*2.2. Description of Analyses*

Various statistical analyses were conducted on three drought categories: deficit, duration, and intensity. As previously used for drought studies in the western United States [7], a drought is defined as two or more years in which the streamflow is below the historical average streamflow. To determine when a streamflow station experienced drought, historical volumetric values were averaged and each yearly streamflow value of the eight future projections was subtracted from the average historical streamflow. Yearly droughts were explored as this is appropriate for analysis of changes in water supply which is generated over a water year (October 1 to September 30 of next year) and meets various demands throughout the year. A positive difference between the long-term average and the yearly streamflow represents a deficit in the given year. If a streamflow deficit occurred in two or more consecutive years, a drought occurred. Three drought categories were used to conduct data analysis for all eleven streamflow stations: (1) drought deficit, (2) duration, and (3) intensity. Overall drought deficit was calculated by summing the deficit for each of the years in which the drought occurred. Drought duration was found by adding the years in which consecutive streamflow deficits occurred. Drought intensity was determined by dividing drought deficit by the drought duration.

The variability in streamflow across California rivers only permits analysis against the corresponding historical data. To accurately compare data among the rivers, drought deficit, duration, and intensity were standardized with a z-score based on the mean (u) and standard deviation (σ) for each streamflow station (both for the historical and projected drought quantities). Each drought measure (deficit, duration, and intensity) was transformed into a standardized z-score. The two tailed difference in means *t*-tests were conducted on the standardized data of aggregated streamflow drought measures, at a significance level of 0.05, comparing the projected values to historical values.

The variability for individual streamflow stations was also evaluated using a similar *t*test analysis on the non-standardized streamflow values for all the three drought measures (deficit, duration and intensity) and presented for as box plots and as extreme values (largest drought).

#### **3. Results**

#### *3.1. Aggregate Analysis of California Streamflow Stations*

Table 1 represents the two tailed *t*-test results for each of the drought categories with the highlighted boxes significant at a level of 0.05. This summary is for all eleven stations aggregated into one composite standardized time series. The largest impacts are seen in the deficit and duration drought quantities. The Warm Dry model (for both RCP 4.5 and 8.5) produces larger drought deficits and duration. For RCP 4.5, the Average and Cool Wet scenarios produce lower drought conditions for deficit, intensity and duration. The largest impacts are seen in drought deficits and durations.

**Table 1.** Aggregated streamflow analysis using two tailed difference in means *t*-tests with a significant difference in drought categories. Highlighted boxes indicate a significant difference (at a 0.05 level) between historical (1950–2015) and model (2020–2099) projected means. Red represents a higher projected mean than historical. Blue represents a lower projected mean than historical.

