how the concentrated precipitation changes over time.


Boolean model, kernel density estimation, Laslett’s theorem, method-of-moments estimation, NARCCAP, regional climate model (RCM), setvalued autoregression (SVAR)

Full Text (PDF format)