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Water Resources Research
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Supporting Information for
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Projected changes in snowfall extremes and interannual variability of
snowfall in the western United States
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A. C. Lute1, J. T. Abatzoglou2, and K. C. Hegewisch2
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1Water
Resources Program, University of Idaho, Moscow, ID, USA, 2Department
of Geography, University of Idaho, Moscow, ID, USA,
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Contents of this file
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1. text01.txt (Appendix 1) Discussion of potential sources of snowfall biases in
the MACA product, methods of bias evaluation, and results.
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2. ts01.txt (Table S1) Mean biases between downscaled station data and
observed station data and their significance statistics.
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2.1. Column “metric”, the metric for which biases were evaluated.
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2.2. Column “mean bias”, the station and model averaged bias between
downscaled station data and observed station data for the given metric.
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2.3. Column “Percent of Stations with >25% of Models Significantly Different”,
the percent of stations at which more than 25% of the 20 GCMs were
found to be significantly different from observed station data for the given
metric.
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2.4. Column “Mean Percent of Models Significantly Different”, the station
averaged percent of the 20 GCMs that were found to be significantly
different from observed station data for the given metric.
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3. fs01.tif (Figure S1) Multi-model mean percent bias in annual SFE from the
MACA product compared to SNOTEL observations.
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4. fs02.tif (Figure S2) Multi-model mean percent bias in the CV of annual SFE
from the MACA product compared to SNOTEL observations.
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5. fs03.tif (Figure S3) Multi-model mean percent bias in ∑ 𝐒𝐅𝐄𝟗𝟎 from the MACA
product compared to SNOTEL observations.
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Introduction
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This appendix provides an evaluation of the skill of the MACA downscaled GCM
product at capturing observed characteristics of Western United States snowfall
as measured by Snowpack Telemetry (SNOTEL) stations. Processing of the two
datasets is described in the main article and methods of comparison are detailed
in the appendix text. The appendix also contains a table summarizing biases
between the two datasets for a suite of snowfall metrics, and three figures to
illustrate spatial patterns in snowfall biases.
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Appendix 1: Comparison of downscaled GCM output to observations at
SNOTEL stations
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A total of 20 CMIP5 GCMs [Taylor et al., 2012] were statistically
downscaled using the MACA method [Abatzoglou and Brown, 2012] and
additionally bias corrected to SNOTEL stations using the non-parametric
EDCDFm quantile-mapping method [Li et al., 2010] for temperature and an
analogous method that preserves ratios of quantiles for precipitation. The
secondary bias correction discretizes data to the resolution of SNOTEL
observations (2.54 mm, 0.1°C for precipitation and temperature, respectively)
and is designed so that the daily statistics of temperature and precipitation of the
downscaled output match those at each station. Daily SFE is derived using daily
temperature (T) and precipitation (P) and the precipitation phase probability
function of Dai [2008]. Potential biases are introduced in studies that blend
observational and downscaled climate projections. Specific sources of potential
biases arising from GCMs include the ability to simulate: (i) serial correlation and
daily sequencing of T and P, (ii) co-variability of daily T and P, and (iii) correct
magnitude of natural climate variability. Sources of potential biases arising from
downscaling include: (i) ability of statistical methods to resolve T and P in
complex terrain, (ii) non-stationarity of statistical methods to resolve sub-grid
scale changes in surface energy balance arising from changing land-surface
properties (e.g., snow-albedo feedback) [Salathe et al., 2009], and (iii) bias
correction algorithms. Finally, the use of the precipitation phase probability
function of Dai [2008] may entrain bias.
Evaluating how well modeled data represents observed data is
complicated by issues of precipitation gauge undercatch and snow pillow
overcatch at SNOTEL stations [e.g. Serreze et al., 1999; Lute and Abatzoglou,
2014], which can lead to daily SFE exceeding daily P as well as cumulative
winter SFE exceeding cumulative winter P. Consequently, methods that estimate
daily SFE from T and P may often underestimate observed SFE. We remove this
potential source of uncertainty from our methods by recalculating daily SFE
observed at SNOTEL stations using the transfer function of Dai [2008] with daily
average T and cumulative P.
We evaluate the ability of our procedure to reproduce statistical
properties for annual SFE, the CV of annual SFE, and the cumulative SFE of top
decile events ( ∑ 𝑆𝐹𝐸90 ) over the historical model experiments (1950-2005)
relative to SNOTEL observations. For each variable and station we calculated
the percent bias (model/observation*100-100) for each of the 20 CMIP5 models
and report the average model bias and the percent of models that were
statistically different (p<0.05) from observations. For the latter, we used a twosample t-test for annual SFE given its relative Gaussian distribution, and a nonparametric Wilcoxon rank sum test for ∑ 𝑆𝐹𝐸90 each year. Bootstrap resampling
with replacement (n=1000) was used to estimate a range of modeled CV of
annual SFE. Data was considered statistically different when at least 95% of the
differences between observed CV and resampled modeled CV were of the same
sign. We also considered biases in mean winter (November through March) T
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and P and determined statistically significant differences using two-sample ttests, but we report these in the context of the primary SFE metrics.
A positive mean bias of +7.4% was found for modeled annual SFE (Figure
S1), which is logical given the small positive bias in MACA product cumulative
winter precipitation (+3.2%) and small negative bias in mean winter temperature
(-0.11C). T and P biases result in positive biases in the frequency of snowfall
days (5-15% for most stations, not shown) that contribute to positive biases in
annual SFE, particularly in Arizona, the Blue Mountains, and Southern
Cascades. These biases were primarily due to the truncation of daily precipitation
amounts to adhere to SNOTEL instrument resolution. Unlike the respectable
agreement between modeled and observed annual SFE, the magnitude of
modeled CV of annual SFE is widely under predicted (mean bias=-8.2%) (Figure
S2). Moreover, most models are significantly different from observations. Given
that winter precipitation amounts are strongly correlated with winter SFE,
particularly in the colder regions [Mote et al., 2006], this lack of variability
appears to be tied to the underestimation of variance in winter precipitation
simulated by GCMs as highlighted in previous studies [e.g., Rupp et al., 2013].
Positive biases in ∑ 𝑆𝐹𝐸90 (mean = +15.5%) were found in the MACA product
relative to observations (Figure S3). However, most models were not significantly
different from observations, likely due to the large interannual variability of this
metric. The positive biases are consistent with the overall positive bias in SFE,
but may be compounded by stronger serial correlation in GCM output that is
downscaled that tends to promote prolonged extreme snowfall events. Additional
analyses at the GCM level are required to further assess these differences.
The MACA method alleviates substantial biases between downscaled
GCM output from historical forcing and that observed at individual stations for
some variables (not shown). However downscaling is unable to eliminate all
discrepancies, particularly for factors intrinsic to temporal variability in the GCMs.
Thus, we caution trying to directly compare metrics that are contingent on serial
correlation and low-frequency variability to observations. In particular, we note
that the underrepresentation of interannual SFE variability by GCMs may
enhance relative changes in modeled high and low snowfall years and the CV of
annual SFE given that such changes are a function of signal-to-noise ratio.
However, as we focus on changes in downscaled GCMs run under historical
forcing and RCP 8.5 experiments, we posit that our results have contextual
purpose.
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T Nov-Mar
Mean Bias
-0.11C
Percent of Stations with
>25% of Models
Significantly Different
17.9%
Mean Percent of
Models Significantly
Different
12.3%
P Nov-Mar
+3.2%
0.0%
0.0%
Annual SFE
+7.4%
1.6%
1.5%
CV Annual SFE
-8.2%
74.5%
52.8%
∑ 𝑆𝐹𝐸90
+15.5%
2.5%
2.2%
Metric
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Table S1. Mean biases between downscaled station data and observed station
data and their significance statistics
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Figure S1. Multi-model mean percent bias in annual SFE from the MACA
product compared to SNOTEL observations. Larger (smaller) markers indicate
stations for which more than 25% of models (25% of models or less) were
significantly different from observations.
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Figure S2. Multi-model mean percent bias in the CV of annual SFE from the
MACA product compared to SNOTEL observations. Larger (smaller) markers
indicate stations for which more than 25% of models (25% of models or less)
were significantly different from observations.
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Figure S3. Multi-model mean percent bias in ∑ 𝑆𝐹𝐸90 from the MACA product
compared to SNOTEL observations. Larger (smaller) markers indicate stations
for which more than 25% of models (25% of models or less) were significantly
different from observations.
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References
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