A nonparametric approach for paleohydrologic reconstruction of annual streamflow ensembles

As multicentury records of natural hydrologic variability, tree ring reconstructions of streamflow have proven valuable in water resources planning and management. All previous reconstructions have used parametric methods, most often regression, to develop a model relating a set of tree ring data to a target hydrology. In this paper, we present the first development and application of a K nearest neighbor (KNN) nonparametric method to reconstruct naturalized annual streamflow ensembles from tree ring chronology data in the Upper Colorado River Basin region. The method is developed using tree ring chronologies from the period 1400-2005 and naturalized streamflow from the period 1906-2005 at the important Lees Ferry, Arizona, gauge on the Colorado River to develop annual streamflow ensembles for this gauge for the 14001905 period. The proposed KNN algorithm was developed and tested using cross validation for the overlap period, i.e., the contemporary observed period for which both the tree ring and streamflow data are available (1906-2005). The cross-validated streamflow reconstructions for the selected contemporary period compare very well with the observed flows and also with published parametric streamflow reconstructions for this gauge. The proposed nonparametric method provides an ensemble of streamflows for each year in the paleohydrologic reconstruction period (1400-1905) and, consequently, a more realistic asymmetric confidence interval than one obtained through most parametric approaches. Also, the K nearest neighbors are obtained only from the tree ring chronology data, and thus, the method can be used to reconstruct structured and even nonnumerical data for use in water resources modeling.