Reconstructing Streamflow Time Series in Central Arizona Using Monthly Precipitation and Tree Ring Records

Abstract

An adaptive, three-way interpolation model based on multiple discriminant analysis, multiple linear regression, and normal ratio methods was used to reconstruct streamflows for three gauges in central Arizona for the period from 1580, using available annual tree ring indices and monthly precipitation. The reduction in mean absolute error compared to the use of the long-term mean for the period reconstructed from tree ring data only (1580?1863) was roughly 30% for both annual and spring streamflow; the corresponding reduction in mean absolute error when monthly precipitation values were included was roughly 60%. The reconstruction procedures were noted to produce a negative bias due to the positive skewness of the streamflow values. Procedures to correct for this bias and restore the variance of the streamflow time series are described. Reconstructed and adjusted annual and spring (February?May) streamflows are provided for the Verde and Salt Rivers and the Tonto Creek. A harmonic analysis of the reconstructed and adjusted annual streamflow time series from 1848 through 1989 shows a 70-year cycle (P-value > 99.5% ) and a 5.2-year cycle (P-value > 99.9% ) for each of the three gauges. Correlation coefficients between the 70-year-cycle-projected streamflow and the reconstructed and adjusted streamflow for the period 1589?1847 were between 14.6% and 20.5% for the three gauges, all significant at P- value > 99% .