4.3.1. Model Calibration

The resulting pre-development relationships between seasonal average X2 and annual average Delta outflow are displayed in Figure 10. Equation (3) fitting parameters and regression statistics are summarized in Table 7. Step changes in contemporary relationships between annual Delta outflow volume and seasonal average X2 position were observed following construction of Shasta Dam in 1944. Hutton et al. [101] observed statistically significant trends in seasonal outflows, with decreasing trends observed in four months (February, April, May and November) and increasing trends observed in two months (July and August). The authors discussed linkages between outflow trends and changes in upstream flows and coincident developments such as reservoir construction and operation, out-of-basin imports and exports, and expansion of irrigated agriculture. The resulting contemporary pre- and post-WY 1945 relationships between seasonal average X2 and annual Delta outflow volume are shown in Supplementary Material D (Figures D-3 and D-4) and regression statistics are summarized in Table 7. Although a physical basis exists for developing independent correlations for the pre- and post-1945 February–June relationships, we note that the derived fitting parameters are not statistically different from one another.

**Figure 10.** Pre-development seasonal X2–outflow relationships (Model 2). See Equation (3) and Table 5 for model fitting parameters.

**Table 7.** Model fitting parameters and regression statistics for Equation (3): relationships between X2 position and Delta outflow under pre-development (Model 2) and contemporary (Model 3) conditions X2 is in units of km from Golden Gate and outflow units are in BCM per year.

