3.1.3. Tree-Ring Data

Sixty-nine tree-ring site chronologies of total ring width were assembled as part of our work (Figure 1). Each chronology typically represents many (e.g., 15 or more) trees at a specific location. Initial screening criteria were a minimum time coverage of the period 1636–2003, and geographical location within a box delineated by latitudes 34.5 N to 44.0 N and longitudes 118 W to 125 W.

We started with files of measured ring widths obtained from two studies conducted for CDWR [20,85] and supplemented those with additional files from the International Tree-ring Data Bank [86]. Ring widths were standardized uniformly into site chronologies using Matlab functions following similar protocol to that in the ARSTAN standardization package [87]. This includes fitting ring-width series with a cubic smoothing spline [88], computing core indices as the ratio of ring-width to the smooth spline and averaging the indices over cores to get the site chronology. Trend in variance indistinguishable from age or size effects was removed using the method recommended by [89]. From an assessment of the persistence in the standard chronologies and the annual flows, we decided to use the residual version [90] of the site chronologies in the reconstruction modeling. The residual chronology is an average over core indices whose low-order autocorrelation has been removed fitting the index to an autoregressive (AR) model. We used a modified Akaike information criterion [91] to select the AR order. Site chronologies are averages over fewer and fewer trees toward the early part of the tree-ring record. Adequacy of sample size for each chronology was assessed by the expressed population signal [92]. Secondary screening eliminated any site chronology whose Pearson correlation with annual flows over the available period of data overlap (subset of the WYs 1906–2018 period) was either statistically insignificant or unstable over time at significance level α = 0.05. The temporal stability of correlation was tested using a difference-of-correlation test [93] of the null hypothesis that the sample correlations for the first and second halves of the overlap are from the same population.

Additional tree-ring data and processing information are included in the Supplementary Materials section. Sites and metadata are listed in Supplementary Material A. Chronology development is described in more detail in Supplementary Material B. Additional electronic data files are also included Supplementary Materials and identified in Supplementary Material A: files of original tree-ring width measurements; a time series matrix of the residual site chronologies; a time series matrix of observed and reconstructed flows, with confidence intervals on the reconstruction.
