Table 1. Summary Statistics of Sub-Period Reconstruction Models Sequence a Start b Calibration c Validationd Years n-p-q R2adj m RE RMSE 1 762 1906-2003 3-3-1 0.60 9 0.58 3.46 2 1182 1906-2002 6-5-1 0.74 9 0.73 2.78 3 1365 1906-2002 9-4-1 0.77 9 0.76 2.64 4 1473 1906-2004 4-4-1 0.57 9 0.54 2.63 a Sequence number of sub-period model (1 is earliest). b Start year of reconstruction sub-period. c Calibration statistics: years, calibration period; n, the number of chronologies available; p, the number of potential predictors in the predictor pool; q, the number of predictors in the final model; R2adj, the adjusted coefficient of determination. d Validation statistics (cross-validation): m, the number of observations left out in "leave-m-out" validation; RE, the reduction of error statistic; RMSE, the root-mean-square error of cross-validation, in billion cubic meters (BCM). Text S4. Statistics of residual site chronologies. 6.1 Column "N", tree-ring site number, as on map in Figure 1 in paper 6.2 Column "Length", total length (years) 6.3 Column "Seg", minimum segment length (shortest segment of ring widths, in years) 6.4 Column "Mean", full-period mean 6.5 Column "StDev", standard deviation 6.6 Column "Skew", skewness coefficient 6.7 Column "Sig", statistical significance of skew (0 = not significant at 0.05 alpha-level; 1 = significant at 0.01 alpha); note that none of the estimated skew coefficients fell into the intermediate range of significant at 0.05 but not at 0.01. 6.8 Column "r1", lag-1 autocorrelation 6.9 Column "NLow", smallest sample size (number of cores) in any year 6.10 Column "NHigh", largest sample size (number of cores) in any year 6.11 Column "SSS_Min", minimum sub-sample signal strength statistic (Wigley et al. 1984) in any year 6.12 Column "EPS_L", minimum expressed population signal statistic (Wigley et al. 1984) in any year 6.13 Column "EPS_H", maximum expressed population signal statistic (Wigley et al. 1984) in any year N Length Seg Mean StDev Skew Sig r1 NLow NHigh SSS_Min EPS_L EPS_H 1 1044 256 0.999 0.236 -0.04 0 -0.05 3 21 0.88 0.85 0.97 2 1448 259 1.001 0.212 -0.05 0 -0.01 1 35 0.65 0.64 0.98 3 662 265 0.994 0.292 0.03 0 -0.03 3 20 0.92 0.91 0.98 4 533 259 1.003 0.257 -0.41 1 -0.05 4 27 0.89 0.87 0.98 5 600 268 1.001 0.251 -0.19 0 -0.02 3 12 0.90 0.82 0.93 6 1324 434 1.000 0.172 -0.30 1 -0.01 2 27 0.82 0.80 0.97 7 638 262 0.999 0.189 -0.36 1 -0.03 3 45 0.87 0.86 0.99 8 854 264 0.999 0.252 -0.09 0 -0.06 3 47 0.91 0.90 0.99 9 822 256 1.001 0.224 -0.28 1 -0.05 3 29 0.87 0.85 0.98 10 760 251 0.999 0.158 -0.41 1 -0.02 2 43 0.48 0.46 0.96 11 1243 263 0.999 0.229 0.07 0 -0.03 4 42 0.79 0.77 0.98 Text S5. Summary statistics of single-site regression models of flow on residual site tree-ring chronologies. 7.1 Column "N", tree-ring site number, as on map in Figure 1 in paper 7.2 Column "Site_Name", tree-ring site name 7.3 Column "Spec", tree species: (PSME=Pseudotsuga menziesii, PIED=Pinus edulis) 7.4 Column "Yr", end-year for calibration of flow with lagged residual site chronology; start year for all models was 1906; final year of chronologies differs from this because two trailing years of chronology were required to allow lags t+1 and t+2 to be used in the predictor pool 7.5 Column "Lags", flow in year t was regressed on residual chronologies lagged this many years from t 7.6 Column "R2", coefficient of multiple determination for the regression 7.7 Column "F", overall F-level of regression of flow on lagged chronologies; all are significant at alpha-level of 0.001. 7.8 Column "RE_A", reduction-of-error (RE) statistic for calibraton on first half of period covered by Yr_Start to Yr_end and validation on second half. RE statistic computed as in Fritts et al. (1990). A positive RE is regarded as evidence of positive skill when the model is applied to data not used to calibrate the model 7.9 Column "RE_B", reduction-of-error statistic for calibraton on second half of period covered by Yr_Start to Yr_end and validation on first half 7.10 Column "Model(s)", Membership of chronology in one or more of the four sub-period regression models beginning in A.D. 762, 1182, 1365 and 1473 (see Table 1 in paper) N Site_Name Spec Yr Lags R2 F RE_A RE_B Model(s) 1 Harmon Canyon PSME 2003 0,-1 0.42 35.1 0.46 0.26 2,3,4 2 Beef Basin PSME 2003 0,-1,1 0.39 21.0 0.48 0.27 1,2,3 3 Navajo Canyon PSME 2003 0,-1 0.41 33.5 0.40 0.44 3,4 4 Slickrock PIED 2003 0,-1,1 0.41 67.7 0.46 0.41 4 5 Wells Draw PIED 2003 0,-1 0.37 28.8 0.39 0.39 4 6 Eagle PSME 2002 0,-1,-2,1 0.48 44.8 0.50 0.48 1,2,3 7 Pump House PIED 2000 0,-1 0.47 82.2 0.48 0.39 3 8 Wild Rose PIED 2000 0,-1 0.51 48.1 0.61 0.37 2,3 9 Trail Gulch PSME 2000 0,-1,-2 0.57 63.4 0.47 0.59 2,3 10 Lands End PSME 2002 0,1 0.35 25.8 0.44 0.18 3 11 Green Mtn Res PSME 2002 0,-2 0.23 29.2 0.27 0.05 1,2,3 Text S6. Weights measuring relative importance of each tree-ring chronology to the sub-period reconstruction models listed in Table 1 of the paper. 8.1 Column "N", tree-ring site number, as on map in Figure 1 8.2 Column "Site", site name 8.3 Column "Model-1", relative weights on chronologies for model beginning A.D. 762 column in Table 1 in the text. The four sub-period models are listed as in Table 2 in the text. 8.4 Column "Model-2", relative weights on chronologies for model beginning A.D. 1182 The weights have been scaled so that the weight is 1.0 for the chronology most important to the reconstruction 8.5 Column "Model-3", relative weights on chronologies for model beginning A.D. 1365 sub-period reconstruction model 8.6 Column "Model-4", relative weights on chronologies for model beginning A.D. 1473 N Site Model-1 Model-2 Model-3 Model-4 1 Harmon Canyon NULL 0.59 0.57 0.99 2 Beef Basin 0.77 0.59 0.58 NULL 3 Navajo Canyon NULL NULL 0.52 0.87 4 Slickrock NULL NULL NULL 0.90 5 Wells Draw NULL NULL NULL 1.00 6 Eagle 1.00 0.75 0.75 NULL 7 Pump House NULL NULL 0.65 NULL 8 Wild Rose NULL 0.86 0.88 NULL 9 Trail Gulch NULL 1.00 1.00 NULL 10 Lands End NULL NULL 0.39 NULL 11 Green Mtn Res 0.34 0.27 0.29 NULL Literature cited in the auxiliary material: Bloomfield P. (2000) Fourier analysis of time series: an introduction, second edition. 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