2.2.1. Difference from the Baseline

This study employed difference as a parsimonious metric to represent changes in future conditions from historical conditions. This is a standardized metric applied extensively in climate change related studies [29]. Specifically, the 40-year period, 1951–1990, was used as the historical baseline period. Compared to late 1990s and early 2000s, this period is relatively less impacted by anthropogenic climate change. Additionally, this 40-year window allows enough sample size to represent a wide range of natural variability in hydroclimatic variables. Similar studies have normally used 30-year periods [34]. Two 40-year future periods, mid-century (2020–2059) and late-century (2060–2099), were considered. Mean annual precipitation, and maximum and minimum temperature in the baseline period and future periods were computed and compared. Differences (from the baseline) were subsequently derived. Specifically, when looking at precipitation variables, the focus was on relative differences (i.e., percent different from the baseline); for temperature variables, absolute difference (in degree Celsius) was used.

In addition to annual precipitation and temperature, wet season precipitation and seasonal temperature were also applied as important indices in planning studies [45]. Wet season precipitation accounts for a majority portion of the annual precipitation. Seasonal temperature typically affects water supply and demand. For instance, spring temperature impacts snowmelt timing and amount. Summer temperature impacts evapotranspiration demand. Changes in wet season precipitation and seasonal temperature were also explored in this study.

### 2.2.2. Drought Index

Numerous drought indices have been developed for drought monitoring, assessment and prediction purposes [46–48]. Among these indices, the most widely used index might be the Standardized Precipitation Index (SPI) [49] because of its parsimonious (only requiring precipitation as input) and standardized (can be used across different spatial and temporal scales) nature. Despite its popularity, more and more studies noted that evapotranspiration also plays an important role in drought development [50–52]. This is particularly true in a warming climate for dry regions where evapotranspiration is an important component of the water budget. For instance, the most recent 2012–2015 California drought was a typical "warm drought" characterized by record-low precipitation and snowpack as well as record-high temperature [45,53–55]. As a result, SPI may not be the most appropriate index for drought analysis in California which contains many arid or semi-arid areas.

Most recently, based on the same concept employed in defining the SPI, Vicente-Serrano et al. [56] proposed a Standardized Precipitation-Evapotranspiration Index (SPEI). It first calculates the discrepancies between precipitation (P) and potential evapotranspiration (PET) on a monthly time scale (D = P − PET). Monthly discrepancies can be aggregated to other time scales (e.g., 3-month, 6-month, 12-month, among others) to calculate SPEI values at corresponding temporal scales. Next, a three-parameter Log-logistic distribution is selected to model the discrepancy time series. The probability distribution function of D is calculated according to the fitted Log-logistic distribution (F(x)). Lastly, the SPEI value is determined as the standardized values of F(x) following the approximation of Abramowitz and Stegun [57]:

$$SPEI = \mathcal{W} - \frac{\mathbb{C}\_0 + \mathbb{C}\_1 \mathcal{W} + \mathbb{C}\_2 \mathcal{W}^2}{1 + d\_1 \mathcal{W} + d\_2 \mathcal{W}^2 + d\_3 \mathcal{W}^3} \tag{1}$$

where *W* = −2 ln(*p*); *p* is the probability of exceeding a determined D value; and *C*0, *C*1, *C*2, *d*1, *d*2, and *d*<sup>3</sup> are preset constant coefficients. A positive (negative) SPEI value indicates wet (drought) conditions. Depending on the specific values, a drought event can be classified into different categories. Typically, a SPEI value less than −2 indicates extreme drought conditions. A value ranging from −2 to −1 denotes moderate drought conditions. A SPEI greater than −1 but less than 0 represents mild drought conditions.

SPEI has been shown to be a robust index. It compares favorably to other popular drought indices [58–63]. The PET is calculated using the Thornthwaite equation [64] which only requires temperature data as input. As such, the SPEI index implicitly considers the impact of temperature on drought situation, making it suitable in assessing drought conditions in future warming scenarios (represented by different model projections in the current study). For detailed explanations on the concept and calculation of the SPEI index, the readers are referred to [56]. The SPEI values on annual scale (SPEI-12), two-year scale (SPEI-24), three-year scale (SPEI-36), and four-year scale (SPEI-48) were chosen in this study. Drought occurs in California at those time scales regularly. It is meaningful to look at future drought at those scales for adaptive planning purpose.

Figure 3 exemplifies the SPEI-12 calculated for the three representative regions from each of the coastal, Central Valley, and eastern areas in the historical period: (1) the highly urbanized San Francisco Bay region; (2) the largest water supply source of the State: Sacramento River region; and (3) the driest Colorado River region. The San Francisco Bay region and the Sacramento River region have similar patterns due to their geographic proximity. The SPEI index for both regions well captures the 1983 and 1997 wet conditions as well as the 1976–1977, 1988–1992, 2007–2009, and the 2012–2013 droughts. The Colorado River region differs from those two regions in terms of annual precipitation (driest) and temperature (hottest). Long-duration droughts occur more frequently after 1990s in this region.
