Errors in streamflow drought statistics reconstructed from tree ring data

Hydrologic variables such as streamflow may be reconstructed for years prior to the observational record through the use of historical tree ring data. Reconstructed records provide additional information for the estimation of statistics relating to rare events such as large and persistent water deficits. However, the reconstruction process can introduce bias and inflate the errors of estimated statistics. The biases and standard errors of streamflow drought statistics derived from such reconstructed records are evaluated for idealized conditions by employing a Monte Carlo simulation method. Both the bias and the standard error depend to some degree on the goodness of fit of the reconstruction model, the calibration sample length, the reconstruction sample length, and the autocorrelation of the reconstructed variable. The bias is most dependent on the goodness of fit of the reconstruction model. Standard errors are often strongly dependent on several of these factors. For a given drought statistic the sample length of an observed record which yields the same standard error as the longer reconstruction is called the effective sample length. Effective sample lengths are found to be less than 50% of the total reconstructed record length in many cases