Annual Cycle Variability of Precipitation, Temperature and Streamflow in the
Western United States
Subhrendu Gangopadhyay1, 2, Somkiat Apipattanavis2, Balaji Rajagopalan1, 2
Upmanu Lall3, 4, and Martyn Clark1
1
2
Cooperative Institute for Research in Environmental Sciences
University of Colorado
Boulder, Colorado
Department of Civil, Environmental and Architectural Engineering
University of Colorado
Boulder, Colorado
3
4
Department of Earth and Environmental Engineering
Columbia University
New York City, New York
International Research Institute for Climate Prediction
New York City, New York
Submitted to
Journal of Climate
February 2004
Corresponding author:
Subhrendu Gangopadhyay
CSTPR/CIRES
University of Colorado
Campus Box 488
Boulder, CO 80309-0488
------------------------------p: 303-735-6316
f: 303-735-1576
e: subhrendu.gangopadhyay@colorado.edu
Abstract
There is a growing body of scientific literature, which shows that low frequency
components of the climate system such as ENSO (El Niño-Southern Oscillation) have
significant influence on some regional annual cycle variability of climate variables. In
this paper we analyze the influence of such low frequency modulations, and other
possible mechanisms on the annual cycles of precipitation, temperature and streamflow in
the western United States. We consider two periods, 1950-1975 and 1976-2000 to
compare the shifts in precipitation, temperature and streamflow across this region. The
analysis is carried out in the frequency domain for all the three variables (precipitation,
temperature and streamflow) using the technique MTM-SVD (multi-taper singular value
decomposition). For streamflow, we also used principal component analysis (PCA) to see
the consistency between this time-domain and frequency domain approaches.
Results show an increase in temperature over the later period, and an
intensification of the precipitation and streamflow annual cycles. We found that for
precipitation and streamflow more than 85 percent of the study area experienced
significant shifts, and an early occurrence of peak streamflows over the period
1976-2000. The median shift for the region for both precipitation and streamflow were
found to be 6 days. In case of temperature the entire region experienced shifts between 8
and 12 days. We also carried out analysis for selected sites in the study area to isolate the
seasons during which these shifts occurred. Proposed physical mechanisms related to
warming, and intensification of ENSO events post 1980 were analyzed using climate
composites of SLP (sea level pressure), SST (sea surface temperature), and winds.
2
Finally, PCA of western US streamflows were used to compare results with the frequency
domain MTM method, and we found that both these approaches provided consistent
results.
3
1. Introduction
Annual cycle variability though seems random, there is an increasing body of
scientific evidence that coherent low-frequency variability in the climate system such as
the ENSO (El Niño-Southern Oscillation) have significant influence on modulating this
variability (e.g., Compo et al. 2001). In addition to the variability attributed to such
natural low-frequency modes in the climate system, signatures of recent climate trends
have been observed in several regional and global variables. For example, (i) increased
land and ocean temperatures, in particular over mid-latitudes (e.g., Weber et al. 1994);
(ii) changes in extreme weather events (e.g., McCabe et al. 2001); and (iii) changes in
spring phenology at mid- and high latitudes (e.g., Myneni et al. 1997). These trends
might be due to natural variability of the climate system but in recent years have gained
much attention due to potential links attributed to anthropogenic stresses (IPCC 2001).
Instrumental records of land surface temperature have shown increases and have
been reported widely (e.g., Karl et al. 1991; Karl et al. 1993; and Quintana-Gomez 1999).
The third IPCC (2001) report states about 0.6oC increase in global mean temperature over
the last century. Regionally, in North America and Europe, mean surface temperature has
increased by about 0.5oC over the last 50 years. Such regional changes in surface
temperature affect the intensity and type of precipitation (rain or snow) and snow cover
extent in mid- and high latitudes. Increases in annual precipitation totals in the United
States and Canada, and decrease in lower-latitude precipitation have been observed
during the last-century (e.g., Bradley et al. 1987; Groisman and Easterling 1994).
Groisman and Easterling (1994) report a 20% increase in the annual snowfall and rainfall
4
in Canada during the last four decades. Also, global climate model simulations of
enhanced greenhouse conditions show increase in global average precipitation of about
10%. This is characterized by fewer but more intense convective events at lower and
middle latitudes, and more frequent moderate to high intensity non-convective events at
higher latitudes (Hennessey et al. 1997). Increased precipitation over the contiguous
United States in the 20th century are in line with simulation results and is attributed to an
increase in the frequency of heavy precipitation events (e.g., Karl and Knight 1998;
Groisman et al. 2001).
In addition to higher precipitation amounts in the higher latitudes, increased
surface temperature has resulted in a systematic decrease of snow-covered areas.
Analysis of Northern Hemisphere records of snow-covered areas by Groisman et al.
(1994) over the period 1972-1992 has shown an approximate 10% reduction. This has
been linked to an increase in spring temperatures and a lower albedo from reduced snow
extent. Lowering the albedo has created a positive feedback mechanism resulting in
subsequent decreases of snow-covered areas.
The manifestation of increased precipitation, a reduction in snow-covered areas
due to increased temperature, and changes in spring phenology are possible indications of
a shift in seasons. In this paper, we investigate the shifts in the annual cycle of
precipitation, temperature and streamflow in the western United States. The study region
covers 11 states spanning 84 climate divisions in the western US (Figure 1). The major
river basins of this region such as the Colorado and the Columbia are snowmelt
dominated, and shifts in seasons can impact peak runoffs and the timing of the peak. For
example, increased winter temperatures could reduce the amount of snow and make more
5
precipitation fall as rain than snow, and coupled with higher spring temperatures could
initiate earlier runoff and peak streamflows. Shift in the seasonality of western US
precipitation and streamflow have been noted by Bradley (1976), Rajagopalan and Lall
(1995), and Cayan et al. (2001) among others. Early flows associated with warmer
winters in California have been observed by Dettinger and Cayan (1995). Trends in snow
water equivalent (SWE) computed by Mote (2003) for the Pacific Northwest show strong
declines in SWE in spite of increases in precipitation, and appear consistent with an
increase in spring temperatures. The Pacific Northwest region is shown to be quite
sensitive (Hamlet and Lettenmaier 1999) under a range of different climate models, and
show increased winter flows and a reduction in spring-summer flows. Similar
observations of increased winter runoff and decreased spring runoff under double CO2
global warming scenario have been reported by Lettenmaier and Gan (1990).
From the various observations and research carried out globally and in the
western US region it is evident that there has been shifts in seasonality, in particular an
increased winter-spring temperature. This has subsequently impacted precipitation, snowcover extent and shifts in streamflow peaks. In this paper we systematically diagnose the
shifts in precipitation, temperature and streamflow; the possible mechanisms for the shifts
and amount of shifts in seasons during the mid and later parts of the 20th century. We use
the spectral method MTM-SVD (multi-taper singular value decomposition) method in the
frequency domain to analyze precipitation, temperature and streamflow annual cycles.
For streamflow, we also use principal component analysis (PCA) to identify the leading
modes of variability across the western US region.
6
The data used in this study is given in section 2. A description of the MTM-SVD
and PCA methodologies is given in Section 3. Section 4 describes the application of this
methodology with a discussion of the results. A summary of the research and conclusions
end the presentation (Section 5).
2. Data
The datasets used in this study include: (1) monthly precipitation and average
temperature time series for the 84 climate divisions in 11 states for the period 1895-2000;
(2) 84 streamflow time-series from USGS (United States Geological Survey) stream
gages covering the 11 states for the period 1940-2000 (see Figure 1); and (3) principal
components of ENSO time-series. Further details of these datasets are provided in the
following sections.
2.1 Precipitation and Temperature Datasets
Monthly precipitation and average temperature time series for the 84 climate
divisions covering Arizona (7 climate divisions), California (7), Colorado (5), Idaho (10),
Montana (7), Nevada (4), New Mexico (8), Oregon (9), Utah (7), Washington (10), and
Wyoming (10) for the period 1895-2000 were obtained from the NOAA (National
Oceanic and Atmospheric Administration) CDC (Climate Diagnostic Center) website
http://www.cdc.noaa.gov/Timeseries/. All analysis was carried out using a “modified”
time-series for precipitation and temperature. This “modified” series was obtained by
dividing the original time-series for each climate division by its grand mean. The grand
7
mean for each variable was calculated from the subset of years (e.g., 1950-1975; 19752000) of monthly data at the 84 climate divisions.
2.2 Streamflow Datasets
Monthly streamflow time series from 84 USGS stream gauging stations covering
the 11 states: Arizona (10 stations), California (11), Colorado (11), Idaho (7), Montana
(13), New Mexico (6), Nevada (1), Oregon (6), Utah (4) and Washington (15), were
obtained from the USGS website http://water.usgs.gov. The time series at these 84
locations were serially complete for the period 1940-2000. Annual streamflows were
derived from these monthly streamflows for all the locations. Monthly streamflows were
modified similar to precipitation and temperature series in the MTM-SVD analysis.
2.3 Principal Components of Sea Surface Temperature (SST) Time-series
The first principal components (PC1) of tropical (5S-15N), subtropical (15N-45N)
and north Pacific sea surface temperature for January-April from 1940-2000 were used as
well for investigating the large-scale atmospheric circulation anomalies that may
contribute to changes in the streamflow response.
3. Methodology
The two statistical methods used in this study are, (1) the frequency domain
technique MTM-SVD and (2) in time-domain, PCA.
3.1 Multi-taper Singular Value Decomposition (MTM-SVD)
8
To study the effect of low frequency modulation on the annual and sub-annual
variability of precipitation and temperature over the western US we used the frequency
domain MTM-SVD method of Mann and Park (1999). The frequency domain MTMSVD provides a robust diagnosis tool to analyze key low-frequency modes of large-scale
climate by capturing the coherent space-time variations across multiple climate state
variables.
The MTM-SVD is particularly useful in isolating narrow band frequency domain
structure (Mann and Park 1994, 1996) that traditional time-domain univariate and
multivariate decomposition methods such as PCA and CCA (canonical correlation
analysis) fail to isolate. The method relies on the assumption that climate modes are
narrow band and evolve in a noise background that varies smoothly across the
frequencies. Details of the MTM-SVD methodology development are given in Mann and
Park (1999). Here, we briefly describe the MTM-SVD methodology for decomposing the
data set into a few modes (typically manifested as narrow band signals) in the range of
frequencies resolvable by the data set.
The analysis was carried out using the “modified” time-series as described above.
Spectral domain equivalents of each grid point (centroid of climate division, total of 84)
series are computed based on the multi-taper spectral analysis (Thomson 1982; Park et al.
1987). A small number (corresponding to K orthogonal data tapers) of independent
spectral estimates for each modified series are computed,
N
Yk( m ) ( f )   wt( k ) yn ei 2 πftΔt
(1)
t 1
where t = 1 month (0.0833 year), is the sampling interval, with {wt( k ) }tN1 being the kth
member of the orthogonal sequence of tapers (“Slepian” tapers), k = 1,…, K; m = 1,…, M
9
are the number of time series used for the analysis, and N is the length of time series. For
the given level of sampling (t) and the length of the series (N), the smallest resolvable
frequency is called the Rayleigh frequency, fR = 1/(Nt). Each eigen-taper carries
independent information in a frequency band of half-bandwidth of p 
fR (p is a
constant), at any given frequency. The level of compromise between the variance and
frequency resolution of the Fourier transform depends on the choice of K. Mann and Park
(1994) suggest p = 2 and K = 3 as an excellent compromise between frequency resolution
and also providing sufficient degrees of freedom for signal-noise decomposition. For
each frequency point to be resolved by this analysis, a M  K matrix A(f) is formed for
each of the M series,
 w1Y1(1)

w Y (2)
A( f )   2 1
 ...

(M )
 wM Y1
w1Y2(1)
w2Y2(2)
...
...
...
...
wM Y2( M )
...





wM YK( M ) 
w1YK(1)
w2YK(2)
...
(2)
where w can be used to provide an appropriate areal weight. Note that each row is
computed from a different series (grid point), and each column using a different taper.
Subsequently, a complex singular value decomposition is performed through,
K
A( f )  λ k ( f )u k ( f )  v*k ( f )
(3)
k 1
10
where the kth dominant mode explains k (relative fraction) variance. The left complex
eigenvector uk represents the empirical orthogonal functions (EOFs) in the spatial
domain, and vk, the complex right eigenvector represents the EOFs in the spectral
domain. These eigenvectors can be inverted to obtain the smoothly varying envelope of
the kth mode of variability at frequency f (Mann and Park, 1996). The localized fractional
variance (LFV) provides a measure of the distribution of variance by frequency, and
above a select confidence level threshold (e.g., 90%, 95%), represents a dominant narrow
band mode. The confidence levels are computed based on the locally white noise
assumption, and are constant outside the secular band. Mann and Park (1996) describe a
bootstrap method used to obtain the confidence bands. In general, the computed principal
eigen-value spectrum (described above) yields a number of narrow-band peaks. The
temporal reconstruction was examined by composting all the reconstructed series in a
select frequency band (e.g., the annual cycle). The reconstruction also yields the spatial
patterns associated with the given time scales, and their relative amplitude and phase
relationships.
3.2 Principal Component Analysis (PCA)
Principal component analysis was used only in the analysis of streamflow data.
The theory of principal components in the context of the present application is outlined in

this section. The starting point in the PCA analysis is the data matrix X  x1 , x2 ,, xq

consisting of p years (rows) of annual streamflows ( x ) at the q locations (q=84, number
of columns). Note that X is a space-time dataset. If we standardize matrix X , the
covariance or correlation matrix of this dataset is the q  q matrix S ,
11

S
1
T
X X
( p  1)
(4)
T
where X is the transpose of matrix X . A singular value decomposition of S (Press et
al. 1992) yields,
S
 UWV
T
(5)
where U and V are the q  q orthogonal matrices and W is a diagonal matrix of order q
with the eigen values as its elements. Since S is symmetric, U  V . Each column of
U (or V ) represents the eigen vectors corresponding to a given eigen value. The

principal component matrix Z  z1 , z 2 ,, z q
Z

XU
 is then obtained by projecting X on U ,
(6)
Each column of Z , z corresponds to a principal component, which are mutually
orthogonal. The space-time data X can therefore be decomposed into time components
Z that are uncorrelated and a space component represented by the eigen vectors in
U (or V ).
A factor-loading matrix F that represents the correlation between the
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original variables in X and the principal components in Z (after standardization) can be
defined as,
F

1
T
X Z
( p  1)
(7)
The factor loadings can be used to interpret the association between the original variables
and the derived principal components.
The steps in the application of these methodology and discussion of the results are
provided in the next sections.
4. Results and Discussions
4.1 LFV Spectrum
Using the monthly precipitation, temperature and streamflow data from the 84
climate divisions and the 84 stream gages, we constructed the localized fractional
variance spectrums. The LFV spectrums were constructed jointly using both precipitation
and temperature and for each variable independently. For precipitation and temperature
we used 106 years of data (1895-2000), and for streamflow 61 years of data (1940-2000).
Independent and joint spectra for precipitation, temperature and streamflow are shown in
Figure 2. The LFV spectrum helps to identify dominant frequencies above select
confidence level thresholds. The low frequency joint precipitation-temperature spectrum
(Figure 2a) shows no significant peaks at the 90% confidence level. However, significant
13
peaks at the 90% confidence level for the annual cycle and its higher order harmonics
such as the sub-annual cycle, etc was found to exist. Existence of non-significant peaks in
the joint LFV spectrum at the low frequencies is possibly masked by the smooth variation
in temperature field. The single variable temperature spectrum (Figure 2c) similarly also
showed no significant peaks at the 90% confidence level for the lower frequencies.
Precipitation with its intermittent property is inherently more variable. Plotting the LFV
spectrum (Figure 2b) for only precipitation showed significant peaks at the 90%
confidence level for several low frequencies. The low frequencies (cycles/year) were
identified to be 0.0674 (~ 15 year), 0.1875 (~ 5 year), and 0.3721 (~ 3 year). The annual
(1 cycle/year), and its higher order harmonics (e.g., 6-month or sub-annual cycle) were
also significant at the 90% confidence level. The low frequencies identified from the
precipitation LFV spectrum correspond to oscillations in the decadal time scale and also
in the time scales of ENSO events, approximately between 2 to 5 years was. This
spectrum was used in subsequent analysis of precipitation and temperature fields.
Since both precipitation and streamflow in the study region are known to be highly
variable, for streamflow, a joint LFV spectrum was constructed using precipitation and
streamflows (Figure 2d). Unlike the joint precipitation-temperature spectrum this
spectrum adequately captures the joint modes of precipitation and streamflow variability.
Similar to the precipitation spectrum we observed that the significant frequencies (at 90%
level) are the quasi-decadal (15-18 years cycle) and an ENSO frequency
(0.4482 cycles/year). Similarly, the high frequency joint spectra showed the annual cycle
and its higher order harmonics to be significant.
14
The next step was to analyze the spatial distribution of the precipitation,
temperature, and streamflow fields for the selected significant frequencies identified
above. We restrict our attention to frequencies in the ENSO band and the annual cycle.
4.2 Fixed Frequency Reconstructions
Reconstruction at selected low frequencies in the ENSO band: 0.1875, 0.3721
cycles/year for precipitation and temperature; 0.4482 cycles/year for streamflow and the
annual cycle are described in the following sections.
4.2.1 Low Frequency
Spatial reconstructions for frequencies 0.1875 and 0.3721 cycles/year were
carried out independently for both precipitation and temperature. The result from these
spatial reconstructions is amplitude and phase of the precipitation and temperature signal
at each climate division centroid. Given the amplitude and phase for each of these
variables spatially, we created vector plots, shown in Figure 3, to analyze the relative
strength of the signal spatially for a given frequency. In the ENSO frequency band
(0.1875 – 0.3721 cycles/year), for precipitation (Figures 3a and 3c), for example, the
results clearly show the known regions of the western US where the effects of the ENSO
signal are strongly felt. Note the opposing ENSO signal in Arizona and southwestern
California with the Pacific Northwest. It is known that (e.g., Ropelewski and Halpert,
1986) for winter precipitation, during El-Niño years, the Pacific Northwest is dry and its
wet over California and Arizona. The reverse happens during the La- Niña years. The
lengths of the arrows show the relative magnitude of the signals over the study area. For
15
temperature, the arrows are relatively smaller along the coastlines than inland. This is
physically intuitive as there is little temperature variation along coastal areas. The
frequency of 0.3721 cycles/year i.e., approximately the 3-year cycle has a predominant
counter-clockwise distribution of the temperature signal (Figure 3d). Apart from the
central, and extending to the northwest corner of the study area, the strength of the
temperature signal is relatively weak. This counter-clockwise pattern in temperature is
typical for El-Niño years when positive winter temperature anomalies are observed in the
northern parts of the western US and normal to negative temperature anomalies are
observed in the southern parts. The 0.1875 cycles/year frequency (Figure 3b) on the other
hand has a more complex spatial distribution, but clearly depicts certain ENSO
characteristics. For example, during El-Niño years, there exist significant variability in
temperature across the Pacific Northwest, which is characterized with positive
temperature anomalies. In general during La- Niña years, temperature anomalies over the
western US is largely uniformly distributed. Also both for precipitation and temperature
during summer months, the effects of ENSO is less significant.
Similarly for streamflow spatial reconstruction was done for the significant ENSO
frequency of 0.4482 cycles/year. From Figure 3e, the impact of ENSO is evident in the
form of a north-south contrast in streamflow amplitudes. In general, we see higher
streamflow amplitudes in the southwestern region and lower streamflow amounts in the
Pacific Northwest.
These observations for precipitation, temperature, and streamflow at the ENSO
frequencies are consistent with observations in contemporary literature (e.g., Ropelewiski
and Halpert 1986, 1989; Redmond and Koch 1991; Cayan and Webb 1992; Kayha and
16
Dracup 1993; Dettinger et al. 1998; Higgins et al. 2000), and provides confidence that
this frequency domain MTM-SVD analysis adequately reproduces the characteristic
features of low frequency phenomenon such as the ENSO over the western United States.
4.2.2 High Frequency
Similar to the low frequency spatial reconstructions, we did spatial
reconstructions for the annual cycles of precipitation, temperature and streamflow (see
Figure 4).
We observed that most of the precipitation annually occurs along the coastal
region and along the eastern border of the study area. The dry regions of Arizona,
southern Utah, California-Nevada border, and northwestern Idaho are characterized with
small amplitude. The temperature annual cycle exhibited strong seasonality, and was
shown to be present uniformly over the entire western US region.
Like precipitation for streamflow, we observed that along the coastal region and
along the eastern border of the study area the presence of a strong signal of annual cycle.
Streamflows in the northwest Washington and in southern Arizona show weak signals of
annual cycle. Though there are only a few gauging stations in the central region of the
study area, the arid interior West was quite clearly marked in the analysis.
In the next section we present a detail analysis to quantify the shifts in the
precipitation, temperature, and streamflow annual cycles over about 30 year time-periods
during pre- and post 1970’s.
4.3 Shifts in Annual Cycle
17
4.3.1 Precipitation and Temperature
To quantify the shifts in precipitation and temperature in the study area, we
further considered two periods, 1950-1975 and 1976-2000. The choice of these periods
was guided by the fact that post 1980 there has been a large number of ENSO events, and
we are interested to investigate how this low frequency component might influence the
annual cycle.
In order to calculate the phase shifts in the annual cycle over these two periods,
we first did a spatial reconstruction independently for the two periods, 1950-1975 and
1976-2000 (Figures 4a-4d). The phases obtained from these reconstructions were then
subtracted and converted to days for each of the 84 climate divisions (Figure 5). The
spatial distribution of the phase shifts in days is show in Figure 6a (for precipitation) and
Figure 6b (for temperature). In case of precipitation the shifts in the annual cycle are both
positive and negative. A positive shift implies an overall displacement of the annual cycle
curve for the period 1976-2000 to the left of the 1950-1975 annual cycle curve suggesting
an early occurrence of for example the peak events. A negative phase shift on the other
hand implies that similar events are occurring later and the annual cycle over the period
1976-2000 is generally displaced to the right of the annual cycle during 1950-1975. We
restricted the phase shifts for precipitation to within 30 days and it covered 72 climate
divisions, approximately 86 percent of all the climate divisions considered in this study.
Smaller phase shifts for precipitation were observed for regions where the annual cycle is
strong and has a well-defined annual variation, for example along the coastlines of
California and Oregon, and along the eastern margin of the study area (also see Figure 4).
18
Larger shifts (greater than 30 days) in precipitation were observed in the desert regions of
the study area for example, in western Arizona and southwestern Nevada. This is
intuitive, because for example, a single large storm can skew the distribution of the
precipitation annual cycle in these regions. Unlike precipitation, where the shifts have a
complex spatial distribution, the shifts in temperature are more clearly organized. Over
the two-analysis period (1950-1975; 1976-2000), we obtained a shift in temperature
ranging from 8 to 12 days and confirm contemporary studies (e.g., Mote, 2003). Also we
note the trend of an increase in phase shift with increasing latitude. The next question is,
are these shifts significant?
The western US spans regions of varied land cover types with extensive arid
zones and significant topographies. The effect of this widely varying geographical setting
on precipitation is evident in Figures 4a-b. So we expect considerable variation in the
levels of significance that can be attributed to the precipitation phase shift across the
climate divisions. Confidence limits were estimated through MTMSVD analysis of
bootstrapped historical time-series for the two individual analysis periods. Significant
precipitation phase shift was defined as the median phase shift across the 84 climate
divisions and this was estimated to be 6 days. The spatial distribution of these climate
divisions is shown in Figure 7a. This mostly includes climate divisions covering the,
Pacific Northwest, New Mexico, and Colorado. Phase shifts of temperature were found to
be significant at the 95 percent confidence level for all sites and ranged between 1 to
4 days (Figure 7b).
4.3.2 Streamflow
19
For streamflow we used the same two periods 1950-1975, and 1976-2000 to
diagnose shifts in the annual cycle. From Figure 6c, we see that shifts in annual
streamflow at all the stream gage locations apart from two sites are positive. This implies
that the peaks of streamflows over the period 1976-2000 are occurring earlier than the
ones over 1950-1975. Like precipitation, we restricted our attention to shifts within 30
days, and found that 74 out of the 84 sites (i.e. 88 percent of the study area) showed shifts
to within a month. We also estimated that the regional median significance of streamflow
shifts to be 6 days. The significant sites are shown in Figure 7c. These significant sites
generally follow the same spatial distribution as the significant precipitation climate
divisions, and show the obvious dependence of streamflow on precipitation.
However from Figures 6 and 7, we can only infer the magnitudes of the shift and
not the seasons during which the shifts are actually occurring. Also, we would like to
verify whether shifts as estimated from the above analysis are also evident at individual
sites using the raw annual time series. Results from selected individual site
reconstructions are described in the next section.
4.4 Annual Cycle Site Reconstructions
For precipitation (Figure 8) we considered two climate divisions, Arizona climate
division 2 (Northeast) and Utah climate division 6 (Uinta Basin). The Arizona climate
division was found to have the maximum negative shift of 28 days and the Utah site
showed a positive shift of 14 days. The top panel of Figure 8 was plotted using the timereconstructed annual cycle following the MTMSVD methodology. Once again, these two
plots show that the annual cycle as a whole has shifted. For example, in the case of the
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Utah climate division, the annual cycle is displaced to the left, confirming the positive
shift we inferred from the phase shift analysis above. Similarly, the Arizona site has an
overall rightward displacement, which confirms our negative shift inference in the earlier
analysis.
The bottom panel of Figure 8 is plotted using raw data for these two climate
divisions. In case of the Arizona site, we see that the winter peak in December during the
1950-1975 period is shifted to January during the 1976-2000 period (-28 day shift). The
summer peak in August however presents no shift. At the Utah site, we see that the
winter peak in December during 1950-1975 is shifted slightly towards January during
1976-2000, but the major shift is observed for the summer peak, which in the later period
is occurring in May instead of June, which was the case in the earlier period. The overall
effect of this lower rightward shift (December to January) of the winter peak and greater
leftward shift (June to May) of the summer peak results in a net earlier occurrence of the
annual cycle (14 day shift). At the both these sites we can also see an intensification of
the annual cycle during the 1976-2000 period over the 1950-1975 period.
Similarly, for temperature we considered two climate divisions where the shifts
were 8 days (Arizona climate division 2) and 12 days (Washington State climate
division 1). The top panel of Figure 9 was plotted using the MTMSVD timereconstructed annual cycle, and the bottom panel corresponds to the observed historical
time-series at these two locations for the 1950-1975 and 1975-2000 periods. Since the
shifts in temperature are less than a month, the exact period over which the shifts have
occurred is difficult to conclude. Nonetheless, we see that (bottom panel, Figure 9)
historically over these two periods, there has been an increase in the magnitude of
21
temperature. For the Washington site, which is at higher latitude, this increase in
temperature is more clearly visible. At the both the sites we see noticeable increase in
winter temperatures.
For streamflow we selected two sites, San Carlos River near Peridot, Arizona, and
the Coyote Creek near Golondrinas, New Mexico (Figure 10). Shifts in the annual cycle
peaks at the Arizona and New Mexico sites were found to be –14 days (late) and 26 days
(early) respectively. In the San Carlos River (AZ), the shift is in the winter peak. The
annual cycle peak in December during the period 1950-1975 is displaced towards January
in the later period (1976-2000), and is evident in Figures 10a and 10c. In case of Coyote
Creek, the shift in the peak is during summer, and from Figure 10b the peak appears to
have shifted from June (during 1950-1975) to May (during 1976-2000). Similar to
precipitation at the both these sites we see an intensification of the annual cycle during
the 1976-2000 period over the 1950-1975 period (Figures 10c and 10d).
So we hypothesize that the shifts we are observing in the annual cycle both in
case of precipitation and streamflow is due to intensification. Increased winter
temperatures increase the moisture holding capacity of the atmosphere leading to more
precipitation, which then results in the shifts of the precipitation annual cycle, and hence
the annual cycle of streamflow.
We next explore possible physical mechanisms to explain this hypothesis using
composites of vector winds, sea-surface temperature (SST), and sea-level pressure (SLP).
Also for streamflow, we conduct a principal component analysis between SST and
streamflows to develop further insights of inter annual variability.
22
4.5 Mechanisms of Shift in Annual Cycle
Most of the precipitation over the western US occurs during the winter season
(DJF) and in early Spring (MAM). We thus focus our analysis to the wintertime
conditions of wind, SST and SLP in the northern hemisphere during the two periods,
1950-1975 and 1976-2000. Climate composites were created using climate diagnosis
tools available through the CDC (Climate Diagnostic Center)-NOAA website
www.cdc.noaa.gov.
The proposed mechanism for shifts in precipitation from our analysis thus far is
an increase in precipitation intensity. Increase in precipitation intensity would require
additional moisture transport. In Figure 11 we present the wintertime 850 mb vector wind
composite as a difference between the later (1976-2000) and earlier (1950-1975) periods.
Note the direction of the winds over the sub-tropical Pacific Ocean blowing inland into
continental US. To get additional moisture we need a warmer ocean, and as winds blow
over warmer waters it would carry the additional moisture into the land. SST composites
are shown, similar to wind composites as a wintertime difference, in Figure 12. The
wintertime SST is about 1 oC warmer along the western US coastline regions over the
1975-2000 period than during 1950-1975. So these two composites (Figures 11 and 12)
confirm that there is additional moisture transport to this region. Coupled with this
increased moisture transport, increases in temperatures which enables the atmosphere to
retain this additional moisture provides a plausible mechanism for the seasonal shifts that
we have identified.
Furthermore, post 1980 we have seen a number of large ENSO events (not shown,
moving window MTM spectrum) and it is well understood that these tropical anomalies
23
do perturb the atmospheric circulation in the mid-latitudes (Clark et al., 2001). In case of
ENSO events the enhanced tropical convection results in intensification of the Hadley
circulation and a strengthening and eastward extension of the Pacific sub-tropical jet.
This also results in a deepening of the Aleutian low, and this is shown in Figure 13 (DJF
SLP difference between 1976-2000 and 1950-1975). This strengthened sub-tropical jet
entrains additional moisture from the Pacific Ocean, and increases the likelihood of
precipitation over the southwestern United States and a drier Pacific Northwest. This also
explains why we are observing significant shifts in precipitation and streamflows along
the southwestern US and in parts of Washington State (see Figure 7).
4.6 Principal component analysis of interannual variability of streamflow with SST
Principal component analysis is carried out using 61 annual (1940-2000)
streamflow data at the 84 streamflow gauging sites. The principal component spectrum
(Figure 14) shows that the first two leading principal components (PC1 and PC2) explain
about 58% of the total variance of the regional streamflows. PC1 explains 34% of the
total variance. This leading mode shows a north-south opposition pattern with dominant
mode of variation centered in the northern Idaho for the positive loading, and at the
border of Arizona and New Mexico for the negative loading (Figure 15a). PC2 explains
24% of the total variance and is manifested as the dominant mode of variation for the
western Colorado streamflows (Figure 15b). The spatial distribution of loadings for PC1
and PC2 show relatively minimal overlapping, suggesting that these two modes
complement each other. The two leading modes for regional streamflows also suggest
24
that there are organized modes of variability that may show associations with the largescale climate patterns.
To test this hypothesis we carried out a spectral coherence analysis between each
of the annual streamflow principal components, and January-April SST principal
components (see section 2.3). Before carrying out the spectral coherence analysis we
tested that both the PCs are significantly different from a background white-noise
process. Figure 16 shows the power spectrum of these two principal components, along
with the confidence levels. The spectrum of PC1 shows dual dominant timescales at the
90% confidence level including significant narrowband variability in the 15-18 year
inter-decadal range and in the 2.1-2.2 year quasi-biennial range (Figure 16a), while the
spectrum of PC2 shows the dominant timescale at the same confidence level in the
10-11 year quasi-decadal range only (Figure 16b). The next step then was to analyze
possible relationships between the PCs and coherent large-scale modes of SST
variability.
Spectral coherence between PC1 and tropical PC1 SST that corresponds to the
ENSO mode, show significant coherence at the 99% confidence levels (Figure 17a). For
PC2 we found, at the 99% confidence level significant coherence with the North Pacific
PC1 SST. The north Pacific PC1 SST corresponds to the Pacific Decadal Oscillation
(PDO, Schneider et al. 2002). We also found that these results are consistent with climate
composites of SSTs (not shown). The significant correlation between SST and the PC1
streamflow shows in the tropical Pacific area and the significant correlation between SST
and the PC2 streamflow shows in the north Pacific.
25
5. Summary and Conclusions
Analysis was carried out to understand the shifts in seasonality of the annual cycle
of precipitation, temperature and streamflow in the western United States. Two statistical
techniques, MTM-SVD and PCA were used in the analysis. Monthly precipitation and
temperature data from 84 climate divisions and monthly streamflows from 84 gauging
sites were used in the study. The first step in the analysis was to identify significant low
frequencies from joint and independent local fractional variance (LFV) spectra of the
three variables. Spatial reconstruction (amplitude and phase) at these selected frequencies
was done for precipitation, temperature and streamflow to determine the signal
distribution spatially. Spatial reconstruction was also done for the annual cycle for two
periods, 1950-1975 and 1976-2000. The next step was to analyze the shifts in the annual
cycle between these two periods. These shifts were computed both regionally and for
selected sites. The sites were chosen where the shift either early or late was a maximum.
From the LFV spectra, frequencies in the ENSO band, 0.1875 cycle/year (~ 5 yr
cycle), 0.3721 cycle/year (~ 3 year cycle), 0.4482 cycle/year (~ 2 year cycle) were
identified to be the significant (90% level) low frequency ( 0.5 cycle/year) components.
In addition, quasi-decadal and quasi-biennial frequencies were also found to be
significant. In this study, we restrict our attention to frequencies in the ENSO band. The
annual cycle and its higher-order harmonics (e.g. sub-annual cycle) were also found to be
significant. Spatial reconstruction at these low frequencies showed results consistent with
ENSO patterns in the region (e.g. a drier Pacific Northwest versus a wetter Southwest),
and provides confidence that the MTM-SVD method can adequately isolate this narrow
band variability regionally.
26
Analysis of the shifts of the annual cycle for the period 1976-2000 from
1950-1975 show that more that 85 percent of the study area have significant shifts
between 30 days (positive – early; negative – late) for precipitation and streamflow. For
temperature, the entire western US region experienced significant shifts, and this ranged
between 8 and 12 days. We also found that the temperature shifts were all positive and
greater at higher latitudes. These findings corroborate well with other studies (e.g. Mote
2003). Smaller shifts for precipitation and streamflow were observed for regions where
the annual cycle is strong and has a well-defined annual variation, for example along the
coastlines of California and Oregon. Larger shifts were generally observed in the desert
regions, and this is because, for example, a single large storm event can skew the
distribution of the precipitation and hence the streamflow annual cycles in these regions.
The next step was to explore physical mechanisms governing the shifts. Increased
winter temperatures increases the moisture holding capacity of the atmosphere, which
then leads to more precipitation. At the same time, there have been enhanced ENSO
activities in the post-1980 period. ENSO strengths the sub-tropical jet which then entrain
additional moisture from the Pacific Ocean. We believe that these two mechanisms drive
the shifts in precipitation and hence streamflow in the western US. Also we found that the
shifts in both precipitation and temperature are mostly concentrated in the Southwest and
Pacific Northwest (see Figure 7). These mechanisms were verified using climate
composites of SLP, SST and 850 mb vector winds.
The last step in this study was to study the interannual variability of streamflow
using PCA. We found that the first two principal components (PC1 and PC2) for annual
streamflow in this region explain nearly 58 percent of the variability in regional
27
streamflow. Also, PC1 and PC2 had significant coherence (99% level) with the tropical
PC1 SST (ENSO) and North Pacific PC1 SST (PDO).
Overall, we see that the western US region has experienced a positive shift (early
occurrence of annual streamflow peaks) in the later period (1976-2000). This is driven by
shifts in the precipitation annual cycle, which also has been largely positive (more than
70 out of 84 climate divisions, see Figure 6) for the region. The causes for this shift we
believe are increased winter temperatures and enhanced ENSO activities during the later
period. However, further research is necessary to develop a continued understanding of
these driving mechanisms in the climate system.
ACKNOWLEDGEMENTS
This research was funded by NSF grant XXXX and the CIRES/NOAA Western
Water Assessment Program.
28
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Figure Captions
Figure 1. Location of the 84 climate divisions, and 84 stream gage sites across the
western United States.
Figure 2. Low frequency (up to 0.5 cycles/year) local fractional variance (LFV)
spectrum: (a) joint precipitation and temperature; (b) only precipitation; (c) only
temperature; and (d) joint precipitation and streamflow.
Figure 3. Selected fixed frequency spatial reconstructions: (a) precipitation
(0.1875 cycles/year);
(b)
(0.3721 cycles/year);
(d)
temperature
temperature
(0.1875
cycles/year);
(0.3721 cycles/year);
and
(c)
(e)
precipitation
streamflow
(0.4482 cycles/year). Precipitation and temperature data are for 106 years (1895-2000),
and 61 years for streamflow (1940-2000).
Figure 4. Spatial reconstruction of the annual cycle: (a) precipitation, 1950-1975;
(b) precipitation, 1976-2000; (c) temperature, 1950-1975; (d) temperature, 1976-2000;
(e) streamflow, 1950-1975; and (f) streamflow, 1975-2000.
Figure 5. Estimation of phase shift between two periods P1 and P2, (a) early; (b) late.
Figure 6. Shifts in the annual cycle (days) over the two periods, 1950-1975 and
1976-2000 for, (a) precipitation, (b) temperature, and (c) streamflow.
35
Figure 7. Significant phase shift sites for, (a) precipitation, (b) temperature, and
(c) streamflow.
Figure 8 Shifts in the annual cycle at selected sites for precipitation, 1950-1975 (black
line), 1976-2000 (red line): (a-b) reconstructed annual cycle; (c-d) raw time-series.
Figure 9. Same as figure 8, but for temperature.
Figure 10. Same as figure 8, but for streamflow.
Figure 11. Northern hemisphere 850mb vector wind composite for DJF, 1976-2000
minus 1950-1975.
Figure 12. Global SST composite for DJF, 1976-2000 minus 1950-1975.
Figure 13. Global SLP composite for DJF, 1976-2000 minus 1950-1975.
Figure 14. Principal component spectrum of annual western U.S. streamflows.
Figure 15. Eigen vectors of, (a) PC1; (b) PC2, showing the spatial distribution of the
streamflow principal component loadings.
36
Figure 16. Power spectrum of western U.S. streamflow principal components, (a) PC1
and (b) PC2, and the confidence levels.
Figure 17. Spectral coherence: (a) western U.S. PC1 of streamflow and tropical PC1
SST; (b) western U.S. PC2 of streamflow and North Pacific PC1 SST, and confidence
levels.
37