Calibration & Validation

Methods

Because the observed flow record for the Canadian River is highly skewed towards high flows, resulting in a non-linear relationship between the observed flow record and the tree-ring chronologies, the observed record was transformed into log 10 units prior to calibration. A forward stepwise regression procedure was then used to calibrate the log-transformed observed flow record with a pool of potential predictors consisting of tree-ring chronologies from Colorado and New Mexico. Five chronologies were selected by the stepwise procedure for the reconstruction model. Validation statistics were computed using a leave-one-out (cross-validation) approach. After calibration and validation, the reconstructed flows were back-transformed from log units to the original units (acre-feet).

Predictor Chronologies: Wet Mountains (CO), Montrose (CO), McPhee (CO), Disappointment Valley (CO), Mill Canyon (NM) [all residual chronologies except Mill Canyon]

Note: the calibration and validation statistics below were computed during the model development and reflect the relationship between the log-transformed observed flow record and the tree-ring predictor. The scatterplot below in Figure 1 shows the relationship between the back-transformed observed flows and the reconstructed flows, which have a lower R2. Also, the Standard Error of the Estimate and Root Mean Square Error reported below are in log units, and the RMSE can't be used to compute confidence intervals.

(For explanations of these statistics, see this document (PDF), and also the Reconstruction Case Study page.)

Figure 1. Scatter plot of observed and reconstructed Canadian River annual flow, 1937-1997.

Figure 2. Observed (gray) and reconstructed (blue) Canadian annual flow, 1937-1997. The observed mean is illustrated by the dashed line.