Event Type:

Probability Seminar

Date/Time:

Thursday, July 30, 2015 - 14:00 to 15:00

Location:

KIDDER 364

Guest Speaker:

Jorge Ramirez

Institution:

Universidad Nacional de Colombia

Abstract:

We present an application of piecewise deterministic Markov processes to the study of the hydrological cycle. We formulate a model for the dynamical response of an arbitrary watershed to a rainfall input in the form of a Poisson process. The resulting high dimensional SDE tracks the streamflow and runoff at every stream and hillslope in the watershed. An invariant measure absolutely continuous with respect to Lebesgue measure is shown to exist, and explicitly computed in terms of the probabilisitic description of the rainfall, and the geometry of the river network. Interesting corollaries about the behavior of moments of streamflow are derived, as well as scaling properties of the probability of extreme streamflow events with respect to river network size and geometry. The results shed light into the relationship between the uncertainty associated with rainfall and that of the streamflow.

Host: