3.1.1. Hydrology Data

The hydrology data used in this work were drawn from California state data sources and include secondary (i.e., processed) sources such as water balances and model simulations. Table 1 presents a summary of the data used in our work, including sources.

A widely used measure of Central Valley hydrology is the Eight River Index (8RI), which constitutes the unimpaired Sierra Nevada runoff to the Sacramento, Feather, Yuba, American, Stanislaus, Tuolumne, Merced, and San Joaquin Rivers. The 8RI represents a theoretical quantity that removes anthropogenic influences such as reservoir impoundments and land use modifications and thus does not reflect actual runoff conditions. The 8RI data for WYs 1906–2018 were obtained from the website of the California Data Exchange Center [81] and served as the predictand (after transformation) in the tree-ring reconstruction model described below. The previously described Bulletin 5 [65] streamflow data, which can be used to compute the 8RI beginning in WY 1872, was used for additional validation of the tree-ring runoff reconstructions.


**Table 1.** Summary of model calibration and validation data.

(1) measure of Central Valley Runoff.

We adopted publicly available simulation output of the valley floor hydrology [25] to calibrate a pre-development relationship between Central Valley unimpaired runoff and Delta outflow on an annual basis. The simulation assumes pre-development land use in the Central Valley and Delta as presented in Fox et al. [24] and associated natural vegetation evapotranspiration as presented in Howes et al. [41]. Furthermore, the simulation uses historical flows from the surrounding upper-elevation watersheds as boundary inputs; these boundary inputs represent unimpaired runoff data corresponding to WYs 1922–2014, a 93-year period inclusive of widely varying hydrologic conditions.

We used historical estimates of freshwater flows to the San Francisco Estuary (i.e., Delta outflow) spanning WYs 1912–2018 to calibrate a contemporary relationship between Central Valley unimpaired runoff and Delta outflow on an annual basis. Due to the complexity of direct observation of Delta outflow, these estimates are not based on tidal flow measurements. Rather, these estimates are computed from a budget of inflows and diversions from the Delta [27,82] As discussed below under Modeling Approach, we used calibrated runoff–outflow relationships (rather than historical data) to reconstruct contemporary Delta outflow conditions. We decided to use reconstructed flows for the contemporary period to provide a homogeneous time series for comparison with predevelopment conditions. Otherwise, flow differences between the two periods could be perceived to be due to statistical artifacts, such as the compression of variance of reconstructed flows relative to variance of observed flows over a common period [53,83].
