Incorporating the Spatio-Temporal Distribution of Rainfall and Basin Geomorphology into Nonlinear Analyses of Streamflow Dynamics: Methodology Development and a Predictability Study

Many recent studies have been devoted to the investigation of the nonlinear dynamics of rainfall or streamflow series based on methods of dynamical systems theory. Although finding evidence for the existence of a low-dimensional deterministic component in rainfall or streamflow is of much interest, not much attention has been paid to the nonlinear dependencies of the two and especially on how the spatiotemporal distribution of rainfall affects the nonlinear dynamics of runoff at flood time scales. In this paper, a methodology is presented which incorporates the dynamics of runoff, spatio-temporal structure of precipitation and catchment geomorphology simultaneously into a nonlinear analysis of streamflow. The proposed framework is based on “hydrologically-relevant” rainfall-runoff phase-space reconstruction acknowledging the fact that rainfall-runoff is a stochastic and spatially extended rather than deterministic and multivariate system. The methodology is applied to two basins in Central North America using 6hour streamflow data and radar images for a period of five years. The proposed methodology is used to: (a) quantify the nonlinear dependencies between runoff dynamics and the spatio-temporal dynamics of precipitation; (b) study how runoff predictability is affected by the trade-offs between the level of detail necessary to explain the dynamics of forcing and the reduction of complexity due to the smoothing effect of the basin; and (c) explore the possibility of incorporating process-specific information (in terms of catchment geomorphology and an a-priori chosen uncertainty model) into nonlinear prediction. Preliminary results are encouraging and indicate the potential of using the proposed methodology to understand via nonlinear analysis of observations (i.e., not based on a particular rainfall-runoff model) runoff predictability and limits to prediction as a function of the complexity of spatio-temporal forcing relative to basin geomorphology.