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Supplementary Figures for The inherent uncertainty of
precipitation variability, trends, and extremes due tointernal variability, with implications for Western US
water resources

Karen A. McKinnon1∗ and Clara Deser2
1

Department of Statistics and Institute of the Environment and Sustainability; Universityof California, Los Angeles; Los Angeles, CA 90095; kmckinnon@ucla.edu
2National Center for Atmospheric Research; Boulder, CO 80305

Supplementary Figure 1: The sea surface temperature (SST) anomaly pattern associatedwith PDOt⊥ , the component of the traditional Pacific Decadal Oscillation time series thatis orthogonal to the El Niño-Southern Oscillation time series. The SST anomaly pattern iscalculated by regressing the annual mean PDOt⊥ time series onto the annual mean, linearly
detrended SST anomalies from HadISST.

Supplementary Figure 2: The empirical coherence (black line) and 95% range of coherence
values from the synthetic mode times series between (a) ENSO and PDO⊥ , (b) ENSO andAMV, and (c) PDO⊥ and AMV.

Supplementary Figure 3: The selected block size at each gridbox for CESM1-LE and theGPCC observations. Block size is chosen for each gridbox and month using the methods ofWilks (1997); the maps show the maximum value across months. The CESM1-LE ensemble
mean shows the average selected block size across members. Member 1 is shown as an
example of the block size given a single record, which is more readily compared to theGPCC-based observational estimate. The average across ensemble members of the difference
between the GPCC- and CESM1-based block sizes shows that, in most regions of the world
outside of North America and Europe, the GPCC dataset suggests a larger block size. The
dry subtropics are excluded since some months climatologically have no rain.

Supplementary Figure 4: The DJF-average value of βF estimated in each member of theCESM1-LE independently. The large differences across maps indicates that the estimatedforced component is being dominated by sampling of internal variability.

Supplementary Figure 5: The signal to noise ratio for the forced component for winter (left)
and summer (right) estimated using low frequency component analysis (Wills et al. 2018).
The forced component is assumed to be contained in the first low frequency pattern (LFP).
The LFPs are estimated in each member of CESM1-LE as a linear combination of the first
30 EOFs for monthly precipitation. The signal is defined as the mean of the first LFP acrossthe ensemble, and the noise is the standard deviation across the ensemble.

Supplementary Figure 6: As in Figure 6, but for high-frequency variability (frequency >1/10y).

Supplementary Figure 7: As in Figure 6, but for the magnitude of the 150-year event. Returnperiods are estimated empirically in each 85-year member of either the CESM1-LE or then+0.12
CESM1-synth-LE as m−0.44(Gringorten, 1963), where n is the number of years in the record,and m is the rank of each event. While more sophisticated estimates of the probability ofextremes are possible, such as by using extreme value theory, the simpler empirical approachis sufficient for our purposes of intercomparison between ensembles. When using the full
CESM1-LE, which contains 3400 member-years, the choice of weighting scheme becomes
irrelevant, and the 150-year event can be estimated as the 23rd most extreme value acrossthe member-years. Comparing this estimate to the use of the Gringorten formula for eachmember individually shows that the Gringorten approximation for the 85-year records islargely unbiased (Panel b).

Supplementary Figure 8: Validation of the synthetic ensemble methodology for water resource metrics in the Upper Colorado River Basin (see outline in Figure 10). (a, b) The
distribution of DJF Upper Colorado River Basin precipitation across the full CESM1-LEand CESM1-synth-LE. (c) The time series of the frequency of dry years in overlapping 31year periods across the full CESM1-LE (black), the first member of the CESM1-LE (lightblue), and the CESM1-synth-LE mem1, which is based on the first member of the CESM1LE alone (dark blue). The 5%-95% range across the two ensembles is shown in gray for theCESM1-LE and light blue for the CESM1-synth-LE mem1. (d) The change in the frequencyof dry years from the first (1921-1951) to the last (1985-2005) 31-year period. All colors are
the same as in (c). (e, f) As in (c, d) but for wet years. (g, h) As in (c, d) but for whiplashyears.

9References

10

Gringorten, I. I. (1963), A plotting rule for extreme probability paper, Journal of Geophysical11

Research, 68 (3), 813–814.