TESTING FOR NONSTATIONARITY IN THE FIRST TWO MOMENTS OF PEAK
FLOW DATA IN CALIFORNIA
Nancy Ann Barth
B.A., University of California, Berkeley, 2001
THESIS
Submitted in partial satisfaction of
the requirements for the degree of
MASTER OF SCIENCE
in
GEOLOGY
at
CALIFORNIA STATE UNIVERSITY, SACRAMENTO
SUMMER
2010
ii
TESTING FOR NONSTATIONARITY IN THE FIRST TWO MOMENTS OF PEAK
FLOW DATA IN CALIFORNIA
A Thesis
by
Nancy Ann Barth
Approved by:
__________________________________, Committee Chair
David Evans, Ph.D., Department of Geology CSU, Sacramento
__________________________________, Second Reader
Charles Parrett, M.S., Retired Surface Water Specialist, US Geological Survey
__________________________________, Third Reader
Timothy Horner, Ph.D., Geology Professor, CSU, Sacramento
____________________________
Date
iii
iv
Student: Nancy Ann Barth
I certify that this student has met the requirements for format contained in the University format
manual, and that this thesis is suitable for shelving in the Library and credit is to be awarded for
the thesis.
__________________________, Department Chair
David Evans, Ph.D.
Department of Geology
v
___________________
Date
Abstract
of
TESTING FOR NONSTATIONARITY IN THE FIRST TWO MOMENTS OF PEAK
FLOW DATA IN CALIFORNIA
by
Nancy Ann Barth
Stationarity in the mean and standard deviation of annual peak discharge were
examined at 34 USGS streamflow-gaging stations. All stations were determined to be
free of significant upstream regulation, diversion, land-use change, or urbanization
effects and were representative of California’s varying hydrologic regions. Data from the
last 60 years (1947-2006 water years) were used for all sites, and the records were split
into two equal blocks (1947-1976 and 1977-2006) so that changes in means and standard
deviations (moments) of the logs of annual peak flows could be detected using
nonparametric statistical tests. The Mann-Whitney Rank Sum Test and the BrownForsythe test were used to determine if differences in the mean and standard deviation,
respectively, between the two 30-year periods were significant. A change in mean or
standard deviation was considered to be statistically significant if the p-value of the twosided test statistic was less than or equal to 0.10 (10% level of significance). The ShapiroWilk test for normality of annual peak flow data also was used for the entire 60 years of
record to ascertain if the data were normally distributed. The logs of the annual peak flow
data were considered to not be normally distributed if the p-value of the w test statistic
vi
was less than 0.05 (5% level of significance). A second method for visualizing trends in
the mean and standard deviation over the entire 60-year test period was applied using
Locally Weighted Scatterplot Smooth (LOWESS) curves.
Two sites showed a significant decrease in the means of annual peak discharge,
and five sites showed a significant change in standard deviation-- three sites showed a
significant increase, while two sites showed a significant decrease. Overall, the test
results indicate that differences in the means are not significantly different from zero and
can thus be considered stationary over the 60-year (1947-2006) period. However, the test
results for differences in standard deviation of annual peak discharge were not definitive.
While five sites showed a statistically significant change over the 60-year period, about
10 percent of the 34 test sites, or 3-4 sites, could be expected to show a significant change
by chance alone. Interestingly, the three sites with a significant increase in standard
deviation are in the northern part of California, while the two sites with a significant
decrease are in the northern Sierra-Nevada Range and southern California.
Average annual temperature and precipitation are the most likely explanatory
variables that account for significant changes in the standard deviation of the annual peak
discharge throughout the 60 years. Additional statistical parametric t and f tests were
performed on the mean and standard deviation, respectively, for both the average annual
temperature and precipitation for those climate divisions in which the 34 gage-sites are
located. All climate divisions tested showed a statistically significant increase in average
annual temperature, while all but the central California coastline showed a statistically
significant increase in the standard deviation of average annual precipitation.
vii
Pearson sample correlation tests were run among annual peak discharge, average
annual precipitation and the Multivariate ENSO Index (MEI) to identify any relationships
between the three time series. High correlations were not only found among concurrent
annual peak discharges within climate divisions, but between the annual peak discharges
and average annual precipitation. No correlation was found between peak discharge and
MEI, but sites in central and southern California showed the highest correlation between
average annual precipitation and MEI. While some correlations were found among the
three time series, no definitive relationship was found that would relate any changes in
standard deviation in annual peak discharge to longer-lived climate patterns such as
ENSO.
_______________________, Committee Chair
David Evans, Ph.D.
_______________________
Date
viii
ACKNOWLEDGMENTS
I would like to thank Charles Parrett, my primary thesis advisor from the U.S.
Geological Survey, for not only presenting me with the opportunity to study such an
interesting and relevant topic for my thesis work, but for the many hours he has dedicated
to my understanding of such complex statistical tests. I would also like to thank Dr. Jery
Stedinger from the Civil Engineering Department at Cornell University for his thorough
review of the statistical methods used in this study. Thanks to Dr. David Evans my thesis
advisor from the Geology Department at California State University, Sacramento for his
help in reviewing the methodologies employed in this study. In addition, thanks to Donna
Knifong from the U.S. Geological Survey for her technical support with the Geographic
Information System (GIS) graphics.
ix
TABLE OF CONTENTS
Page
Acknowledgments.................................................................................................................... ix
List of Tables ........................................................................................................................... xi
List of Figures ........................................................................................................................ xii
Chapter
1. INTRODUCTION ………………………………………………………….………….....1
Background ................................................................................................................... 1
Study Area Description ................................................................................................ 2
2. METHODOLOGY ............................................................................................................. 5
Statistical tests for nonstationarity in the first two moments ………………………. 5
Non-statistical test for trends in the first two moments ………………………….... 10
3. RESULTS ........................................................................................................................ 11
4. DISCUSSION ................................................................................................................... 22
5. CONCLUSIONS............................................................................................................... 27
Appendix A. Testing for Nonstationarity in the First Two Moments of Average Annual
Temperature and Precipitation for Selected California Climate Division………………… . 32
Appendix B. Correlation Tests between Annual Peak Discharge, Average Annual
Precipitation, and ENSO Anomalies…………………………………….…………… 45
Appendix C. Data …………………………………………………………………………... 76
References ......................................................................................................................... ... 142
x
LIST OF TABLES
Page
1.
Table 1 Results of nonparametric test for change in mean………………….… 29
2.
Table 2 Results of nonparametric test for change in standard deviation……… 30
3.
Table B.1 Latitude and longitude of basin centroids per climate division….… 50
4.
Table B.2 Correlation coefficients for climate division 1…………...…………….. 52
5.
Table B.3 Correlation coefficients for climate division 2…………..…………….... 53
6.
Table B.4 Correlation coefficients for climate division 4………………………….. 54
7.
Table B.5 Correlation coefficients for climate division 5………………….………55
8.
Table B.6 Correlation coefficients for climate division 6…………….…………... 56
9.
Table C.1 Annual peak stream-flow data for 34 USGS stations……………… 76
10.
Table C.2 Calculated average monthly temperature and precipitation values for
climate divisions…………………………………………………………….. 118
11.
Table C.3 Multivariate ENSO Index bimonthly data…………………………127
12.
Table C.4 Standardized annual peak, precipitation and MEI values……….....130
xi
LIST OF FIGURES
Page
1.
Figure 1 Map of 34 USGS stream-gaging stations used in study…………..…. ..3
2.
Figure 2 Map of California climate divisions……………………………………4
3.
Figure 3 2001 water year hydrograph for station number 11317000 …...……....6
4.
Figure 4 Log of annual peak discharges for station number 11317000…………7
5.
Figure 5 Results of nonparametric test for change in mean…………………….13
6.
Figure 6 LOWESS smooth curves for station 11476500…...…….…………….14
7.
Figure 7 LOWESS smooth curves for station 11532500.…….…..…………… 15
8.
Figure 8 Results of nonparametric test for change in standard deviation…....... 16
9.
Figure 9 LOWESS smooth curves for station 11132500……………...….…… 17
10.
Figure 10 LOWESS smooth curves for station 11317000…………..……….....18
11.
Figure 11 LOWESS smooth curves for station 11318500………...…...……… 19
12.
Figure 12 LOWESS smooth curves for station 11413000……………..……… 20
13.
Figure 13 LOWESS smooth curves for station 11478500………………...…... 21
14.
Figure A.1 Results of parametric tests for changes in climate data div 1………37
15.
Figure A.2 Results of parametric tests for changes in climate data div 2…....... 38
16.
Figure A.3 Results of parametric tests for changes in climate data div 4…....... 39
17.
Figure A.4 Results of parametric tests for changes in climate data div 5...…… 40
18.
Figure A.5 Results of parametric tests for changes in climate data div 6...…….41
19.
Figure B.1 Multivariate ENSO Index plot ……………………………..……... 47
20.
Figure B.2 Multivariate ENSO Index plot with El Nino and La Nina events.....47
xii
21.
Figure B.3 Box plots of correlations between concurrent annual peak flows.....57
22.
Figure B.4 Climate Div 1 correlations and distance between centroids..….…...57
23.
Figure B.5 Climate Div 2 correlations and distance between centroids……......58
24.
Figure B.6 Climate Div 4 correlations and distance between centroids ….……58
25.
Figure B.7 Climate Div 5 correlations and distance between centroids ….……59
26.
Figure B.8 Climate Div 6 correlations and distance between centroids ……….59
27.
Figure B.9 Box plots of correlation between precipitation and annual peaks…. 60
28.
Figure B.10 Time series of precipitation and annual peaks station 11478000….64
29.
Figure B.11 Time series of precipitation and annual peaks station 11413000….65
30.
Figure B.12 Time series of precipitation and annual peaks station 11317000… 66
31.
Figure B.13 Time series of precipitation and annual peaks station 11318500.. ..67
32.
Figure B.14 Time series of precipitation and annual peaks station 11132500….68
33.
Figure B.15 Time series of precipitation in climate div 1 and MEI….….……...70
34.
Figure B.16 Time series of precipitation in climate div 2 and MEI …….……...71
35.
Figure B.17 Time series of precipitation in climate div 4 and MEI …….……...72
36.
Figure B.18 Time series of precipitation in climate div 5 and MEI …….……...73
37.
Figure B.19 Time series of precipitation in climate div 6 and MEI …….……...74
xiii
1
Chapter 1
INTRODUCTION
Background
The U.S. Geological Survey (USGS) is updating flood frequency statistics at
streamflow-gaging stations throughout California for the first time in over 30 years.
Updated flood-frequency data will result in more effective planning, management, and
use of the State’s land and water resources, both of which are coming under
unprecedented demand in the 21st Century. Better flood-frequency information also will
help protect lives and property. This new study has the benefit of using an additional 30
years of peak discharge data, as well as new methodologies for incorporating historical
flood information to more accurately predict characteristics of flood frequency
distributions. Yet with global climate change likely to affect long-term streamflow
characteristics, a fundamental assumption of flood frequency analysis, stationarity (no
systematic change over time of the annual flood data), is being questioned (Milly, et al.,
2008).
Reliable estimates of the magnitude and frequency of annual peak flows at both
gaged and ungaged sites requires data and predictive equations based on stationary
hydrologic parameters. Thus, in order to determine flood frequency, statistical parameters
(moments), mean, standard deviation, and skew, used to fit probability distributions to
recorded data must also be stationary. Much attention has been given to the implications
of nonstationarity in annual peak discharge data (Milly et al, 2008), and different
mathematical approaches for calculating flood-frequency statistics from assumed
2
nonstationary hydrologic systems have been suggested (Strupczewski and Kaczmarek,
2001, Cunderlik and Burn, 2003, and Leclerc and Ouarda, 2007). Other studies have used
long-term simulated flow records to determine the effects of nonstationarity in the first
two moments of annual maximum flows in various hydrological settings (Strupczewski et
al, 2001 and Renard et al, 2008). Little work has been done, however, particularly in
California, to test for nonstationarity in the first two moments of annual peak flow data
based solely on existing long-term flow records. This paper presents the results of testing
for nonstationarity in the first two moments (mean and standard deviation) using
nonparametric statistical tests of annual peak-flow data from 34 California streamflowgaging stations whose flow records indicate little or no effects from land-use changes or
streamflow regulation.
Study Area Description
The study area used to test for nonstationarity in annual peak flow data includes
all of California except the desert region east of the Sierra-Nevada Range and the desert
region of southern California (Figure 1). Except for these desert regions, the 34 sites
included in this study generally are dispersed throughout northern, central and southern
California, with the largest concentration of sites along the coast and in the foothills and
mountains of the Sierra-Nevada. The sites are representative of the diverse hydrologic
conditions within California and the associated basins are located within the following
five climate divisions: (1) North Coast Drainage, (2) Sacramento Drainage, (4) Central
3
Coast Drainage, (5) San Joaquin Drainage, and (6) South Coast Drainage
(http://www.esrl.noaa.gov/psd/data/usclimate/map.html#California) (Figure 2).
Figure 1. Map of 34 USGS stream-gaging stations. These 34 sites were used to test for
nonstationarity in the first two moments of peak flow data in California.
4
Figure 2. Map of California climate divisions.
5
Chapter 2
METHODOLOGY
Statistical tests for nonstationarity in the first two moments
To test whether the first two moments (mean and standard deviation) of annual
peak flow data are nonstationary, changes in the moments were examined at currently
operated USGS stream-gaging stations (through water year 2006). The water year spans a
window from October 1st to the following September 31st. For example, the annual peak
data recorded in water year 2001 is the largest instantaneous peak discharge from
October 1st 2000 to September 31st 2001 (Figure 3). All stations included in this study
were sites for which information in the USGS databases indicated no upstream regulation
or diversion effects, nor any significant effects due to land-use change or urbanization. In
addition, sites that had zero flows were not included in this study. To ensure the overall
sampling window would include the period of possible climate-change effects over the
last 30 years (Hansen et al, 2006 and Duffy et al, 2007), data from the last 60 years
(1947-2006) were used for all selected sites. Thus these sites represent unregulated
systems for which nonstationarity, if any, could be the result of climate change forcings.
A list of all 34 USGS streamflow-gaging stations and their annual peak discharge values
used in this study are listed in Table C1 at the end of this report.
6
Figure 3. 2001 water year hydrograph for station number 11317000. Arrow indicates the
recorded instantaneous annual peak discharge for the 2001 water year (195 cfs)
(http://waterdata.usgs.gov/nwis).
The 60-year period at each site was split into two equal blocks (1947-1976
and1977-2006) so that nonstationarity in the mean and standard deviation of the logs of
annual peak flows could be detected using nonparametric statistical tests. The use of
nonparametric statistical tests does not require that the data are normally distributed.
Because the USGS and other Federal Agencies use the Log Pearson Type III (LP3)
distribution to fit the log of annual peak data and their related mean, standard deviation,
and skew (moments) to determine magnitude and exceedance probabilities (IACWD,
1982), it is assumed that the population of data is not best fit by a normal distribution.
Thus the nonparametric Mann-Whitney U test (Helsel and Hirsch, 2002) and the Brown-
7
Forsythe test (Brown and Forsythe, 1974) were used to determine if the mean and
variance (square of the standard deviation), respectively, of annual peak discharges in the
first half of a station’s peak discharge record were significantly different from those in
the second half (Figure 4). A difference in mean or standard deviation was considered to
be significant if the p-value of the resulting two-sided u-test or f-test statistic,
respectively, was less than or equal to 0.10 (10% level of significance). The additional
Shapiro-Wilk normality test was performed for each site to determine if the sample data
was indeed drawn from a normal distribution (Shapiro and Wilk, 1965).
Figure 4. Log of annual peak discharges (cubic feet per second) for station number 11317000.
Annual peak record covers 60 years (1947-2006).
8
Testing for normality in the 60 years of data was determined first for each site
using the following equation (Shapiro and Wilk, 1965):
(1)
where
ai = (a1, …, an) =
mT = (m1, …, mn) denotes the vector of expected values of standard
normal order statistics
V = corresponding n x n covariance matrix
yi = (y1, …, yn) denotes a vector of ordered random observations
= the mean of the observations
Failure of normality was delineated if the p-value of the two-sided w-test statistic was
less than 0.05 (5% level of significance).
Testing for a significant change in a station’s mean between the two 30-year
blocks was assessed using the Mann-Whitney U test using the following equation for
large-sample approximations (Helsel and Hirsch, 2002):
if Wrs > mw
Zrs =
if Wrs = mw
(2)
if Wrs < mw
where
Wrs = sum of ranks from the group having the smaller sample size
=
i i= 1, n (using either group when sample sizes are equal: n=m)
where
µW
= 0.5n(N + 1) is the mean (mW)
9
σW = (nm(N + 1)/12)0.5 is the standard deviation (sW)
where
N
= n + m, n is the sample size of one group and m is the second sample
size of the other group
and
Zrs = compared to a table of the standard normal distribution for
evaluation of the test results
A difference in mean was considered statistically significant if the significant if the twosided u test statistic was less than or equal to 0.010 ( 10% level of significance).
Finally, to test for significant changes in the second moment, the standard
deviation, the Brown-Forsythe test for equality of variances was employed. This
statistical test performs a one-way analysis of variance (ANOVA) on the transformation
of the response variable, in this case the log of annual peak discharge. Thus the spread (or
variance—the standard deviation squared) of the response variable is defined as the
absolute deviations from the median of the sample using the following equation (Brown
and Forsythe, 1974):
(3)
where
is the median of the sample group and Yij is the value of the jth
sample of the ith group
The f statistic of the transformed data is calculated by (Brown and Forsythe, 1974):
(4)
where
N
is the total number of observations, p is the number of groups, nj is
the number of observations in group j
10
and
is the mean of the Zij for group I
(5)
is the mean of all Zij
(6)
A difference in standard deviation was considered statistically significant if the
significant if the two-sided f test statistic was less than or equal to 0.010 ( 10% level of
significance).
Non-statistical test for trends in the first two moments
A second method for visualizing changes in the mean and standard deviation over
the entire 60-year test period was applied using Locally Weighted Scatterplot Smooth
(LOWESS) curves (Helsel and Hirsch, 1992). The LOWESS smoothing procedure is an
iterative weighted least-squares regression method that weights data points more highly if
they are close in both the X and Y directions to the point being fitted. The effect of
outliers thus is minimized using LOWESS, and trends are easily visualized from the
resultant smoothed curves through the data. Trends in mean are discerned from a
LOWESS curve through the logs of the annual peak discharge. Trends in standard
deviation are discerned from separate LOWESS curves drawn through the positive and
negative residuals from the first LOWESS curve through the peaks. A LOWESS curve
through the positive residuals represents a smoothed median of the residuals, or a
smoothed curve of the upper quartile of the peaks. Likewise, a LOWESS smooth curve
through the negative residuals represents a smoothed curve of the lower quartile of the
annual peaks. The difference between the upper and lower quartiles (inter-quartile range)
11
is analogous to the variance of the peaks. An increasing spread between the upper and
lower LOWESS curves indicates an increasing variance of the peaks, and a decreasing
spread indicates a decreasing variance.
Chapter 3
RESULTS
Results from the Shapiro-Wilk test for normality and the nonparametric statistical
tests for the first two moments using the Mann-Whitney U test and the Brown-Forsythe
test, respectively, are shown in Tables 1 and 2. The results from the Shapiro-Wilk test
verify that at least one third of the stations’ data were not normally distributed. Results
from the Mann-Whitney U test indicated that only two sites out of 34 showed a
statistically significant change in their mean from the first 30 years of record to the
second 30 years. Both sites showed a decrease in their means (USGS stations 11476500
and 11532500) and are located along the northern coastline of California (Figure 5).
LOWESS curves for the two stations with significant changes in mean are shown in
Figures 6 and 7.
In contrast, results from the nonparametric Brown-Forsythe test showed that five
of 34 sites had a statistically significant change in their standard deviations from the first
30 years of record to the second 30 years. Three sites showed a significant increase in
standard deviation (USGS stations 11478500, 11317000 and 11318500), while two sites
showed a significant decrease (USGS stations 11132500 and 11413000) (Figure 8). Sites
12
with an increase in their standard deviation were located along the northern California
coastline and the central Sierra-Nevada mountain range, while the two sites with a
decrease in their standard deviation were located in the northern Sierra-Nevada mountain
range and along the southern coastal range. LOWESS curves for the five stations that had
statistically significant change in their standard deviations are shown in Figures 9-13.
13
Figure 5. Results of nonparametric test for change in mean. Only two of 34 sites showed a
statistically significant change in the mean of annual peak discharge from 1947-2006.
14
Figure 6. LOWESS smooth curves for station 11476500. Station 11476500 recorded a
statistically significant decrease in the mean from the first 30-year period (1947-1976) to
the second 30 years (1977-2006) using the nonparametric Mann-Whitney U test (p-value
= 0.10). The middle red line plots the mean of the annual discharge values (1947-2006),
the upper and lower blue dashed lines plot the means of the positive and negative
residuals, respectively. The width between the dashed lines represents the inter-quartile
distance (variance). The vertical green line delineates the first 30 years of data from the
second 30 years.
15
Figure 7. LOWESS smooth curves for station 11532500. Station 11532500 showed a
statistically significant decrease in the mean from the first 30-year period (1947-1976) to
the second 30 years (1977-2006) using the nonparametric Mann-Whitney U test (p-value
= 0.05). The middle red line plots the mean of the annual discharge values (1947-2006),
the upper and lower blue dashed lines plot the means of the positive and negative
residuals, respectively. The width between the dashed lines represents the inter-quartile
distance (variance). The vertical green line delineates the first 30 years of data from the
second 30 years.
16
Figure 8. Results of nonparametric test for change in standard deviation. Five of 34 sites
showed a statistically significant change in the variance of annual peak discharge from
1947-2006.
17
Figure 9. LOWESS smooth curves for station 11132500. Station 11132500 showed a
statistically significant decrease in the standard deviation from the first 30-year period
(1947-1976) to the second 30 years (1977-2006) using the nonparametric BrownForsythe f test (p-value = 0.09). The middle red line plots the mean of the annual
discharge values (1947-2006), the upper and lower blue dashed lines plot the means of
the positive and negative residuals, respectively. The width between the dashed lines
represents the inter-quartile distance (variance). The vertical green line delineates the first
30 years of data from the second 30 years.
18
Figure 10. LOWESS smooth curves for station 11317000. Station 11317000 showed a
statistically significant increase in the standard deviation from the first 30-year period
(1947-1976) to the second 30 years (1977-2006) using the nonparametric BrownForsythe f test (p-value = 0.06). The middle red line plots the mean of the annual
discharge values (1947-2006), the upper and lower blue dashed lines plot the means of
the positive and negative residuals, respectively. The width between the dashed lines
represents the inter-quartile distance (variance). The vertical green line delineates the first
30 years of data from the second 30 years.
19
Figure 11. LOWESS smooth curves for station 11318500. Station 11318500 showed a
statistically significant increase in the standard deviation from the first 30-year period
(1947-1976) to the second 30 years (1977-2006) using the nonparametric BrownForsythe f test (p-value = 0.10). The middle red line plots the mean of the annual
discharge values (1947-2006), the upper and lower blue dashed lines plot the means of
the positive and negative residuals, respectively. The width between the dashed lines
represents the inter-quartile distance (variance). The vertical green line delineates the first
30 years of data from the second 30 years.
20
Figure 12. LOWESS smooth curves for station 11413000. Station 11413000 showed a
statistically significant decrease in the standard deviation from the first 30-year period
(1947-1976) to the second 30 years (1977-2006) using the nonparametric BrownForsythe f test (p-value = 0.09). The middle red line plots the mean of the annual
discharge values (1947-2006), the upper and lower blue dashed lines plot the means of
the positive and negative residuals, respectively. The width between the dashed lines
represents the inter-quartile distance (variance). The vertical green line delineates the first
30 years of data from the second 30 years.
21
Figure 13. LOWESS smooth curves for station 11478500. Station 11478500 showed a
statistically significant increase in the standard deviation from the first 30-year period
(1947-1976) to the second 30 years (1977-2006) using the nonparametric BrownForsythe f test (p-value = 0.04). The middle red line plots the mean of the annual
discharge values (1947-2006), the upper and lower blue dashed lines plot the means of
the positive and negative residuals, respectively. The width between the dashed lines
represents the inter-quartile distance (variance). The vertical green line delineates the first
30 years of data from the second 30 years.
22
Chapter 4
DISCUSSION
The results of applying the nonparametric Mann-Whitney U test and the BrownForsythe test to annual peak-flow data at long-term California gage sites with no
substantial regulation or land-use change indicates stationarity in the mean over the past
60 years (1947-2006) (Figure 5). While five sites showed a statistically significant
change in the standard deviation over the past 60-year period, about 10 percent of the 34
test sites used in this study, or 3-4 sites, could be expected to show a significant change
by chance alone. Collectively, more sites showed an increase in variance (standard
deviation squared) than a decrease, even though only three were statistically significant
(Figure 8). Although the test results suggest variance may be increasing, the test results
are not definitive. The majority of sites that showed nonstationarity in their standard
deviation, four out of five sites, lie in the northern portion of the state (Figure 8). Sites
located in the northern third of the state show an overall increase in standard deviation,
although station 11413000 (North Yuba River below Goodyears Bar) showed a
statistically significant decrease in standard deviation. The southern Sierra-Nevada
mountain range and central coastline show mixed standard deviations and none that were
statistically significant. The southern coastline of California also showed a mixed
population, but site 111325000 (Salsipuedes Creek near Lompoc) showed a statistically
significant decrease in standard deviation.
23
The LOWESS smooth curves offer a visual, non-statistical approach to evaluate
changes in the mean and variance throughout a station’s 60-year annual peak discharge
record. LOWESS plots were generated for those sites that showed a statistically
significant change in their first two moments, i.e., two sites for the mean and five sites for
the variance (Figures 6-7 and Figures 9-13, respectively). Of the two sites that showed a
statistically significant change in their mean, unfortunately, only one of two LOWESS
smooth curves showed a modest visual decrease in mean (station 11532500, Figure 7).
Yet four of five LOWESS curves visually showed modest changes in the inter-quartile
distances (variance) between the positive and negative residuals from the first LOWESS
curve of the logs of the annual peak discharges. Thus, comparisons between the results of
the statistical tests and the LOWESS curves are not clear cut for annual peak discharge
records.
This study tested for nonstationarity in the first two moments (mean and standard
deviation) of annual peak discharge over a longer-term, 60-year window to minimize
noise that is attributed to smaller sample sizes. All 34 sites had continuous streamflow
records (no missing years of flow) and no zero flows. Thus, a relatively small number of
sites qualified to be included in this study. The sites were spatially distributed throughout
California’s broad hydrologic regimes and varying elevations. The majority of the sites
were located along the lower elevation coastal range and higher elevation Sierra-Nevada
range. The remaining sites were located in the northern and central valleys. Nonetheless,
despite having a smaller number of stations in this study, more sites than expected
showed a statistically significant change in their standard deviations from the first 30-
24
year block to the second 30 years. Perhaps these changes in annual peak flows are related
and thus influenced by changing cyclic variations in climate forcings, such as the El-Niño
Southern Oscillation (ENSO) episodes or the inter-decadal, long-term Pacific Decadal
Oscillations (PDO).
Two additional tests were run to investigate potential explanations for the
apparent tendency toward increased variance but not in the mean in California’s annual
peak discharge over the last 60-year period. First, statistical parametric t and f tests were
performed on the mean and standard deviation, respectively, of average annual
temperature and precipitation for five climate divisions for which the 34 stream-gaging
stations in this study were located. They included (1) North Coast Drainage, (2)
Sacramento Drainage, (4) Central Coast Drainage, (5) San Joaquin Drainage, and (6)
South Coast Drainage
(http://www.esrl.noaa.gov/psd/data/usclimate/map.html#California) (Figure 2). As
discussed in Appendix A, all five climate divisions showed a statistically significant
increase in their average mean temperature but not standard deviation. Thus California,
too, has recorded a steady increase in average annual temperature similar to what has
been documented on a global scale (Milly, et al., 2008) (Figures A1-A5). Additionally,
all but one climate division, the Central Coast Drainage, showed statistically significant
changes in the standard deviation in average annual precipitation (Figures A1-A5). Thus,
both annual peak discharge and precipitation throughout the corresponding climate
divisions have recorded some statistically significant changes from the first 30-year block
to the second 30 years.
25
The second set of tests that were run were the Pearson sample correlation
tests between annual peak discharge, average annual precipitation per climate division,
and a longer-term, cyclic climate forcing, ENSO. As discussed in Appendix B, there were
high correlations among concurrent flows for all stations within a climate division
regardless of the distance between their basin centroids. Each climate division certainly
recorded the same hydrologic response to regional-scale annual weather fluctuations.
There were relatively high correlations between annual peak discharge and the average
annual precipitation that fell within the corresponding climate divisions. Therefore, if
these time series were highly correlated during the 60-year window, perhaps the longerterm ENSO anomalies that control longer-lived climate patterns would share the same
relationships.
No correlation was found between annual peak discharge and the longer-lived
climate forcing, ENSO. The correlation between annual average precipitation and the
Multivariate ENSO Index (used to monitor ENSO anomalies) from 1950-2006 varied
among climate divisions (Figures B15-B19). There was no correlation in the northern
third of the state, nor along the Central Coast Drainage. Yet the San Joaquin Drainage
(central valley and central Sierra-Nevada mountain range) and the South Coast Drainage
showed increased, albeit small, correlation values. These results appear to agree with
weather patterns attributed with shifts in ENSO anomalies. When the drier
La Niña anomalies are present, the jet stream moves further north to the Pacific northwest
and southern British Columbia (Appendix B). When the wetter El Niño anomalies are
present, the jet stream is guided down to southern California; these El Niño events
26
typically bring increased precipitation to southern California. Furthermore Figure B2,
shows that over the last 30 years (1977-2006) there were more
El Niño events than from 1950-1976. These conditions would allow for more favorable
opportunities of increased precipitation ranges (variability) over the last 30 years in
central and southern California. However, sites in central and southern California
recorded mixed results of increases or decreases in annual peak discharge during this
same period.
Figures B10-B14 plot both annual peak discharges for the five sites that showed a
statistically significant change in standard deviation and average annual precipitation.
These figures visually confirm the statistical tests of changes in the standard deviations
over the second half of the 60-year record and the high correlation between the two time
series. Figures B15-B19 also shows the increased variability in the second half of the
record and the relatively strong correlation between average annual precipitation and
MEI. The highest correlations between these time series are found when both time series
record strong annual anomalies (positive and negative deviations). Yet despite the
statistical and correlation tests, these studies did not definitively relate a change in
variation from a small scale (annual peak discharge within an individualized basin) to the
average precipitation that fell within a region, to the large-scale, longer-lived climate
forcing ENSO.
27
Chapter 5
CONCLUSIONS
Nonparametric statistical tests, the Mann-Whitney U and the Brown-Forsythe
tests, were used to test for nonstationarity in the first two moments (mean and standard
deviation), respectively, of California’s annual peak flow data over a 60-year period
(1947-2006). Thirty-four USGS stream-gaging stations with no upstream regulations or
diversions, continuous annual peak flow data, and nonzero discharges were used for this
analysis. Only two stations in northern California near the coast showed a statistically
significant change in their mean over the 60 years; these finding indicate stationarity in
the first moment. However, five sites showed a statistically significant change in standard
deviation. Three stations showed an increase while two showed a decrease. The stations
were distributed along the northern and southern coastline and in the northern and central
Sierra-Nevada range. Thus, stationarity in the second moment is not as clear.
Two additional statistical tests were run to evaluate if climate forcing may have
influenced the variation of annual peak flow. The parametric t and f tests were used to
test for nonstationarity in the mean and standard deviation, respectively, in the average
annual temperature and precipitation for those climate divisions for which the 34 streamgaging sites are located. All regions showed a uniform statistically significant increase in
mean temperature and all but one, the Central Coast Drainage, showed statistically
significant increases in standard deviation in average annual precipitation over the last 30
years. Pearson sample correlation tests were run between annual peak discharge, average
annual precipitation and the Multivariate ENSO Index (MEI) to identify any relationships
28
between the three time series. High correlations were not only found among concurrent
annual peak discharges within climate divisions, but between annual peak discharges and
average annual precipitation. No correlation was found between annual peak discharge
and MEI, but central and southern California showed the highest correlation between
average annual precipitation and MEI. While correlations were found between the three
time series, no definitive relationship was found that would relate the increased standard
deviation in annual peak discharge to longer-lived climate patterns such as ENSO.
29
Table 1. Results of nonparametric test for change in mean from 1947-2006 (water years) using the MannWhitney U test. The p-value is considered to be statistically significant if ≤ 0.10 (10% level of
significance). P-value codes are defined as: (1) an increase, (2) a statistically significant increase, (3) a
decrease, (4) a statistically significant decrease.Climate divisions realte to Figure 2.
30
Table 2. Results of nonparametric test for change in standard deviation from 1947-2006 (water years) using
the Brown-Forsythe test. The p-value is considered to be statistically significant if ≤ 0.10 (10% level of
significance). P-value codes are defined as: (1) an increase, (2) a statistically significant increase, (3) a
decrease, (4) a statistically significant decrease.Climate divisions realte to Figure 2.
31
APPENDICIES
32
APPENDIX A
TESTING FOR NONSTATIONARITY IN THE FIRST TWO MOMENTS OF
AVERAGE ANNUAL TEMPERATURE AND PRECIPITATION FOR SELECTED
CALIFORNIA CLIMATE DIVISIONS
Chapter A.1
INTRODUCTION
To test whether the first two moments (mean and standard deviation), of the
average annual temperature and precipitation for selected California climate divisions,
are stationary, changes in the moments were examined for a 60 year block (1947-2006).
This study was designed to parallel the results of testing for nonstationarity in the first
two moments of annual peak discharge during this same time sampling window. It has
been shown that over the last 30 years, a global increase in temperature has been recorded
(Hansen et al, 2006 and Duffy et al, 2007), but have these general global temperature
increases also been recorded in California? A change in average annual temperature and
precipitation patterns throughout California would influence a drainage basin’s
hydrologic response to the changing climate conditions and thus would have some effects
on the recorded annual peak discharge collected at a stream gage within the drainage
basin (Miller, 2003).
33
Chapter A.2
METHODOLOGIES
California is divided into seven climate divisions as described by the National
Oceanic and Atmospheric Administration (NOAA)
(http://www.esrl.noaa.gov/psd/data/usclimate/map.html) (Figure 2). This study evaluated
climate data for five climate divisions. The 34 USGS streamflow-gaging stations for
which the annual peak discharges were being tested for nonstationarity (Figure 1) are
located within five climate divisions: (1) North Coast Drainage, (2) Sacramento
Drainage, (4) Central Coast Drainage, (5) San Joaquin Drainage, and (6) South Coast
Drainage (http://www.esrl.noaa.gov/psd/data/usclimate/map.html#California) (Figure 2).
Average annual temperature and precipitation for each of the five climate divisions were
calculated from 1947-2006 (water years—October 1st to September 31st of the following
year) using monthly data from NOAA (http://www.esrl.noaa.gov/psd/cgibin/data/timeseries/timeseries1.pl).
Statistical test for nonstationarity in the first two moments
Within each of the five climate divisions, the 60-year period was split into two
equal blocks (1947-1976 and1977-2006) so that nonstationarity in means and standard
deviations of the average annual temperature and precipitation could be detected using
parametric statistical tests. Because the data is comprised of annual averages rather than
annual extreme values, this study assumed the average data would likely be normally
distributed. Thus parametric statistical tests were used. T and f tests were used to
34
determine whether the mean and standard deviations, respectively, of average annual
climate data in the first half of a climate division’s record were significantly different
from those in the second half. A difference in mean or standard deviation was considered
to be significant if the p-value of the resulting two-sided t or f-test statistic was less than
or equal to 0.10 (10% level of significance). The f-test statistic was computed first,
because the equation for computation of the t-statistic depends on whether an equal or
unequal standard deviation is found. The f-test statistic (f) was computed using the
following equation:
f=
where
and
(A1)
are the sample variances
If the f-test statistic is significantly different from one (sx2 = sy2) the sample variances are
considered to be significantly different. To compute the t-statistic, the following equation
was used:
t=
where
and
,
sx = sy
(A2)
are the sample means and sx and sy are the sample standard
deviations of the data in the first and second groups, n and m are the corresponding
sample sizes, and s is the pooled sample standard deviation calculated from:
s=
(A3)
35
and
t=
,
sx ≠ sy
(A4)
Equation A2 was used for equal variances while equation A4 was used for unequal
variances (Helsel and Hirsch, 1992).
Non-statistical test for trends in the first two moments
A second method for visualizing changes in mean and standard deviation over the
entire 60-year test period was applied using Locally Weighted Scatterplot Smooth
(LOWESS) curves (Helsel and Hirsch, 1992). The LOWESS smoothing procedure is an
iterative weighted least-squares regression method that weights data points more highly if
they are close in both the X and Y directions to the point being fitted. The effect of
outliers thus is minimized using LOWESS, and trends are easily visualized from the
resultant smoothed curves through the data. Trends in mean are discerned from a
LOWESS curve through the average annual temperature and precipitation. Trends in
standard deviation are discerned from separate LOWESS curves drawn through the
positive and negative residuals from the first LOWESS curve through the climate data. A
LOWESS curve through the positive residuals represents a smoothed median of the
residuals, or a smoothed curve of the upper quartile of the climate values. Likewise, a
LOWESS smooth curve through the negative residuals represents a smoothed curve of
the lower quartile of the climate values. The difference between the upper and lower
36
quartiles (inter-quartile range) is analogous to the variance of the annual data values. An
increasing spread between the upper and lower LOWESS curves indicates an increasing
variance of the annual climate data, and a decreasing spread indicates a decreasing
variance.
Chapter A.3
RESULTS
All of the climate divisions, 1, 2, 4, 5, and 6, for which the parametric t test was
run to look for significant changes in the mean of the average annual temperature over a
60 year window (1947-2006), uniformly showed a statistically significant increase from
the first 30 year block to the second 30 years. However, the f test showed no statistically
significant change in standard deviation in any climate division. The non-statistical
LOWESS plots clearly record an increase trend in the average annual temperature in all
five climate divisions (Figures A1-A5).
Climate divisions 1, 2, 5 and 6, all showed statistically significant increases in
their standard deviations of the average annual precipitation from the first 30-year block
to the second 30 years using the parametric f test. However, climate division 4, the
Central Coast Drainage, showed an increase in the standard deviation of average annual
precipitation but it was not statistically significant. Notably, none of the five climate
divisions showed a statistically significant change in the mean of average annual
precipitation over the 60-year window. The non-statistical LOWESS plots visually
showed changes in the inter-quartile distances (variance) between the positive and
37
negative residuals from the first LOWESS curve of the average annual precipitation
throughout the 60-year period (Figures A1-A5). Yet comparisons between the results of
the statistical tests and the LOWESS curves for variance were not as clear as the
relationships for the average annual increase in temperature.
Figure A1. Results of parametric tests for changes in climate data division 1. Figure A1a. plots
the LOWESS curves for a statistically significant increase in average annual temperature and
Figure A1b. plots the LOWESS curves for a statistically significant increase in standard deviation
of average annual precipitation. The middle red line plots the mean of the values (1947-2006),
the upper and lower blue dashed lines plot the means of the positive and negative residuals,
respectively. The width between the dashed lines represents the inter-quartile distance (variance).
The vertical green line delineates the first 30 years of data from the second 30 years.
38
Figure A2. Results of parametric tests for changes in climate data division 2. Figure A2a. plots
the LOWESS curves for a statistically significant increase in average annual temperature and
Figure A2b. plots the LOWESS curves for a statistically significant increase in standard deviation
of average annual precipitation. The middle red line plots the mean of the values (1947-2006),
the upper and lower blue dashed lines plot the means of the positive and negative residuals,
respectively. The width between the dashed lines represents the inter-quartile distance (variance).
The vertical green line delineates the first 30 years of data from the second 30 years.
39
Figure A3. Results of parametric tests for changes in climate data division 4. Figure A3a. plots
the LOWESS curves for a statistically significant increase in average annual temperature and
Figure A3b. plots the LOWESS curves for an increase in standard deviation of average annual
precipitation. The middle red line plots the mean of the values (1947-2006), the upper and lower
blue dashed lines plot the means of the positive and negative residuals, respectively. The width
between the dashed lines represents the inter-quartile distance (variance). The vertical green line
delineates the first 30 years of data from the second 30 years.
40
Figure A4. Results of parametric tests for changes in climate data division 5. Figure A4a. plots
the LOWESS curves for a statistically significant increase in average annual temperature and
Figure A4b. plots the LOWESS curves for a statistically significant increase in standard deviation
of average annual precipitation. The middle red line plots the mean of the values (1947-2006),
the upper and lower blue dashed lines plot the means of the positive and negative residuals,
respectively. The width between the dashed lines represents the inter-quartile distance (variance).
The vertical green line delineates the first 30 years of data from the second 30 years.
41
Figure A5. Results of parametric tests for changes in climate data division 6. Figure A5a. plots
the LOWESS curves for a statistically significant increase in average annual temperature and
Figure A5b. plots the LOWESS curves for a statistically significant increase in standard deviation
of average annual precipitation. The middle red line plots the mean of the values (1947-2006),
the upper and lower blue dashed lines plot the means of the positive and negative residuals,
respectively. The width between the dashed lines represents the inter-quartile distance (variance).
The vertical green line delineates the first 30 years of data from the second 30 years.
Chapter A.4
DISCUSSION AND CONCLUSIONS
Results of the parametric statistical t and f tests applied to the average annual
temperature and precipitation for climate divisions 1, 2, 4, 5 and 6 indicate a quantifiable
change in climate conditions from the first 30 years of record (1947-1976) to the second
30 years (1977-2006). While published literature show an increase in mean air
temperature on a global scale, the results of this study also show that an increase in
42
temperature has been recorded at a regional level throughout California. There is a
uniform increase in average annual temperature along not only the California coastline,
but also the inland valleys of California and the Sierra-Nevada mountain range. The nonstatistical LOWESS approach clearly plots this increase in mean average annual
temperature and further validates the lack of significant change in variability (standard
deviation squared) over the last 60 years.
In contrast, the results of this study show an increase in standard deviation in
average annual precipitation. All but one climate division, the Central Costal Drainage,
showed statistically significant increases in average annual precipitation over the last 60
years. Interestingly, not one climate division in this study showed a statistically
significant change in the mean average annual precipitation. Moreover, the non-statistical
LOWESS curves showed modest changes in variability as opposed to the definitive
visual increase found in the mean of average annual temperature.
The average annual temperature and precipitation data, as before mentioned, were
calculated from October 1st to September 31st of the following year to mimic results of
annual peak flow data collected over this period (i.e., a water year). For a particular year,
an average annual temperature data point is not as sensitive as precipitation when
including all values. Because California receives the majority of its precipitation during
the months of October to April (seven months), the remaining five months would have
much lower values. Including these low values would unnecessarily reduce the mean and
have a dampening effect on outliers on a yearly level. However, to maintain consistency
between the water year data for which annual peak data is collected and the precipitation
43
that would have fallen during that same period, all months were included. Yet
remarkably, a change in the variance in the average annual precipitation was still
captured using both statistical and nonstatistical measures.
This study has not only captured a smaller regional scale change in temperature
over the last 60 years, which on a global scale is one catalyst for changes in climate
patterns, but has also recorded an increased variability in annual precipitation. The
increased average annual temperature in various drainage basins would have differing
hydrologic effects. This could affect how precipitation is stored in a basin, rainfall versus
snowfall, and would further affect the timing of annual peak flow runoff. Additionally, an
increased variability in average annual precipitation would not only present substantial
challenges for water resource managers to properly regulate runoff in California’s
streams and rivers, but the hydrologic and environmental conditions would in turn be
affected. Thus, further analyses of causes for these observed changes in mean
temperature and variance in precipitation is recommended. Perhaps correlation test
between the longer-lived climate pattern, such as the El-Niño Southern Oscillation
(ENSO) events that affect California’s annual storm tracks and related weather patterns,
and average annual precipitation might account for these longer-term changes (Appendix
B).
Thus, nonstationarity in the first moment, the mean, of average annual
temperature was found using the parametric statistical t test in all five climate divisions
reviewed in this study. The entire California coastline, the inland central valley and the
Sierra-Nevada range all recorded this regional increase in average annual temperature
44
over the last 60 years (1947-2006). Nonstationarity in the second moment, the standard
deviation, of the average annual precipitation was found using the parametric statistical f
test in four out of five climate divisions. All climate divisions showed an increase in
variability between the first 30-year block to the second 30 years. Effective comparisons
could be made between the statistical test results and the non-statistical LOWESS plots
for changes in the mean of average annual temperature, but were not as reliable for the
changes in variability in average annual precipitation.
45
APPENDIX B
CORRELATION TESTS BETWEEN ANNUAL PEAK DISCHARGE, AVERAGE
ANNUAL PRECIPITATION, AND ENSO ANOMALIES
Chapter B.1
INTRODUCTION
California’s annual precipitation patterns are largely influenced by the position of
the jet stream and the associated storm tracks during its rainy seasons, October to April
(Kingtse and Higgins, 1998). These storm tracks are driven by larger-scale climate
patterns from the northern Pacific. Abnormally wet or dry annual precipitation patterns in
California are thought to be influenced by persistent circulation patterns across the
Pacific (i.e., El-Niño Southern Oscillation (ENSO) anomalies) (Kingtse and Higgins,
1998). ENSO anomalies are shorter-lived, lower frequency climate oscillations that have
an average 3-5 year cycle and are influence by the Pacific Ocean sea surface temperatures
(SSTs) (Miller, 2003). El Niño is characterized by unusually warm temperatures and La
Niña by unusually cool temperatures in the western equatorial Pacific
(http://www.elnino.noaa.gov/). El Niño is named for its positive phase and La Niña for its
negative phase (Miller, 2003). Thus, California’s abnormally wet precipitation patterns
are believed to occur when a strong, positive phase of ENSO, El Niño, occurs and
abnormally dry conditions are guided by negative phased, La Niña events (Miller, 2003).
During the warm episode of ENSO (El Niño), the eastern shift in the
trough [jet stream] typically sends the storm track, with huge amounts of
46
tropical moisture, into California, south of its normal position of the
Pacific Northwest. Very strong El Niños will cause the trough to shift
further south with the average storm track position moving into Southern
California. During these times, rainfall in California can be significantly
above normal, leading to numerous occurrences of flash flood and debris
flows. With the storm track shifted south, the Pacific Northwest becomes
drier and drier as the tropical moisture is shunted south of the region.
(http://www.srh.noaa.gov/jetstream/tropics/enso_impacts.htm)
During a cool episode of ENSO, La Niña, the annual jet stream is variable and moves
farther north in latitude. This increases the annual precipitation in the northwestern
United States and southwestern Canada
(http://www.cpc.noaa.gov/products/analysis_monitoring/ensocycle/nawinter.shtml).
ENSO anomalies are monitored using the Multivariate ENSO Index (MEI). This
MEI uses six climate variables over the tropical Pacific to calculate standardized
departures for each season and the 1950-1993 reference periods
(http://www.esrl.noaa.gov/psd/people/klaus.wolter/MEI/) (Figure B1). All standardized
positive values record the El Niño phase, associated with California’s wetter annual
precipitation values, and negative standardized values record the drier, La Niña events.
Over the 1950-2006 MEI time series, the first 27-year period (1950-1976) is dominated
by La Niña events, while the last 30 years (1977-2006) are dominated by El Niño events
(Figure B2).
47
Figure B.1 Multivariate ENSO Index (MEI) plot . The bimonthly deviations of the ElNiño Southern Oscillation (ENSO) anomalies are measured by (MEI). The positive red,
warm phase episodes are associated with El Niño and the negative, cool phase episodes
are associated with La Niña episodes.
Figure B.2. Multivariate ENSO Index (MEI) plot with El Niño and La Niña events. Note
the first half of the record (1950-1976) is dominated by the drier patterns of La Niña and
the second half of the record (1977-2006) is dominated by the wetter patterns of El Niño.
48
This study analyses whether the frequency of these extreme wet and dry
precipitation events, related to persistence and magnitude of ENSO anomalies, over the
last 57 years (1950-2006) can be detected in long-term annual peak discharge records and
average annual precipitation records. Pearson correlation sample coefficients (r) were
calculated to test for frequency relations between annual peak discharge records, average
annual precipitation records, and ENSO (MEI) values.
Chapter B.2
METHODOLOGY
The log values of annual peak discharge records at 34 USGS streamflow-gaging
stations over sixty years (1947-2006) were used in these correlation tests (Figure 1).
Annual peak discharge is the highest recorded instantaneous flow recorded at a stream
gage during a water year (October 1st to September 31st of the following year). All annual
peak flows were deemed not to be influenced by upstream regulation or diversions.
Average annual precipitation was calculated for five of seven climate divisions in
California over the same 60 year period and over the same annual time interval (i.e., a
water year). Appendix A in this report further describes these methods. The following
five climate divisions contain the 34 USGS stream-gaging stations: (1) North Coast
Drainage (6 sites), (2) Sacramento Drainage (11 sites), (4) Central Coast Drainage (5
sites), (5) San Joaquin Drainage (7 sites), and (6) South Coast Drainage (5 sites)
(http://www.esrl.noaa.gov/psd/data/usclimate/map.html#California) (Figure 2). Table C3
contains the bimonthly values of the standardized MEI from which standardized average
49
annual MEI values were generated for this study. It must be noted that the annual time
series used for the MEI values span from 1950-2006 and are annual calendar averages.
Finally, to run the Pearson sample correlations, all three time series: annual peak flow,
average annual precipitation and MEI were standardized.
The following equation was used to standardize each annual peak flow and
average annual precipitation value:
(B1)
where
has a normal distribution with mean
deviation
and standard
(modified from Devore, 2008).
Annual standardized values for the MEI time series were calculated by averaging the
standardized MEI values in Table C3. Table C4 lists the standardized values of the
annual peak discharge for stations located within a particular climate division, the
average annual precipitation and the average bimonthly MEI.
The following equations were used to calculate the Pearson sample correlation
coefficients:
(B2)
where
where
(B3)
and
are the sample means (Devore, 2008).
50
Finally, for each of the five climate divisions, the generated Pearson sample
correlation coefficients from equations B2 and B3 were plotted as a function of the
distance between the locations of each stream gage’s drainage basin centroid. Table B1
lists the corresponding latitude and longitude of each gaging-station’s centroid per
climate division.
51
Chapter B.3
RESULTS
Correlations between concurrent annual peak flows per climate division
Over the 60 year period (1947-2006), relatively high correlation coefficients
generated from equations B2 and B3 were found. They ranged between 0.62 (climate
division 6—the South Coast Drainage) to 0.85 (climate division 5--San Joaquin
Drainage) (Tables B2-B6). Figure B3 shows the box plots of Pearson sample correlation
coefficients for concurrent annual peak flow from 1947-2006 (water year) for all climate
divisions. Figures B4-B8 shows the correlations values and their variance as a function of
distance between site pair drainage area centroids. All climate divisions except 2, showed
little change in variance between the high correlation values and the distance between the
drainage basin centroids. The maximum distance between basin centroids in a particular
climate division ranged from 80 miles in climate division 4 to just over 200 miles in
climate division 2. Divisions 1, 5 and 6 all had maximum drainage basins distances
around 160 miles.
52
Table B.2. Correlation coefficients for climate division 1. Listed are the correlations
coefficients between concurrent annual peak discharges for six USGS stream-gaging
stations located within climate division 1, precipitation and MEI, as well as correlations
between average annual precipitation and MEI.
53
Table B.3. Correlation coefficients for climate division 2. Listed are the correlations
coefficients between concurrent annual peak discharges for 11 USGS stream-gaging
stations located within climate division 2, precipitation and MEI, as well as correlations
between average annual precipitation and MEI.
54
Table B.4. Correlation coefficients for climate division 4. Listed are the correlations
coefficients between concurrent annual peak discharges for five USGS stream-gaging
stations located within climate division 4, precipitation and MEI, as well as correlations
between average annual precipitation and MEI.
55
Table B.5. Correlation coefficients for climate division 5. Listed are the correlations
coefficients between concurrent annual peak discharges for seven USGS stream-gaging
stations located within climate division 5, precipitation and MEI, as well as correlations
between average annual precipitation and MEI.
56
Table B.6. Correlation coefficients for climate division 6. Listed are the correlations
coefficients between concurrent annual peak discharges for five USGS stream-gaging
stations located within climate division 6, precipitation and MEI, as well as correlations
between average annual precipitation and MEI.
57
Figure B.3. Box plots of correlations between concurrent annual peak flow (per climate
division).
Figure B.4. Climate division 1 correlation and distance between centroids (six individual
sites).
58
Figure B.5. Climate division 2 correlation and distance between centroids (11 individual
sites).
Figure B.6. Climate division 4 correlation and distance between centroids (5 individual
sites).
59
Figure B.7. Climate division 5 correlation and distance between centroids (seven
individual sites).
Figure B8. Climate division 6 correlation and distance between centroids (five individual
sites).
60
Correlations between annual peak flows and average annual precipitation per
climate division
Over this same 60-year period, relatively high correlation values were found
between annual peak flow data and the average annual precipitation that fell over the
corresponding climate division. Figure B9 shows the box plots of the range in correlation
values for each climate division. The correlation values ranged from 0.66 (climate
division 6) to 0.76 (climate division 4—Central Coast Drainage).
Figure B.9. Box plots of correlation between precipitation and annual peaks.
61
Correlations between annual peak discharge, average annual precipitation and MEI
Since the MEI time series used in this study only spanned 57 years (1950-2006),
correlation coefficients were generated for all time series over this same time window.
There were was no correlation in any climate division between MEI and annual peak
discharge. However, there was a fairly wide range of correlation values between MEI and
average annual precipitation (Tables B2-B6). They ranged between 0.09 (climate division
1—North Coast Drainage) to 0.30 (climate division 6).
Chapter B.4
DISCUSSIONS AND CONCLUSIONS
If California’s longer-term climate patterns are influenced by a larger-scale
climatic forcing, ENSO, then it should follow that annual weather patterns which yield
precipitation would be influenced. Furthermore, if California’s annual weather patterns
are affected, then regional-scale precipitation patterns should be influenced. These
changes in annual precipitation patterns would then affect the amount of potential runoff
in a small-scale drainage basin and would thus influence the magnitude of recorded
annual peak discharge.
This study shows that within each of the five evaluated climate divisions, the
concurrent annual peak flows over a 60-year period (1947-2006) are highly correlated
(Figure B3). There are some differences in the inter-quartile distance of correlation
values between site pairs in each climate division and some variance in mean correlation
values among climate divisions. This may be the result of an unequal number of sites
62
examined per climate division. It might also be a result of different drainage basin
hydrologic responses to the same storms. Another way to visualize the variance among
concurrent annual peak flows within a climate division is to evaluate how the correlation
coefficients change with distances between the drainage basins. The 34 sites used in this
study are not equally distributed between all five climate divisions, and the sites do not
cover the same spatial distances (Figures B4-B8). However, within each climate division,
the relative magnitudes of concurrent annual flows are still highly correlated. This
implies that stream-gaging sites within the same climate division, whether they are closer
in proximity or are further apart, are still capturing a localized regional effect in annual
peak flow. Therefore precipitation was tested as this effect.
Average annual precipitation is one possible explanatory variable that might
describe the high correlation of concurrent annual peak flow per climate division. This
study found relatively high correlations between annual peak flow and average annual
precipitation (Figure B9). Divisions 1 and 2, which record the overall precipitation for
northern California, had the largest inter-quartile distances. Divisions 4 and 5, which
record the overall precipitation for the central portion of California, had the smallest
inter-quartile distances and the higher mean correlations. Climate division 6 had the
lowest mean correlation and a modest inter-quartile distance (Figure B9). The ranges in
inter-quartile distances most likely are related to varying local precipitation events over a
drainage basin versus over a larger, regional scale. As discussed in Appendix A, the
average annual precipitation includes 12 months of precipitation, seven wetter months
and five drier months. Thus the calculated average annual precipitation value is lower due
63
to inclusion of the drier months. Nonetheless, there does seem to be relatively high
correlations between peak flow and precipitation.
Figures B10-B14 shows the standardized annual peak discharge and the average
annual precipitation for its corresponding climate division over the 60-year interval
(1947-2006). The figures further show the relatively high correlations and the strong
alignment of positive and negative deviations from normal. High positive deviations
relate abnormally high flow and precipitation events, while the negative deviations
relate very low flow and drier precipitation patterns. Throughout these time series plots,
each climate division seems to record strong positive and negative deviations from
normal at different intervals. All divisions record strong negative deviations (dry spells)
in 1976 and 1977 and several large high positive deviations (wet periods) in 1969, 1983,
1996. While the timing of these positive and negative deviations differ somewhat
throughout the climate divisions, all regions have recorded abnormally high and low
precipitation events and related annual peak discharge magnitudes throughout this 60
year window. In addition, all climate divisions during the second 30 years (1977-2006)
recorded equal or more high positive deviation events related El Niño anomalies. Perhaps
a longer-term climate forcing can account for these extreme statewide events.
64
Figure B.10. Time series of precipitation and annual peaks, station 11478000.
Standardized annual peak discharge (USGS station 11478500Van Duzen River near
Bridgeville) and average annual precipitation for climate division 1 (1947-2006 water
years).Vertical black line delineates the first 30 years of record (1947-1976) from the
second 30 (1977-2006).
65
Figure B.11. Time series of precipitation and annual peaks, station 11413000.
Standardized annual peak discharge (USGS station 11413000 North Yuba River below
Goodyears Bar) and average annual precipitation for climate division 2 (1947-2006 water
years).Vertical black line delineates the first 30 years of record (1947-1976) from the
second 30 (1977-2006).
66
Figure B.12. Time series of precipitation and annual peaks, station 11317000.
Standardized annual peak discharge (USGS station 11317000 Middle Fork
Mokelumne River at West Point) and average annual precipitation for climate division 5
(1947- 2006 water years).Vertical black line delineates the first 30 years of record
(1947-1976) from the second 30 (1977-2006).
67
Figure B.13. Time series of precipitation and annual peaks, station 11318500.
Standardized annual peak discharge (USGS station 11318500 South Fork
Mokelumne River near West Point) and average annual precipitation for climate
division 5 (1947-2006 water years).Vertical black line delineates the first 30 years of
record (1947-1976) from the second 30 ( 1977-2006).
68
Figure B.14. Time series of precipitation and annual peaks, station 11132500.
Standardized annual peak discharge (USGS station 11132500 Salsipuedes Creek near
Lompoc) and average annual precipitation for climate division 6 (1947-2006 water
years).Vertical black line delineates the first 30 years of record (1947-1976) from
the second 30 (1977-2006).
Correlation tests between annual peak discharge and average annual precipitation
were run against the MEI to determine if there is any relationship between these extreme
precipitation events. We know the strong warm phases of ENSO, El Niño events, bring
an increased potential for heavy annual precipitation and its opposite, La Niña, can yield
drought events to the state of California. However, there was no correlation between
annual peak discharge per climate division and MEI. This is a reasonable result because
there are numerous physiographic and climatic conditions that account for the magnitude
of annual peak discharge in a particular drainage basin. However, there was a wide range
69
in correlations between average annual precipitation and MEI. They ranged from 0.09 in
climate division 1 to 0.30 in division 6. Figures B15-B19 shows the average annual
precipitation versus MEI. These figures further show that from northern to southern
California different climate regions are more closely aligned and sensitive to strong
deviations in the two time series. Precipitation deviations in the central and southern
portions of the state appear to correlate more closely to MEI than the northern portion of
the state. Because strong ENSO anomalies, El Niño and La Niña, shift the jet stream
further south to southern California or to the higher latitudes of the northwestern United
States, respectively, there should be a higher correlation between the climate forcing
(ENSO) that controls the amount of annual precipitation available for the central and
southern portions of California. These correlation tests show this relationship between the
extreme anomalies in the time series, but not across the full 60-year window.
70
Figure B.15. Time series of precipitation in climate division 1 and MEI. Standardized
average annual precipitation and average MEI for climate division 1 (1950-2006 water
years).Vertical black line delineates the first 27 years of record (1950-1976) from the
second 30 (1977-2006).
71
Figure B.16. Time series of precipitation in climate division 2 and MEI .Standardized
average annual precipitation and average MEI for climate division 2 (1950-2006 water
years).Vertical black line delineates the first 27 years of record (1950-1976) from the
second 30 (1977-2006).
72
Figure B.17. Time series of precipitation in climate division 4 and MEI. Standardized
average annual precipitation and average MEI for climate division 4 (1950-2006 water
years).Vertical black line delineates the first 27 years of record (1950-1976) from the
second 30 (1977-2006).
73
Figure B.18. Time series of precipitation in climate division 5 and MEI. Standardized
average annual precipitation and average MEI for climate division 5 (1950-2006 water
years).Vertical black line delineates the first 27 years of record (1950-1976) from the
second 30 (1977-2006).
74
Figure B.19. Time series of precipitation in climate division 6 and MEI. Standardized
average annual precipitation and average MEI for climate division 6 (1950-2006 water
years).Vertical black line delineates the first 27 years of record (1950-1976) from the
second 30 (1977-2006).
This study analyzed whether the frequency of these extreme wet and dry
precipitation events, related to persistence and magnitude of ENSO anomalies, over the
last 57 years (1950-2006) can be detected in long-term annual peak discharge records at
34 USGS stream-gaging stations and average annual precipitation records. Pearson
correlation sample coefficients (r) were calculated to test for frequency relations between
annual peak discharge records, average annual precipitation records, and ENSO (MEI)
values. There were high correlations between concurrent annual peak discharges within
the five climate divisions, and relatively high correlation between annual peak discharge
75
and average annual precipitation in each climate division. These two time series were
likely influenced by the same larger-scale storm patterns. Yet there was no correlation
between annual peak discharge and MEI. However, an increase in correlation values
between average annual precipitation and MEI in the central and southern California
climate divisions (4, 5 and 6) was found and is most likely due to the annual storm tracks
related to strong ENSO, (El Niño and La Niña) events. More importantly, in all climate
divisions the stronger positive and negative deviations of average annual precipitation
and MEI time series, corresponding to abnormally wet and dry precipitation events, were
identified. In addition, all climate divisions during the second 30 years (1977-2006)
recorded equal or more high positive deviation events related El Niño anomalies. Thus
while there were no definitive relations found between all three time series over the entire
57 years (1950-2006), there is evidence to link the strong positive and negative deviations
to recorded annual peak discharge, precipitation and ENSO patterns.
76
APPENDIX C
DATA
Chapter C.1
TESTING FOR NONSTATIONARITY IN THE FIRST TWO MOMENTS OF PEAK
FLOW DATA IN CALIFORNIA
Table C.1. Annual peak stream-flow data used for 34 USGS stream-gaging stations within
California (1947-2006 water years). First column lists the USGS station number, followed by the
date of the recorded annual discharge, the discharge value (cubic feet per second), and finally the
recorded gage-height (http://nwis.waterdata.usgs.gov/ca/nwis/peak).
Z10310000
H10310000
N10310000
310310000
310310000
310310000
310310000
310310000
310310000
310310000
310310000
310310000
310310000
310310000
310310000
310310000
310310000
310310000
310310000
310310000
310310000
310310000
310310000
310310000
310310000
310310000
310310000
310310000
310310000
310310000
310310000
USGS
3846111194958000632003SW1605020165.4
5754.50
WEST FORK CARSON RIVER AT WOODFORDS, CA
19470502 635
19480516 708
19490424 824
19500516 747
19501120 4730
19520520 1100
19530425 813
19540422 701
19550512 596
19551223 4810
19570518 880
19580518 1650
6
19590405 320
3.60
19600409 350
3.70
19610417 237
3.39
19620504 677
4.93
19630201 4890
9.006
19631115 552
3.72
19641223 3100
6.70
19660407 331
3.07
19670524 1590
5.01
19680429 360
2.65
19690513 1240
4.16
19700122 860
3.88
19710626 675
3.50
19720505 387
2.82
19730515 837
3.78
19731111 1100
4.28
77
310310000
310310000
310310000
310310000
310310000
310310000
310310000
310310000
310310000
310310000
310310000
310310000
310310000
310310000
310310000
310310000
310310000
310310000
310310000
310310000
310310000
310310000
310310000
310310000
310310000
310310000
310310000
310310000
310310000
310310000
310310000
310310000
Z11055500
H11055500
N11055500
311055500
311055500
311055500
311055500
311055500
311055500
311055500
311055500
311055500
311055500
311055500
311055500
311055500
311055500
311055500
311055500
311055500
19750519
19751026
19770610
19780514
19790522
19800504
19810424
19811220
19821026
19840511
19850415
19860308
19870516
19880513
19890420
19900415
19910507
19920417
19930519
19940419
19950601
19960516
19970101
19980607
19990528
20000413
20010430
20020414
20030530
20040505
20050518
20051231
1290
4.33
259
2.37
318
2.56
884
3.75
808
3.53
1100
3.87
514
2.89
1730
4.57
795
3.56
999
3.79
744
3.47
1620
4.63
330
2.57
170
2.21
629
3.24
313
2.59
490
2.91
304
2.61
935
3.99
251
2.47
1460
4.81
3040
5.46
8100
7.32
1130
13.24
1110
13.21
656
12.57
415
12.04
772
12.77
898
12.96
462
12.16
2150
14.10
2720
14.35
USGS
3407061170827000606071SW1807020316.9
PLUNGE C NR EAST HIGHLANDS CA
19461120 1705
1.70
19480403 1955
1.83
19490120 69.05
1.14
19491219 1565
1.62
19510429 52.05
1.00
19511230 3605
1.882
19521202 62.05
1.06
19540125 6835
2.56
19550227 49.05
1.01
19560127 16305
2.87
19570228 16305
2.87
19580403 17205
2.92
19590216 6025
2.03
19600208 29.05
0.89
19601106 26.05
0.82
19611202 5365
2.04
19630209 99.05
1.23
1590.00
78
311055500
311055500
311055500
311055500
311055500
311055500
311055500
311055500
311055500
311055500
311055500
311055500
311055500
311055500
311055500
311055500
311055500
311055500
311055500
311055500
311055500
311055500
311055500
311055500
311055500
311055500
311055500
311055500
311055500
311055500
311055500
311055500
311055500
311055500
311055500
311055500
311055500
311055500
311055500
311055500
311055500
311055500
311055500
Z11055800
H11055800
N11055800
311055800
311055800
311055800
311055800
311055800
311055800
19640401
19650409
19651122
19661206
19680308
19690125
19700301
19701129
19711224
19730211
19740107
19750308
19760301
19770103
19780304
19790327
19800129
19810129
19820317
19830227
19831125
19841219
19860215
19870104
19880420
19890204
19900217
19910301
19920212
19930107
19940207
19950305
19960221
19970126
19980224
19990209
20000223
20010212
20011125
20021109
20040226
20050110
20060404
48.05
1.04
3715
1.83
42005
6.07
47705
5.20
1905
1.50
46105
5.96
1005
6
30005
7.41
7855
5.57
4665
4.20
1145
3.08
2485
3.53
3955
4.05
4505
4.20
18305
6.34
3505
3.90
17805
6.29
3565
4.45
4655
5.22
13605
5.30
2505
4.56
1225
4.07
6145
4.69
67.05
3.79
1485
4.06
3305
4.40
4985
4.59
4775
4.57
14205
5.12
15405
6.33
2135
4.31
14705
6.27
1895
4.23
8185
5.51
14505
6.20
375
3.47
1905
4.15
485
3.54
9.75
2.98
3845
4.68
2675
4.38
39205
9.66
6005
5.23
USGS
3408381171116000606071SW1807020319.6
CITY C NR HIGHLAND CA
19461113 2855
3.03
19480403 2505
2.93
19490120 1005
2.43
19491219 1985
2.86
19510429 71.05
2.29
19520116 9375
4.13
1580.00
79
311055800
311055800
311055800
311055800
311055800
311055800
311055800
311055800
311055800
311055800
311055800
311055800
311055800
311055800
311055800
311055800
311055800
311055800
311055800
311055800
311055800
311055800
311055800
311055800
311055800
311055800
311055800
311055800
311055800
311055800
311055800
311055800
311055800
311055800
311055800
311055800
311055800
311055800
311055800
311055800
311055800
311055800
311055800
311055800
311055800
311055800
311055800
311055800
311055800
311055800
311055800
311055800
19521202
19540125
19541111
19560127
19570113
19580203
19590216
19600209
19601105
19611202
19630210
19640401
19650409
19651122
19661206
19671120
19690225
19700228
19701221
19711224
19730211
19740108
19750308
19760911
19761022
19780209
19790327
19800129
19810129
19820317
19830227
19831225
19841219
19860215
19870104
19880301
19890106
19900217
19910301
19920212
19930107
19940207
19950305
19960220
19970126
19980223
19990210
20000223
20010212
20020128
20030316
20031225
1325
6315
1155
8625
16505
13505
3585
42.05
92.05
6485
1635
64.05
2925
13105
30805
2175
70005
2055
1005
7225
4925
1265
1035
3265
8605
25105
3595
36305
1035
3305
11405
2875
2005
5305
1085
1085
2625
1755
4605
8535
19105
1885
22605
4455
13605
22105
375
1625
1055
8.75
2725
80005
2.65
3.73
2.50
4.08
4.862
5.142
3.63
2.45
2.83
4.14
3.06
2.95
3.92
5.86
7.23
3.12
9.39
4.24
4.20
5.72
5.37
4.49
4.46
5.64
7.60
8.16
5.04
9.12
5.33
6.98
6.89
5.40
5.07
5.96
4.57
4.57
5.29
4.93
5.80
6.49
7.68
4.96
7.97
5.74
7.15
8.62
4.65
4.84
4.61
3.51
5.27
80
311055800
311055800
Z11098000
H11098000
N11098000
311098000
311098000
311098000
311098000
311098000
311098000
311098000
311098000
311098000
311098000
311098000
311098000
311098000
311098000
311098000
311098000
311098000
311098000
311098000
311098000
311098000
311098000
311098000
311098000
311098000
311098000
311098000
311098000
311098000
311098000
311098000
311098000
311098000
311098000
311098000
311098000
311098000
311098000
311098000
311098000
311098000
311098000
311098000
311098000
311098000
311098000
311098000
20050110 99005
10.68
20060404 12205
5.852
USGS
3413201181036000606037SW1807010516.0
ARROYO SECO NR PASADENA CA
19461225 600
4.052
19480429 45.0
1.84
19490120 35.0
1.60
19491110 150
2.76
19510429 12.0
1.70
19520116 1090
4.75
19521202 49.0
1.80
19540124 571
4.00
19550430 107
2.39
19560126 815
4.30
19570223 158
2.84
19580403 715
4.23
19590216 351
3.54
19600112 170
2.88
19601106 769
4.30
19620211 1500
5.06
19630209 464
3.75
19640121 182
2.94
19650409 194
3.00
19651122 3160
6.33
19661206 1530
4.80
19671119 1720
4.99
19690125 8540
9.37
19700228 668
3.78
19701129 1330
4.60
19711224 222
2.84
19730211 3740
6.43
19740308 390
3.22
19750306 535
3.58
19760209 590
3.64
19770509 230
2.88
19780304 5360
7.57
19790221 193
2.82
19800216 3080
6.06
19810129 627
3.76
19820317 615
3.74
19830302 2640
6.09
19831225 217
3.06
19841216 139
2.79
19860130 213
3.05
19870105 13.0
1.58
19880229 457D
3.57
19881216 155
2.83
19900217 163
2.86
19910301 921
4.30
19920211 1710
5.25
19930117 1710
5.25
1397.88
81
311098000
311098000
311098000
311098000
311098000
311098000
311098000
311098000
311098000
311098000
311098000
311098000
311098000
Z11124500
H11124500
N11124500
311124500
311124500
311124500
311124500
311124500
311124500
311124500
311124500
311124500
311124500
311124500
311124500
311124500
311124500
311124500
311124500
311124500
311124500
311124500
311124500
311124500
311124500
311124500
311124500
311124500
311124500
311124500
311124500
311124500
311124500
311124500
311124500
311124500
311124500
311124500
311124500
19940207
19950110
19960221
19961222
19980223
19990209
20000220
20010213
20020128
20030212
20040226
20050109
20060102
129
2.69
1730
5.27
584
3.83
569
3.81
4380
7.34
62
2.34
509
3.66
348
3.37
41
2.13
433
3.53
705
4.07
3540
6.76
1120
4.58
USGS
3435481195428000606083SW1806001074.0
SANTA CRUZ C NR SANTA YNEZ CA
19461120 910
4.05
19480410 19.0
1.67
19490311 140
2.63
19500206 1160
4.40
19510302 1.50
1.53
19520115 2690
7.00
19530113 261
5.90
19540124 1540
9.30
19550217 168
5.65
19560126 2040
8.95
19570113 559
6.50
19580403 3580
10.27
19590216 930
6.45
19600201 918
6.40
19601202 35.0
4.03
19620209 4520
9.75
19630209 398
5.29
19640401 145
4.50
19650409 308
5.16
19651229 2030
7.80
19661206 5800
10.30
19680308 472
6.34
19690224 7050
14.456
19700301 910
10.32
19701129 1100
10.42
19711225 436
9.90
19730118 2160
11.29
19740107 648
9.44
19750307 1400
10.10
19760209 234
8.59
19770509 71.0
8.14
19780209 5060
12.37
19790328 673
9.51
19800216 2620
11.15
19810304 735
9.60
19820401 681
10.09
783.38
82
311124500
311124500
311124500
311124500
311124500
311124500
311124500
311124500
311124500
311124500
311124500
311124500
311124500
311124500
311124500
311124500
311124500
311124500
311124500
311124500
311124500
311124500
311124500
311124500
Z11132500
H11132500
N11132500
311132500
311132500
311132500
311132500
311132500
311132500
311132500
311132500
311132500
311132500
311132500
311132500
311132500
311132500
311132500
311132500
311132500
311132500
311132500
311132500
311132500
311132500
311132500
311132500
311132500
19830301
19831225
19850209
19860214
19870306
19880228
19890209
19900218
19910319
19920212
19930223
19940220
19950310
19960220
19970123
19980223
19990209
20000221
20010305
20011230
20030315
20040225
20050221
20060102
3960
12.68
1290
10.32
256
8.50
1650
10.73
203
8.32
1800
10.89
211
8.36
1.90
6.69
31001
1.87
4820
12.82
3200
11.93
313
8.57
3110
12.19
1690
10.92
2220
10.43
4360
13.03
272
8.43
595
9.28
3980
12.79
44
7.73
868
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USGS
3435191202427000606083SW1806001047.1
SALSIPUEDES C NR LOMPOC CA
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3616501211918000606053SW18060005244
ARROYO SECO NR SOLEDAD CA
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USGS
3636341211207000606069SW18060002249
925.52
SAN BENITO R NR WILLOW CREEK SCHOOL CA
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3654011213548000606087SW180600021186
PAJARO R A CHITTENDEN CA
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3702401220417000606087SW18060001106
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USGS
3715161220218000606085SW180500039.22
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USGS
3711551191246000606019SW1804000622.9
PITMAN C BL TAMARACK C CA
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USGS
3743541193328000606043SW18040008181
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MERCED R A HAPPY ISLES BRIDGE NR YOSEMITE CA
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USGS
3743011193955000606043SW18040008321
3861.66
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93
311266500
311266500
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USGS
3823231203132000606009SW1804001268.4
MF MOKELUMNE R A WEST POINT CA
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USGS
3822061203240000606009SW1804001275.1
SF MOKELUMNE R NR WEST POINT CA
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37205
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7300
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390
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558
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3930
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USGS
3830011210239000606067SW18040013536
COSUMNES R A MICHIGAN BAR CA
19470310 3930
6.06
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6.86
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8.72
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202
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1200
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4.90
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97
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USGS
4056231222458000606089SW18020005425
SACRAMENTO R A DELTA CA
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19691221 30000
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11.82
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311342000
311342000
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USGS
4124221205536000606049SW180200021431
PIT R NR CANBY CA
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311348500
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3160
7.86
878
4.54
2300
6.81
237
3.18
3320
7.88
657
4.14
5620
10.39
3920
8.67
7280
11.82
3900
8.70
3100
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841
4.51
268
3.40
915
4.74
1910
6.37
2910
7.44
3760
8.55
3900
8.71
USGS
4023141221415000606089SW18020102927
COTTONWOOD C NR COTTONWOOD CA
19470212 13200
9.84
19480429 9870
8.40
19490319 21900
12.04
19500206 10700
8.63
19501214 14800
10.31
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13.25
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13.88
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14.70
19680220 19400
14.14
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15.48
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19.46
19710116 31300
15.57
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364.00
100
311376000
311376000
311376000
311376000
311376000
311376000
311376000
311376000
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311381500
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70000
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27500
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64400D
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48600
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17.43
12900
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39800
15.86
33000
15.08
20400
12.81
46700
17.23
USGS
4003171220123000606103SW18020103131
MILL C NR LOS MOLINOS CA
19461221 4070
7.65
19480323 7320
10.12
19490311 3870
7.48
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7.48
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385.00
101
311381500
311381500
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311383500
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311383500
311383500
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11.20
5250
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6.23
11800
12.85
7110
10.38
1980
6.47
9270
11.56
2960
7.55
3370
7.93
4020
8.45
6350
9.97
1510
5.80
11000
12.86
5820
10.00
20600
17.10
7120
10.42
5120
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3260
7.27
1500
4.98
2470
6.37
6350
9.88
6500
9.99
2400
6.28
87102
11.425
USGS
4000511215650000606103SW18020103208
DEER C NR VINA CA
19470212 4700
7.88
19480323 6860
9.29
19490311 4250
7.58
19500204 5690
8.54
19501116 4500
7.75
479.2
102
311383500
311383500
311383500
311383500
311383500
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311383500
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103
311383500
311383500
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311390000
20040217 8290
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USGS
3943341214228000606007SW18020105147
BUTTE C NR CHICO CA
19470212 4800
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19490311 2800
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19500206 5920
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19551222 18700
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19610131 3110
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19630131 14200
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19641222 21200
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19660104 3150
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19670121 6830
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19680221 3090
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19690121 12900
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19700124 16500
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19710326 6080
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19720122 1870
3.71
19730116 6820
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3.14
19770101 522
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19780304 7840
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19790214 4710
6.01
19800219 9100
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19801203 2160
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19820411 8500
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19830313 9070
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19831225 8250
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19850208 3090
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19860217 22000
14.52
19870312 6440
8.726
19871202 1800
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19891023 1310
3.95
19910304 5080
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19920220 3780
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104
311390000
311390000
311390000
311390000
311390000
311390000
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311390000
311390000
311390000
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1690
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7330
6.53
9080
7.31
4520
5.44
14800
9.36
USGS
4000111205712000606063SW18020122184
3129.86
SPANISH C AB BLACKHAWK C AT KEDDIE CA
19470212 3790
6.94
19480417 3860
7.00
19490416 938
4.11
19500206 3740
6.90
19501120 5330
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19520202 6040
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19530109 10100
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19540309 5180
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19550508 772
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19551223 13100
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19570224 7100
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19580224 10300
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19610131 2240
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19640121 2190
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19670129 9000
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19710326 8870
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19720229 2700
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19730116 6930
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19740330 10800
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19750325 3170
6.48
19760229 1070
4.39
19770221 249
2.79
19780116 5280
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19790214 2650
6.14
19800113 12700
12.29
19810214 3620
6.97
105
311402000
311402000
311402000
311402000
311402000
311402000
311402000
311402000
311402000
311402000
311402000
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19820216
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20051231
9310
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USGS
3931301205613000606091SW18020125250
N YUBA R BL GOODYEARS BAR CA
19470212 6580
10.48
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9.88
19490514 3150
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19500206 4600
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19501120 26400
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19590112 4460
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19690121 14300
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2453.00
106
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311413000
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USGS
3856101210122000606061SW18020128342
NF AMERICAN R A NORTH FORK DAM CA
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4.82
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USGS
3845491201939000606017SW18020129193
SF AMERICAN R NR KYBURZ(RIVER ONLY) CA
19470502 2010
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19480526 2950
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108
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5.236
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6.40
10.92
5.15
7.59
5.32
7.25
7.57
5.40
7.25
7.71
7.28
5.83
6.58
6.84
10.05
5.47
9.65
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USGS
3855391225033000606033SW1802011636.6
KELSEY C NR KELSEYVILLE CA
19461122
19480323
19490310
19500113
19501203
19520114
19521206
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19551221
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1570
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6800
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4370
4210
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5150
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8020
4490
6600
5840
4140
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543
101
4820
2000
3790
4260
5520
7730
4180
2850
6350
2710
2660
9.38
8.06
7.22
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11.38
10.52
13.85
14.80
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12.80
11.19
12.48
10.12
11.02
10.89
10.02
11.632
10.95
13.48
10.84
12.62
12.12
10.59
13.04
10.17
8.33
11.90
13.04
10.82
6.35
4.28
11.29
8.79
10.62
10.94
11.68
13.31
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1475.44
110
311449500
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4390
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8600
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2490
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6420
13.19
6420
12.19
1440
7.86
4180
10.94
USGS
4010551234630000606023SW18010106537
SF EEL R NR MIRANDA CA
19470303 23700
15.30
19480107 35700
18.90
19490318 42000
20.60
19500118 38200
19.57
19510121 56000
24.10
19511227 53700
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19521207 51600
23.03
19540117 65800
26.27
19541231 16000
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42.70
19570224 33000
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19590112 48300
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19600208 117000
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19630131 64500
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19640120 59000
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19660104 107000
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19690113 70000
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19700123 85800
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111
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311477000
311477000
311477000
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19831207 43300
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21.64
19860217 123000
38.29
19870313 19700
15.91
19871210 42700
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19900108 36400
20.35
19910304 22200
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19920220 13800
13.72
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19950109 81100
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19951212 34000
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19990207 39700
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20000214 40100
22.77
20010222 13800
14.78
20020106 29500
19.97
20021216 53800
26.98
20040217 46600
24.33
20041208 31500
20.53
20051228 88400
32.59
USGS
4029301240555000606023SW180101053113
EEL R A SCOTIA CA
19470212 86100
29.02
19480108 114000
32.60
19490318 140000
35.40
19500118 117000
32.85
19510122 249000
45.39
19511227 262000
46.50
19530109 215000
42.98
19540117 245000
45.20
19541231 52400
23.29
19551222 541000
61.90
19570225 153000
36.11
19580225 202000
40.35
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34.58
19600208 343000
51.45
19610211 113000
31.45
19620214 107000
29.92
19630201 252000
47.00
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39.40
19641223 752000
72.00
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35.50
112
311477000
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311478500
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311478500
311478500
311478500
311478500
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USGS
4028501235323000606023SW18010105222
VAN DUZEN R NR BRIDGEVILLE CA
19470212 128002
19480107 171002
19490222 142002
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19501028 20000
19520201 19500
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358.18
113
311478500
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USGS
21.30
14.16
15.45
17.95
17.60
14.23
11.38
15.60
18.10
22.60
18.206
17.91
15.86
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16.00
14.83
20.34
17.75
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15.05
11.47
14.32
12.85
17.45
19.21
13.12
14.46
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11.36
13.85
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12.53
11.59
8.61
19.14
9.13
19.72
18.06
18.73
13.16
12.19
12.39
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114
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4138271230050000606093SW18010208653
SCOTT R NR FORT JONES CA
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15.56
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19830127 9460
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2623.80
115
311519500
311519500
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34300
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2960
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23600
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USGS
4122361232833000606093SW18010210751
SALMON R A SOMES BAR CA
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19480107 32500
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19490222 6730
6.97
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19580129 34400
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19590112 21000
11.70
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19611219 13100
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19640120 19300
11.23
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43.406
19660106 23600
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19670129 21000
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15.80
19690121 21700
13.59
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20.21
19710118 51700
23.23
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24.84
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10.82
19740116 63500
26.73
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18.15
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19800112 30600
17.82
19801202 12900
11.24
19811219 41300
20.80
19821216 25700
15.20
19831214 17600
12.17
19841112 14600
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482.97
116
311522500
311522500
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311532500
311532500
311532500
311532500
311532500
311532500
311532500
311532500
311532500
19860218
19870312
19871210
19881122
19900108
19910304
19920417
19930317
19931208
19950131
19951230
19970101
19980323
19981121
20000214
20010515
20020106
20021228
20040217
20041209
20051230
39100
19.68
7560
7.96
20200
13.22
24400
14.75
20600
13.39
5830
6.89
8660
8.40
20800
13.44
3210
5.13
32000
17.42
19300
12.88
70800
28.46
34700
18.29
15300
11.32
10900
9.50
4180
6.04
13200
10.41
23700
14.51
18800
12.66
13700
10.56
675002
27.625
USGS
4147301240430000606015SW18010101614
SMITH R NR CRESCENT CITY CA
19461118 50000
24.00
19480106 83100
29.60
19481212 64300
26.42
19500118 91400
30.90
19501029 152000
39.51
19520201 61500
25.60
19530118 139000
37.80
19531123 141000
38.00
19541231 70200
27.45
19551222 165000
41.20
19570226 67100
26.93
19580129 94300
31.30
19590112 90400
30.75
19600208 74300
28.13
19601124 69200
27.28
19611123 71800
27.71
19621202 113000
34.10
19640120 93400
31.22
19641222 228000
48.50
19660106 145000
38.53
19670128 87800
30.35
19680223 77800
28.72
19690113 69400
27.32
19700122 116000
35.18
19710116 128000
36.58
19720122 182000
43.37
19721222 49800
25.63
19731105 106000
33.97
79.26
117
311532500
311532500
311532500
311532500
311532500
311532500
311532500
311532500
311532500
311532500
311532500
311532500
311532500
311532500
311532500
311532500
311532500
311532500
311532500
311532500
311532500
311532500
311532500
311532500
311532500
311532500
311532500
311532500
311532500
311532500
311532500
311532500
19750318 129000
19760226 45400
19770928 15800
19771214 102000
19790111 80300
19791124 76500
19801202 74800
19811219 89600
19830330 88400
19840213 72500
19841112 55700
19860222 96800
19870202 42400
19871210 76900
19881122 111000
19900108 113000
19910304 52700
19920416 31700
19930120 76400
19931208 37000
19950109 81400
19951212 68500
19961118 126000
19980117 93200
19981121 143000
20000111 82300
20001214 12100
20011214 38300
20021227 60200
20031213 81000
20041209 86600
20051230 121000
36.78
24.97
17.77
33.44
30.50
29.94
29.70
31.80
31.64
29.36
26.76
32.78
24.49
30.01
34.58
34.86
26.26
18.54
25.02
19.50
25.60
24.07
29.65
26.81
31.29
25.70
12.85
19.67
23.01
25.56
26.16
29.55
118
Chapter C. 2
TESTING FOR NONSTATIONARITY IN THE FIRST TWO MOMENTS OF
AVERAGE ANNUAL TEMPERATURE AND PRECIPITATION FOR SELECTED
CALIFORNIA CLIMATE DIVISIONS
Table C.2. Calculated average monthly temperature (degrees Fahrenheit) and precipitation (inches)
values for climate divisions 1, 2, 4, 5, and 6 corresponding to Figure 2
(http://www.esrl.noaa.gov/psd/cgi-bin/data/timeseries/timeseries1.pl). A water year is defined from
October 1st to September 31st of the following year.
Climate Div 1Water
year
Water Year average
temp
Water Year
average precip
1947
54.84
2.41
1948
52.95
3.23
1949
52.41
2.48
1950
53.34
2.92
1951
54.81
4.00
1952
53.23
4.24
1953
53.85
4.07
1954
54.11
3.64
1955
52.83
2.43
1956
54.26
4.51
1957
54.39
3.07
1958
55.40
4.93
1959
55.97
2.64
1960
54.52
2.65
1961
54.60
3.23
1962
53.48
2.85
1963
54.29
3.84
1964
53.33
2.64
1965
53.75
3.94
1966
54.33
2.96
1967
54.21
3.84
1968
54.66
2.85
1969
53.43
4.14
119
1970
54.80
3.73
1971
53.43
4.23
1972
53.61
3.13
1973
53.91
3.50
1974
54.33
5.11
1975
53.43
3.56
1976
53.70
2.40
1977
54.81
1.51
1978
55.78
4.35
1979
54.75
2.42
1980
54.73
3.81
1981
56.27
2.55
1982
54.18
5.00
1983
54.63
5.92
1984
55.88
3.76
1985
54.29
2.85
1986
55.54
4.25
1987
55.81
2.24
1988
55.98
2.61
1989
54.88
3.06
1990
55.39
2.43
1991
54.49
2.16
1992
57.04
2.38
1993
55.09
4.18
1994
55.61
2.15
1995
54.90
5.05
1996
56.92
4.02
1997
56.58
4.05
1998
55.35
5.20
1999
53.50
3.74
2000
55.95
3.21
2001
54.97
2.07
2002
55.55
3.24
2003
56.06
4.11
2004
56.40
3.22
2005
55.30
3.50
2006
55.37
4.78
120
Climate Div 2 Water
year
Water Year average
temp
Water Year
average precip
1947
55.73
2.25
1948
53.52
3.01
1949
53.45
2.26
1950
54.73
2.60
1951
55.78
3.59
1952
54.11
4.28
1953
54.93
3.22
1954
55.42
2.84
1955
53.74
2.19
1956
54.83
4.15
1957
55.01
2.67
1958
55.56
4.26
1959
57.58
2.31
1960
56.78
2.32
1961
55.94
2.41
1962
54.79
2.77
1963
55.21
3.89
1964
54.42
2.17
1965
54.88
3.81
1966
55.72
2.22
1967
55.78
3.92
1968
56.15
2.44
1969
54.93
4.02
1970
56.29
2.21
1971
54.76
3.23
1972
55.05
2.04
1973
55.03
3.41
1974
55.21
4.17
1975
54.55
2.90
1976
54.80
1.57
1977
56.06
1.21
1978
55.97
4.14
1979
54.90
2.47
1980
55.18
3.69
1981
57.32
2.28
121
1982
54.13
4.87
1983
54.13
5.27
1984
56.84
3.44
1985
54.28
2.32
1986
55.35
4.22
1987
56.45
1.71
1988
56.48
2.31
1989
54.96
3.04
1990
55.70
2.26
1991
55.06
2.21
1992
57.82
2.28
1993
54.95
4.12
1994
56.28
1.98
1995
54.08
5.23
1996
57.38
3.60
1997
56.56
3.81
1998
54.51
5.02
1999
53.89
2.90
2000
56.73
3.22
2001
56.08
2.03
2002
56.43
2.68
2003
56.85
3.37
2004
56.87
2.73
2005
55.63
3.44
2006
56.63
4.29
Div 4 Water year
Water Year average
temp
Water Year
average precip
1947
57.15
1.10
1948
55.92
1.28
1949
55.66
1.35
1950
56.78
1.41
1951
57.44
1.83
1952
56.63
2.54
1953
56.86
1.58
1954
57.28
1.34
1955
55.77
1.37
1956
56.79
2.31
122
1957
57.83
1.39
1958
58.54
2.88
1959
59.07
1.21
1960
58.13
1.10
1961
57.62
1.08
1962
56.40
1.57
1963
57.24
2.13
1964
56.40
1.10
1965
56.93
1.73
1966
57.62
1.29
1967
57.52
2.36
1968
58.39
1.20
1969
56.82
2.47
1970
58.31
1.47
1971
56.99
1.55
1972
57.08
0.87
1973
57.02
2.50
1974
57.00
2.17
1975
56.59
1.54
1976
57.17
0.88
1977
57.80
0.83
1978
59.04
2.60
1979
57.53
1.58
1980
57.98
2.14
1981
59.06
1.24
1982
57.13
2.74
1983
58.25
3.37
1984
59.32
1.48
1985
57.28
1.45
1986
58.09
2.23
1987
58.24
1.01
1988
58.59
1.21
1989
57.55
1.30
1990
58.12
1.04
1991
56.83
1.33
1992
59.61
1.57
1993
58.63
2.29
1994
58.05
1.27
123
1995
57.64
2.75
1996
59.79
2.05
1997
59.67
2.06
1998
57.98
3.52
1999
56.13
1.65
2000
58.93
2.00
2001
57.70
1.54
2002
57.94
1.54
2003
59.00
1.86
2004
58.93
1.52
2005
57.83
2.53
2006
58.21
2.43
Div 5 Water year
Water Year average
temp
Water Year
average precip
1947
58.46
1.26
1948
56.88
1.45
1949
57.39
1.22
1950
59.33
1.38
1951
60.25
1.85
1952
58.37
2.31
1953
58.68
1.36
1954
59.04
1.38
1955
57.76
1.33
1956
58.87
2.10
1957
58.86
1.31
1958
59.28
2.39
1959
61.28
1.05
1960
60.78
1.02
1961
59.57
1.02
1962
58.25
1.53
1963
58.89
1.72
1964
57.94
1.10
1965
58.46
1.82
1966
59.78
1.13
1967
59.23
2.22
1968
60.04
1.06
1969
58.88
2.73
124
1970
59.92
1.42
1971
58.55
1.42
1972
58.99
0.93
1973
58.53
1.95
1974
59.62
1.73
1975
58.35
1.55
1976
58.53
1.06
1977
59.67
0.69
1978
60.29
2.71
1979
59.26
1.53
1980
59.22
2.17
1981
61.14
1.23
1982
58.22
2.65
1983
58.11
3.20
1984
60.84
1.60
1985
58.33
1.37
1986
59.58
2.35
1987
59.89
0.99
1988
60.44
1.22
1989
59.70
1.32
1990
59.88
1.09
1991
59.14
1.28
1992
61.67
1.36
1993
59.62
2.28
1994
59.99
1.19
1995
58.75
2.74
1996
61.89
1.81
1997
61.09
1.97
1998
58.73
2.89
1999
58.29
1.33
2000
61.33
1.65
2001
60.17
1.31
2002
60.40
1.35
2003
61.01
1.56
2004
61.08
1.21
2005
59.24
2.29
2006
60.53
2.19
125
Div 6 Water year
Water Year average
temp
Water Year
average precip
1947
60.36
1.21
1948
58.92
0.78
1949
58.49
1.00
1950
59.39
1.05
1951
60.80
0.82
1952
59.46
2.25
1953
59.88
0.99
1954
60.97
1.29
1955
59.90
1.07
1956
60.08
1.13
1957
61.38
1.08
1958
61.18
2.28
1959
62.83
0.67
1960
62.08
0.96
1961
61.08
0.54
1962
59.46
1.52
1963
60.36
0.99
1964
59.81
0.86
1965
59.68
1.21
1966
61.03
1.53
1967
60.83
1.82
1968
61.54
1.06
1969
60.32
2.32
1970
61.27
0.84
1971
60.46
1.07
1972
60.68
0.72
1973
59.59
1.68
1974
60.77
1.15
1975
59.34
1.27
1976
60.71
1.13
1977
61.61
1.06
1978
62.55
2.79
1979
60.98
1.75
1980
61.70
2.36
1981
63.58
0.93
126
1982
60.94
1.42
1983
61.64
2.75
1984
63.85
0.85
1985
60.85
1.05
1986
62.00
1.64
1987
61.53
0.74
1988
61.53
1.29
1989
61.53
0.80
1990
62.23
0.74
1991
60.93
1.33
1992
63.42
1.65
1993
61.97
2.56
1994
62.51
1.03
1995
61.36
2.37
1996
63.48
0.96
1997
63.40
1.22
1998
61.53
2.79
1999
60.44
0.80
2000
63.08
0.96
2001
61.07
1.27
2002
61.38
0.45
2003
62.28
1.46
2004
62.48
0.75
2005
61.32
2.67
2006
62.54
1.10
127
Chapter C.3
CORRELATION TESTS BETWEEN ANNUAL PEAK DISCHARGE, AVERAGE
ANNUAL PRECITATION, AND ENSO ANOMALIES
Table C.3. Multivariate ENSO Index (MEI) bimonthly data. The MEI data used to develop standardized
times series (Figures B1 and B2).
MEI Ranks (last update: 4 June 2010)
Bimonthly ranks of the MEI, since the beginning of record in Dec1949/Jan1950. If two MEI values are
identical within the same bimonthly season, their rank is split between them, leading to a ".5" value.
Missing values are left blank.
How can one interpret these ranks? Given that there are 60 (61) numbers in each column, the lowest
number (1) would denote the strongest La Nina case for that bimonthly season, while the highest
number (60 or 61) would indicate the strongest El Nino case. For instance, in December-January
(DECJAN), the strongest La Nina was recorded in 1974, while the strongest El Nino occurred in 1983.
If we use percentiles (say, 30%-tile) to define La Nina, near-normal, and El Nino, MEI ranks from 1-18
denote weak to strong La Nina conditions, while 43-60 (44-61) denote weak to strong El Nino conditions.
If one uses the quintile definition for (moderate or stronger) ENSO events, MEI ranks from 1-12
would denote La Nina, while 49-60 (50-61) would denote El Nino. Finally, the comparison figures on this
website refer to strong ENSO events, such as might be defined by the top 6 (one tenth or smaller)
ranks, such as 1-6 for La Nina, and 55-60 (56-61) for El Nino.
YEAR DECJAN JANFEB FEBMAR MARAPR
AUGSEP SEPOCT OCTNOV NOVDEC
1950
9
9
5
6
3
5
1951
7
7
6
19
21
40
1952
41
34
33
34
22
29
1953
34
39
41
53
52
34
1954
32
33
38
17
4
9
1955
13
16
8
3
1
1
1956
3
5
4
5
5
10
1957
11
25
34
39
54
54
1958
57
56
56
56
51
45
1959
43
48
46
33
29
26
APRMAY MAYJUN JUNJUL JULAUG
5
5
9
14
19
8
37
46
49
50
44
43
12
19
23
36
37
22
33.5
38
34
41
32
33
2
4
4
9
6
9.5
1
1
1
2
2
1
3
6
8
6
4
13
45
51
54
55
54
52
50
45
39
33
34
38
30
24
29
29
27
26
128
1960
1961
1962
1963
1964
1965
1966
1967
1968
1969
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
27.5
22
31
17
8
20.5
14
46
49
13
19
55
56
27
23
23
16
37
46
38
39
6
4
11
17
58
59
2
1
14
21
3
2
41
42
47
48
39
44
49
47
32
30
30
29
60
61
28
26
18
20
25
27.5
28
28
19
21
18
19
19
21
23
27.5
29
29
20
25
20
18
23
17
20
11
14
8
9
8
12
13
18
16
16
13
16
13
16
26
34
41
45
45
47
42
21
16
6
7
3
3
7
8
7
26
23
31
45
51
55
56
56
55
57
55
48
48
26
22
26
32
27
28
32
12
9
7
15
17.5
13
14
12
15
19
14
18
9
8
10
14
27
32
38
41
49
43
51
48
46
40
33
31
39
42
41
40
27
25
11
9
10
8
10
12
2
1
1
2
4
7
7
5
5
5
24
24
22
43
55
58
58
57
58
58
58
51
47
24
9
10
5
3
3
3
1
2
2
7
14
11
12
13
11
6
20
13
11
10
6
2
2
1
1
2
3
7
4
14
35
43
45
53
47
37
36
35
49
37
42
48
46
49
49.5
49
50
53
32
17
15
17
20
20
29
34
38
31
36
39
39
36
43
47
43
44
45
47
54
55
49
47
37
35
35
35
30
44
52
32
28
28
28
30
33
31
32
32
26
40
52
56
57
58
59
60
61
61
61
61
59
57
55
40
31
27
21
39
40
33
23
27
22
28
30
24
19
15
20
11
24
23
16
16.5
26
29
129
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
27.5
52
54.5
56
51
4
6
33
35
35
36
57
58
43
45
42
40
53
53
20.5
18
24
24
59
60
12
10
7
5
16
22
31
33
51
54.5
36
38
44
37
19
25
48
29
30
24
36
36
35
47
54
49.5
48
54
58
58
59
58
59
59
59
57
55
46
45
37.5
31
13
8
6
4
7
4
6
10
14
13
19
16
15
24
24
30
44
52
42.5
46
38
31
31
37
36
36
37
42
44
49
53
53
52
44
51
53
59
59
59
60
57
52
40
39
42
40
53
55
57
57
56
54
53
52
53
46
35
37
45
47
44
49
44
43
56
54
51
49
37.5
41
41
33
30
21
18
18
18
22
18
23
27
25
21
22
20
28
22
25
46
56
60
60
60
60
60
59
60
60
60
58
54
37
25
15
13
11
10
12
10
12
16
15
11
11
12
14
8
11
21
28
20
22
26
25
23
15
17
20
25
34
29
32
36
26
22
25
31
26
42.5
53
47
42
50
48
46
50
52
50
41
30
31
29
35
38
41
39
40
27
35
42
33.5
41
42
42
40
45
47
54
50
50
40
39
38
34
25
21
23
19
15
27
43
44
48
51
52
56
130
Table C.4. Standardized annual peak, precipitation and multivariate ENSO index (MEI)
values. These standardized values are grouped by climate divisions 1,2, 4, 5, and 6.
Division 1--Standardized values
Log
Log
Log
Log
Peak
Peak
Peak
Peak
Q
Q
Q
Q
11532
11476
11522
11477
500
500
500
000
Log
Peak
Q
11478
500
Log
Peak
Q
11519
500
Wate
r year
Water
Year
averag
e
precip
1947
-1.111
-0.905
-0.939
-1.155
-0.869
-0.893
-0.899
1948
-0.236
0.081
-0.373
0.602
-0.477
-0.345
0.306
1949
-1.029
-0.417
-0.149
-1.393
-0.190
-0.697
-1.006
1950
-0.559
0.266
-0.280
-0.629
-0.440
-0.507
-0.985
1951
0.588
1.253
0.249
0.295
0.615
-0.049
0.479
1952
0.840
-0.503
0.191
0.136
0.686
-0.097
0.498
1953
0.662
1.079
0.136
1.040
0.410
0.157
0.924
1954
0.202
1.107
0.472
-0.045
0.592
0.388
-0.151
1955
-1.084
-0.246
-1.482
-1.255
-1.563
0.034
-1.535
1956
1.125
1.412
1.807
1.805
1.699
1.420
1.831
1957
-0.406
-0.334
-0.482
0.148
-0.065
-0.146
0.100
1958
1.581
0.326
0.139
0.674
0.323
0.182
0.786
1959
-0.859
0.244
0.045
0.049
-0.140
0.804
-0.185
1960
-0.853
-0.136
1.267
0.315
1.062
0.717
0.236
1961
-0.237
-0.274
-0.436
-0.241
-0.489
-0.136
0.149
1962
-0.638
-0.202
-0.865
-0.549
-0.565
-1.047
-0.977
1963
0.411
0.677
0.444
0.770
0.632
0.223
0.748
1964
-0.865
0.308
0.321
-0.058
0.146
0.839
-0.114
1965
0.527
2.039
2.001
2.387
2.159
1.633
2.191
1966
-0.520
1.161
1.143
0.197
0.926
0.736
-0.368
1967
0.418
0.188
-0.301
0.049
-0.056
0.490
0.052
1968
-0.643
-0.047
-0.436
0.587
-0.112
0.016
0.693
1969
0.735
-0.268
0.557
0.090
0.461
0.779
0.067
1970
0.297
0.728
0.838
0.945
0.921
0.926
1.190
1971
0.827
0.919
0.941
1.190
0.528
0.483
0.943
1972
-0.340
1.602
0.486
1.312
-0.261
0.061
0.843
1973
0.049
-0.912
-0.172
-0.782
-0.075
-0.227
-0.830
1974
1.766
0.553
1.325
1.451
1.231
0.987
1.781
1975
0.123
0.934
0.959
0.012
0.510
0.461
0.258
1976
-1.113
-1.092
0.004
-0.829
-0.539
-0.424
-0.765
131
1977
-2.068
-3.140
-4.186
-3.056
-4.640
-4.274
-3.218
1978
0.955
0.479
0.170
0.571
0.073
-0.176
0.733
1979
-1.097
0.015
-0.209
-0.403
-0.715
-1.341
-0.524
1980
0.380
-0.079
0.264
0.526
0.480
-0.379
0.717
1981
-0.954
-0.123
-0.724
-0.568
-0.678
-0.849
-0.661
1982
1.648
0.227
1.336
0.906
0.875
0.410
1.405
1983
2.632
0.201
0.830
0.305
0.857
0.767
0.381
1984
0.329
-0.184
-0.106
-0.175
-0.501
-0.618
-0.341
1985
-0.643
-0.695
0.090
-0.412
-0.261
-0.166
-0.670
1986
0.854
0.377
1.336
0.836
1.145
1.109
0.911
1987
-1.284
-1.224
-1.194
-1.245
-0.739
-0.751
-0.529
1988
-0.896
-0.069
-0.126
0.000
-0.428
0.070
-0.361
1989
-0.414
0.643
0.087
0.239
-0.220
0.303
-0.018
1990
-1.087
0.677
-0.346
0.025
-0.632
-0.345
-0.243
1991
-1.370
-0.803
-1.029
-1.575
-0.591
-0.670
-1.316
1992
-1.134
-1.789
-1.686
-1.073
-1.515
-1.949
-0.953
1993
0.780
-0.082
0.932
0.037
0.828
1.322
0.131
1994
-1.384
-1.489
-1.891
-2.331
-1.671
-1.640
-2.094
1995
1.700
0.041
0.761
0.583
1.161
1.428
0.574
1996
0.611
-0.294
-0.440
-0.058
-0.047
1.088
-0.059
1997
0.635
0.889
0.970
1.589
1.130
1.119
1.711
1998
1.865
0.304
-0.005
0.685
0.082
0.105
0.850
1999
0.314
1.134
-0.226
-0.352
-0.348
-0.156
-0.505
2000
-0.255
0.062
-0.213
-0.782
0.048
-0.002
-0.605
2001
-1.473
-3.657
-1.686
-1.996
-1.397
-2.507
-1.752
2002
-0.226
-1.422
-0.637
-0.539
-0.417
-0.507
-0.713
2003
0.699
-0.544
0.194
0.202
0.480
0.869
0.240
2004
-0.243
0.031
-0.005
-0.091
0.423
0.447
0.141
2005
0.054
0.161
-0.546
-0.492
-0.749
-0.248
-0.819
2006
1.415
0.810
0.880
1.528
0.908
0.773
1.325
Division 2--Standardized values
Wate
r year
Water
Year
average
precip
Log
Peak Q
1144950
0
Log
Peak Q
1142700
0
Log
Peak Q
1138150
0
Log
Peak Q
1138350
0
Log
Peak Q
1141300
0
Log Peak
Q
11402000
1947
-0.872
-0.312
-0.184
-0.336
-0.320
-0.122
-0.194
1948
-0.082
-0.772
-0.501
0.511
0.201
-0.276
-0.175
132
1949
-0.866
-1.182
-0.786
-0.409
-0.459
-0.931
-1.686
1950
-0.505
-0.565
-0.295
-0.214
-0.057
-0.515
-0.208
1951
0.522
0.297
1.336
-0.409
-0.380
1.405
0.170
1952
1.244
0.051
-0.008
0.039
0.185
-0.040
0.304
1953
0.139
0.899
0.147
0.585
0.826
0.463
0.853
1954
-0.262
1.102
0.154
-0.066
0.475
0.281
0.140
1955
-0.942
-0.889
-1.344
-1.051
-1.681
-1.134
-1.894
1956
1.107
0.851
1.386
0.837
1.038
1.421
1.131
1957
-0.437
0.303
0.412
0.257
0.318
0.463
0.477
1958
1.228
0.762
0.368
0.421
0.533
0.627
0.874
1959
-0.817
-0.131
-0.361
-0.172
0.292
-0.549
-0.285
1960
-0.803
0.238
0.790
-0.039
0.057
0.855
0.664
1961
-0.710
0.186
-1.452
-0.208
-0.323
-1.718
-0.756
1962
-0.332
-0.173
0.080
-0.191
0.099
-0.297
0.087
1963
0.842
0.465
1.572
1.456
0.761
1.862
1.276
1964
-0.963
0.209
-0.165
0.339
0.392
-0.191
-0.780
1965
0.756
1.080
1.659
1.639
1.589
1.794
1.304
1966
-0.911
0.275
-1.547
-0.897
-0.556
-0.819
-1.329
1967
0.875
0.809
0.379
0.400
0.152
0.052
0.730
1968
-0.680
0.640
-0.016
-0.361
-0.439
-0.311
-0.329
1969
0.975
0.163
0.836
1.271
1.278
0.731
1.064
1970
-0.917
0.944
1.146
1.735
1.681
1.055
1.072
1971
0.145
-0.111
0.195
0.192
-0.426
0.001
0.714
1972
-1.095
-1.000
-1.102
-1.786
-1.397
-0.900
-0.557
1973
0.338
0.562
0.368
0.127
0.288
-0.311
0.451
1974
1.133
0.944
0.328
1.003
0.960
0.557
0.925
1975
-0.195
0.139
0.009
0.207
-0.268
-0.428
-0.385
1976
-1.588
-2.655
-1.110
-1.506
-1.770
-1.393
-1.546
1977
-1.961
-4.988
-2.864
-3.559
-3.731
-2.712
-3.103
1978
1.098
0.373
-0.169
0.383
0.472
-0.522
0.160
1979
-0.649
-0.847
-0.095
0.006
-0.170
-0.815
-0.577
1980
0.632
0.040
1.354
0.989
0.675
1.493
1.098
1981
-0.847
0.202
-0.878
-0.176
-0.573
-0.751
-0.243
1982
1.867
0.562
1.259
1.150
0.602
1.143
0.766
1983
2.277
1.029
0.922
0.745
0.994
0.684
0.699
1985
-0.797
-0.355
-0.781
-1.428
-1.483
-1.155
-0.747
1986
1.188
0.756
1.586
1.199
1.376
1.508
1.562
1987
-1.441
-0.425
-0.531
0.469
0.172
-0.341
-0.419
133
1988
-0.812
-0.451
-1.626
-1.376
-1.642
-0.844
-1.821
1989
-0.054
0.244
0.057
0.851
0.734
0.327
0.429
1990
-0.869
-0.248
-1.241
-0.796
-0.738
-1.007
-1.192
1991
-0.920
0.347
0.433
-0.609
-0.563
0.731
0.210
1992
-0.847
-0.605
-0.656
-0.354
-0.380
-0.850
-0.938
1993
1.080
0.250
0.390
0.305
0.107
0.074
0.229
1994
-1.153
-1.892
-2.094
-1.767
-1.978
-1.746
-1.790
1995
2.239
1.177
0.801
1.098
1.203
0.668
1.179
1996
0.540
0.312
0.504
0.180
0.148
0.791
0.229
1997
0.755
1.152
1.650
2.003
1.926
2.003
1.690
1998
2.022
0.531
0.139
0.471
0.702
0.239
0.307
1999
-0.197
0.452
0.390
-0.005
0.252
0.111
0.649
2000
0.135
-0.234
0.519
-0.657
-0.162
0.349
0.426
2001
-1.104
-0.554
-1.444
-1.777
-1.167
-1.306
-1.506
2002
-0.422
-0.543
-0.781
-1.057
-0.858
-1.084
-1.251
2003
0.297
0.771
-0.714
0.305
0.445
-0.549
-0.102
2004
-0.375
0.771
-0.914
0.339
0.462
-0.897
0.421
2005
0.373
-1.302
0.444
-1.098
-0.966
0.813
-0.155
2006
1.253
0.176
1.433
0.761
0.761
1.438
1.081
Division 2--Standardized values
Log
Log
Log
Peak Q
Peak Q
Peak Q
1031000
1139000
1134850
0
0
0
Log
Peak Q
1137600
0
Wate
r year
Log
Peak Q
1134200
0
1947
-1.138
-0.329
-0.219
-0.885
-0.544
1948
0.568
-0.197
-0.058
-0.459
-0.908
1949
-0.386
-0.011
-0.902
-0.031
0.091
1950
-1.759
-0.131
0.047
-0.811
-0.807
1951
0.942
2.122
-0.498
-0.715
-0.400
1952
0.232
0.341
0.380
1.265
0.590
1953
0.508
-0.028
0.748
0.368
-0.004
1954
-0.316
-0.209
-0.086
-0.737
-0.054
1955
-0.632
-0.407
-1.643
-1.508
-1.336
1956
1.245
2.143
1.503
0.899
1.102
1957
0.664
0.069
-0.004
0.178
-0.310
1958
1.024
0.836
0.597
0.377
1.091
1959
0.438
-1.166
-0.140
-1.452
-0.093
1960
-0.062
-1.057
0.163
0.360
0.312
1961
-0.293
-1.533
-0.769
-1.403
-0.249
134
1962
-0.282
-0.251
-0.185
-0.433
-0.134
1963
0.701
2.163
1.155
1.375
0.158
1964
-0.410
-0.500
-0.183
0.364
-0.563
1965
1.321
1.606
1.662
0.832
1.356
1966
-0.604
-1.125
-0.753
-0.975
-0.409
1967
0.042
0.791
0.228
0.923
0.142
1968
-0.995
-1.022
-0.777
0.228
-0.061
1969
-0.282
0.488
1.033
0.719
0.180
1970
0.911
0.041
1.345
1.415
1.324
1971
-0.689
-0.255
0.080
1.234
0.539
1972
-1.145
-0.934
-1.413
0.974
-1.847
1973
0.087
0.008
0.226
-0.580
0.373
1974
2.257
0.341
1.003
0.451
1.549
1975
-0.237
0.536
-0.183
-0.208
0.511
1976
-1.726
-1.424
-1.913
-1.673
-2.313
1977
-3.170
-1.174
-3.029
-1.550
-2.785
1978
0.958
0.074
0.402
-0.303
0.819
1979
-0.748
-0.035
-0.243
-0.391
-0.544
1980
0.296
0.341
0.591
1.267
0.725
1981
-0.763
-0.587
-1.231
0.143
0.377
1982
1.120
0.894
0.505
1.066
1.444
1983
1.184
-0.055
0.587
0.320
1.807
1985
-0.763
-0.136
-0.777
-1.036
-1.072
1986
1.033
0.814
1.709
1.777
1.186
1987
-0.327
-1.128
0.153
-1.206
-0.981
1988
-0.435
-1.938
-1.462
-0.280
-0.831
1989
1.325
-0.341
0.796
0.557
-1.078
1990
0.311
-1.193
-1.864
-0.908
-2.026
1991
-1.151
-0.646
-0.147
0.193
-0.563
1992
-1.077
-1.229
-0.522
-2.407
-0.155
1993
0.033
0.143
0.331
0.613
0.914
1994
-1.582
-1.463
-1.434
-1.240
-2.099
1995
1.488
0.687
0.952
1.216
1.091
1996
-0.550
1.582
0.129
0.803
-0.434
1997
2.076
2.779
2.319
1.512
0.866
1998
0.701
0.374
0.760
0.798
1.036
1999
-0.422
0.352
0.470
0.535
-0.572
2000
-0.216
-0.290
0.348
-0.958
-0.249
135
2001
-0.933
-0.849
-1.541
-2.266
0.523
2002
0.515
-0.091
-0.532
-0.861
0.222
2003
0.760
0.094
0.317
-0.019
0.841
2004
1.077
-0.718
0.588
0.463
0.606
2005
-0.618
1.160
-0.295
0.756
0.002
2006
0.015
1.447
1.207
0.798
1.041
Division 4--Standardized values
Wate
r year
Water
Year
average
precip
Log
Peak Q
1116050
0
Log
Peak Q
1115900
0
Log
Peak Q
1115200
0
Log
Peak Q
1115650
0
Log
Peak Q
1116950
0
1947
-1.038
-1.202
-0.554
-0.778
-0.630
-1.299
1948
-0.743
-1.243
-1.380
-2.187
0.039
-1.016
1949
-0.637
-0.245
-0.087
-0.785
1.016
-0.257
1950
-0.534
0.209
-0.279
0.203
-0.404
-0.526
1951
0.140
0.731
0.720
1.187
-1.142
0.749
1952
1.268
1.062
0.865
0.836
1.443
1.143
1953
-0.270
0.599
0.131
0.278
0.399
0.250
1954
-0.651
-0.594
-0.714
-0.899
0.432
-0.483
1955
-0.605
-0.403
-0.570
-1.347
-0.196
-1.234
1956
0.904
1.755
1.380
1.514
1.422
1.908
1957
-0.569
-0.649
-0.428
-0.389
0.409
-0.513
1958
1.821
1.202
1.368
1.537
1.913
0.683
1959
-0.852
0.284
0.229
-0.154
0.757
0.564
1960
-1.031
-0.498
0.133
-0.074
0.029
-0.740
1961
-1.058
-1.998
-2.708
-1.100
0.190
-1.052
1962
-0.273
0.193
0.139
0.421
0.630
0.120
1963
0.617
0.929
0.952
1.369
-0.558
1.078
1964
-1.034
-0.612
-0.267
-0.411
-0.179
-0.118
1965
-0.028
0.511
0.213
0.099
-0.804
0.327
1966
-0.722
-1.488
-0.326
-0.487
-0.810
-0.900
1967
0.983
0.713
0.713
1.514
0.097
0.411
1968
-0.868
0.542
-1.421
-1.390
-1.395
0.435
1969
1.159
0.810
1.204
1.346
1.807
1.044
1970
-0.434
0.481
0.547
0.386
-1.161
0.060
1971
-0.309
-0.661
-0.568
-0.544
-0.772
-0.391
1972
-1.404
-1.506
-1.698
-0.484
-1.212
-1.068
1973
1.204
0.835
0.777
0.375
0.956
1.378
1974
0.681
-0.164
0.503
-0.158
-0.308
-0.098
136
1975
-0.332
0.009
0.200
1.244
0.395
0.040
1977
-1.466
-2.860
-2.921
-2.793
-1.315
-1.972
1978
1.365
0.793
0.830
1.203
0.942
1.854
1979
-0.260
0.017
-0.044
-1.139
0.069
-0.211
1980
0.630
0.722
0.796
0.744
0.230
1.396
1981
-0.812
-0.708
0.091
0.092
-0.736
-0.838
1982
1.597
1.732
0.977
0.921
0.463
1.460
1983
2.595
0.959
1.134
1.259
1.663
1.449
1984
-0.428
0.224
0.361
-0.324
-0.044
0.106
1986
0.771
1.338
1.024
0.686
0.780
1.437
1987
-1.175
-0.426
-0.121
-0.287
-1.105
-0.762
1988
-0.850
-1.195
-2.239
-1.769
-1.555
-1.216
1989
-0.706
-1.427
-1.302
-0.756
-1.502
-1.280
1990
-1.120
-1.410
-1.613
-0.935
-2.290
-1.131
1991
-0.669
-0.192
0.149
0.326
0.266
-0.124
1992
-0.288
0.713
-0.235
-0.165
0.331
0.248
1993
0.869
0.246
0.623
1.086
1.150
0.538
1994
-0.762
-0.758
-0.790
-0.732
-0.927
-1.115
1995
1.605
1.015
1.315
1.498
2.016
1.111
1996
0.481
0.144
0.765
0.463
0.388
0.335
1997
0.497
0.802
1.134
0.180
0.675
0.878
1998
2.829
1.318
1.406
0.994
1.906
1.703
1999
-0.148
-0.432
0.369
-0.210
-0.497
0.003
2000
0.410
0.402
0.595
0.194
-0.300
0.266
2001
-0.328
-0.939
-0.344
-0.189
0.236
-0.832
2002
-0.336
0.443
-0.015
-0.400
-1.212
-0.202
2003
0.191
0.944
0.052
0.635
-0.746
-1.038
2004
-0.366
0.785
0.258
0.154
-0.205
0.470
2005
1.252
-0.076
0.328
0.238
0.572
-0.687
2006
1.087
0.952
0.470
0.669
0.824
1.044
Division 5
Wate
r year
Water
Year
averag
e
precip
Log
Peak Q
112375
00
Log
Peak
Q
11317
000
Log
Peak Q
114395
00
Log
Peak Q
113185
00
Log
Peak
Q
11266
500
Log
Peak Q
112645
00
Log
Peak
Q
11335
000
1947
-0.672
-0.686
-0.557
-0.590
-0.690
-0.378
-0.344
-0.560
1948
-0.339
-0.277
-0.684
-0.152
-0.626
0.028
0.083
-0.185
1949
-0.737
-0.264
-0.487
-0.407
-0.240
-0.184
-0.321
0.440
1950
-0.460
-0.508
-0.046
-0.111
-0.014
-0.170
-0.291
0.052
137
1951
0.371
1.968
1.117
1.663
0.966
2.371
2.139
1.019
1952
1.178
0.453
0.229
0.384
0.297
0.473
0.364
0.378
1953
-0.494
-0.573
-0.360
0.256
-0.408
-0.567
-0.562
-0.529
1954
-0.453
-0.227
-0.370
-0.063
-0.532
-0.354
-0.306
-0.574
1955
-0.549
-0.295
-0.716
-0.562
-0.819
-0.401
-0.094
-0.533
1956
0.806
2.115
1.469
1.607
1.616
2.398
2.256
1.360
1957
-0.573
0.701
0.137
0.201
-0.181
-0.041
-0.023
-0.100
1958
1.326
0.628
0.710
0.309
0.806
0.436
0.395
1.068
1959
-1.034
-1.171
0.013
-1.450
0.041
-1.184
-1.235
-0.479
1960
-1.088
-1.007
0.453
-0.886
0.486
-0.792
-1.015
0.289
1961
-1.079
-1.565
-1.549
-1.287
-1.435
-1.825
-1.873
-2.253
1962
-0.190
0.034
0.341
-0.451
0.220
-0.238
-0.519
-0.043
1963
0.138
0.985
1.272
1.747
1.444
1.507
1.061
1.308
1964
-0.944
-0.629
-1.060
-0.122
-1.003
-0.956
-1.004
-0.543
1965
0.321
0.175
1.211
1.878
1.308
1.989
2.134
1.268
1966
-0.898
-0.744
-0.921
-0.908
-0.950
-0.979
-1.093
-0.812
1967
1.027
1.198
0.440
0.435
0.535
0.509
0.849
0.573
1968
-1.020
-1.486
-0.537
-0.822
-0.823
-1.413
-1.285
-0.502
1969
1.922
0.870
1.193
0.272
1.222
0.765
0.981
0.854
1970
-0.381
-0.394
0.800
0.731
0.743
-0.293
-0.438
0.617
1971
-0.383
-0.400
0.334
0.386
0.114
-0.594
-0.570
0.074
1972
-1.247
-1.279
-0.205
-0.829
-0.184
-0.663
-0.169
-0.579
1973
0.540
0.794
0.311
0.231
0.244
0.434
0.680
0.525
1974
0.166
0.190
0.635
0.449
0.793
0.094
0.189
0.110
1975
-0.152
0.649
0.311
0.245
0.320
0.581
0.853
0.274
1976
-1.015
-1.385
-1.840
-0.562
-1.886
-1.382
-1.336
-2.345
1977
-1.664
-1.667
-2.433
-1.771
-2.429
-1.151
-0.919
-2.965
1978
1.873
0.645
0.080
-0.118
0.093
0.391
0.658
0.041
1979
-0.195
0.457
0.378
0.023
0.188
0.283
0.322
-0.093
1980
0.925
0.668
1.422
1.512
1.455
1.223
0.590
1.193
1981
-0.715
-0.483
-0.478
-0.690
-0.478
-0.531
-0.632
-0.232
1982
1.782
1.218
1.504
1.348
1.498
1.251
0.943
1.257
1983
2.746
0.925
0.967
0.823
1.071
0.999
1.149
0.974
1985
-0.465
-0.701
-0.524
-0.787
-0.479
-0.767
-1.139
-0.179
1986
1.253
-0.081
1.576
1.327
1.663
0.505
0.590
1.417
1987
-1.132
-0.724
-1.119
-1.309
-1.254
-1.138
-0.972
-1.128
1988
-0.728
-1.525
-1.830
-2.480
-1.602
-1.360
-1.093
-1.521
1989
-0.552
-0.724
-0.348
-0.416
-0.445
-0.617
-0.809
-0.104
138
1990
-0.960
-1.110
-1.669
-1.473
-1.391
-1.549
-1.856
-1.508
1991
-0.633
-0.319
-1.198
-0.283
-0.908
-0.531
-0.454
-0.131
1992
-0.491
-0.771
-1.370
-1.309
-0.726
-1.050
-1.272
-0.311
1993
1.125
0.753
0.318
0.275
0.168
0.334
0.119
0.161
1994
-0.788
-0.997
-2.070
-1.460
-2.112
-0.996
-0.848
-1.606
1995
1.930
0.784
1.203
0.919
1.261
0.600
1.068
0.920
1996
0.308
2.074
0.251
1.338
0.250
1.422
1.297
0.244
1997
0.574
2.569
1.596
2.284
1.699
2.475
2.301
2.004
1998
2.187
0.870
0.729
0.442
0.793
0.545
0.640
1.079
1999
-0.547
-0.385
0.858
0.163
0.871
-0.028
-0.088
0.850
2000
0.020
0.036
0.770
-0.133
0.653
0.016
-0.016
0.289
2001
-0.582
-0.195
-1.085
-0.986
-1.071
-0.397
-0.438
-1.535
2002
-0.501
-0.833
-0.425
-0.540
-0.762
-0.544
-0.470
-0.680
2003
-0.133
-0.408
-0.253
0.003
-0.582
0.407
0.812
-0.587
2004
-0.754
-1.037
-0.424
-0.794
-0.594
-0.712
-0.888
-0.379
2005
1.136
1.218
0.092
0.617
0.085
1.106
1.226
0.397
2006
0.967
1.510
1.091
1.251
1.119
0.638
0.728
1.214
Division 6--Standardized values
Wate
r year
Water
Year
averag
e
precip
Log
Peak Q
111245
00
Log
Peak Q
110558
00
Log
Peak Q
111325
00
Log
Peak Q
110555
00
Log
Peak Q
110980
00
1947
-0.202
0.150
-0.210
-1.708
-0.490
0.203
1948
-0.898
-2.057
-0.303
-1.220
-0.394
-1.602
1949
-0.540
-0.918
-0.955
0.097
-1.122
-1.777
1950
-0.458
0.288
-0.469
-0.594
-0.551
-0.763
1951
-0.834
-3.505
-1.198
-2.438
-1.320
-2.523
1952
1.506
0.768
0.636
1.468
0.035
0.619
1953
-0.562
-0.563
-0.757
0.593
-1.197
-1.543
1954
-0.067
0.450
0.355
-0.130
0.484
0.168
1955
-0.429
-0.814
-0.855
-0.790
-1.362
-0.998
1956
-0.322
0.610
0.577
0.443
1.093
0.416
1957
-0.410
-0.128
1.039
-0.315
1.093
-0.727
1958
1.546
0.931
0.896
0.673
1.130
0.325
1959
-1.074
0.162
-0.048
0.629
0.395
-0.171
1960
-0.601
0.155
-1.572
-0.286
-1.729
-0.676
1961
-1.299
-1.709
-1.014
-0.634
-1.806
0.376
1962
0.313
1.064
0.374
1.180
0.314
0.841
139
1963
-0.551
-0.322
-0.607
0.470
-0.869
0.024
1964
-0.766
-0.898
-1.272
-1.486
-1.376
-0.628
1965
-0.201
-0.468
-0.193
-0.111
0.056
-0.584
1966
0.320
0.607
0.875
0.470
1.756
1.360
1967
0.805
1.206
1.483
1.152
1.845
0.855
1968
-0.442
-0.225
-0.404
-1.348
-0.413
0.937
1969
1.614
1.318
2.066
0.904
1.821
2.053
1970
-0.804
0.150
-0.444
-0.216
-0.862
0.278
1971
-0.424
0.258
-0.955
-1.190
1.520
0.757
1972
-1.004
-0.270
0.451
-0.368
0.581
-0.490
1973
0.568
0.643
0.178
1.255
0.216
1.478
1974
-0.289
-0.044
-0.790
0.362
-0.770
-0.097
1975
-0.105
0.396
-0.934
0.952
-0.226
0.123
1976
-0.327
-0.625
-0.114
-0.703
0.100
0.191
1977
-0.439
-1.305
0.575
-1.881
0.191
-0.465
1978
2.391
1.128
1.337
1.147
1.174
1.729
1979
0.682
-0.022
-0.046
0.642
0.015
-0.587
1980
1.677
0.753
1.599
0.905
1.154
1.342
1981
-0.656
0.028
-0.934
0.262
0.027
0.233
1982
0.144
-0.016
-0.106
-0.562
0.214
0.220
1983
2.325
0.989
0.776
1.210
0.966
1.235
1985
-0.465
-0.574
-0.462
-1.101
-0.723
-0.816
1986
0.508
0.489
0.231
1.070
0.409
-0.519
1987
-0.966
-0.706
-0.900
-0.525
-1.143
-2.467
1988
-0.068
0.539
-0.900
-1.272
-0.588
0.013
1989
-0.867
-0.684
-0.270
-2.576
-0.026
-0.740
1990
-0.959
-3.370
-0.557
-1.750
0.262
-0.705
1991
0.004
0.849
0.130
1.223
0.232
0.501
1992
0.527
1.101
0.570
0.810
0.996
0.932
1993
2.013
0.867
1.143
0.766
1.053
0.932
1994
-0.488
-0.459
-0.506
0.266
-0.333
-0.868
1995
1.696
0.851
1.262
1.220
1.020
0.941
1996
-0.604
0.503
0.107
0.064
-0.416
0.184
1997
-0.175
0.658
0.901
-0.002
0.610
0.166
1998
2.382
1.043
1.247
1.187
1.011
1.588
1999
-0.874
-0.539
-1.662
0.327
-1.559
-1.379
2000
-0.602
-0.093
-0.612
0.658
-0.413
0.088
2001
-0.104
0.991
-0.920
1.020
-1.376
-0.177
140
2002
-1.442
-1.578
-2.691
-0.931
-2.496
-1.667
2003
0.214
0.123
-0.243
0.088
0.080
-0.024
2004
-0.951
-0.089
2.161
0.362
-0.174
0.315
2005
2.194
1.174
2.313
0.718
1.707
1.439
2006
-0.369
0.387
0.824
-0.188
0.393
0.638
ENSO-Standardized data
Year
Data
1950
-1.092
1951
0.045
1952
-0.030
1953
0.342
1954
-0.935
1955
-1.621
1956
-1.291
1957
0.618
1958
0.784
1959
0.115
1960
-0.288
1961
-0.280
1962
-0.770
1963
0.063
1964
-0.804
1965
0.723
1966
0.257
1967
-0.628
1968
-0.323
1969
0.530
1970
-0.564
1971
-1.422
1972
0.885
1973
-0.446
1974
-1.155
1975
-1.295
1976
-0.124
1977
0.632
1978
0.128
1979
0.537
141
1980
0.552
1981
0.050
1982
1.092
1983
1.648
1985
-0.404
1986
0.448
1987
1.663
1988
-0.515
1989
-0.533
1990
0.388
1991
0.772
1992
1.294
1993
1.090
1994
0.692
1995
0.226
1996
-0.319
1997
1.490
1998
0.840
1999
-0.878
2000
-0.528
2001
-0.180
2002
0.587
2003
0.461
2004
0.427
2005
0.296
2006
0.320
142
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