dendrohydrologic reconstructions: western water...
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Western Water Assessment
Dendrohydrologic Reconstructions:
Applications to Water Resource Management
Connie Woodhouse, NOAA/NGDC,
Boulder, CO
David Meko, University of Arizona,
Tucson, AZ
Ft. Collins
Colorado Springs
DenverWestminster
NE
AZ OKKS
WY
UTNM
C O L O R A D O
South Platte
River Basin
South Platte
River Basint
TUR
MON
Clear Creek
DEE
VAN
S. Platte R. Basin, Clear Creek,
and Tree-Ring Chronologies
used in Reconstructions
Reconstructed Clear Creek Flow, 1685 -1987
tota
lannua
lflo
w,
ac
re-f
ee
t
year
350000
300000
250000
200000
150000
100000
500001700 1750 1800 1850 1900 1950 2000
annual values
5-weight binomial filter
1910 1920 1930 1940 1950 1960 1970 1980
Clear Creek, 1912-1980
observed and reconstructed values
annua
lflo
w,a
cre
-fe
et
Year
350000
300000
250000
200000
150000
100000
50000
Instrumental
Reconstructed
2R = 0.608
1706-09
1778-82
1809-131816-21
1840-42 1845-521861-63 1879-811885-88
1929-36
1953-561976-78
-1.0
-1.0
-1.0
Duration and Severity of Low Flow Events,
(3 or more years), 1685-1987
1739-42
1966-68
1800 1820 1840 1860 1880
1900 1920 1940 1960 1980
1700 1720 1740 1760 1780
annual severity index(cumulative negative departure/ # of years)
MEDIAN and QUANTILE REGRESSION
Quantile regression
(a.k.a. minimum absolute deviations or least absolute regression)
Similar to ordinary least squares regression except:
The goal is to estimate the median of the dependent variable,
conditional on the independent variable, instead of the mean.
The regression line fit is based on the minimization of the sums of the
absolute residuals instead of the sums of the squares of the residuals.
50% of the residuals will be positive and 50% will be negative
A form of median regression:
Residuals from the median regression are weighted to reflect the quantile
selected.
The signs of the residuals will reflect the quantile selected (e.g., for 80th
percentile, 80% of residuals will be positive; 20% will be negative)
Median regression
1910 1920 1930 1940 1950 1960 1970 1980
year
tota
la
nnua
lflo
w,
ac
refe
et
400000
300000
200000
100000
0
observed
reconstructed, OLS
reconstructed, median
0 20 40 60 80 100
0.9
0.8
0.7
0.6
0.5
n(days)
co
rre
latio
ns
Correlations between water-year total flow
and n-day low flows
1
0.8
0.6
0.4
0.2
0
-0.2
Site
DEE EL
1
EL2
HO
2
JEF
KA
2
LYN
MO
N
TUR
VA
N
ALT
DEV
PAR
CSM
Co
rrela
tions
annual average daily flow
annual 7-day low flow
difference between average daily
and 7-day low flows
Correlations between tree-ring
indices and flow variables
500000
400000
300000
200000
100000
0
yearflo
w,
ac
refe
et
1910 1920 1930 1940 1950 1960 1970 1980
Clear Ck., 1912-1980
Reconstructed values for 10th and 90th percentiles
and observed values
observed
reconstructed,
10% and 90%
90th
percentile
10th
percentile
1. INTRODUCTION
Water resource planning is based primarily on 20th century instrumental
records of climate and streamflow. However, even the longest gage records
capture only a limited portion of the range of natural variability possible. Tree-
ring reconstructions of streamflow (i.e., dendrohydrologic reconstructions) have
proven to be useful for augmenting existing instrumental streamflow records
(e.g., Stockton and Jacoby 1976, Loaiciga et al. 1993, Meko and Graybill
1995, Cleaveland 2000). In this study, we are working with water engineers
from the City of Westminster (Colorado) to generate reconstructions and data
for Clear Ck. (the main source of water for Westminster) that are useful for water
resource management. We explore two approached: 1) the generation of
measures of drought (frequency, severity, and duration) over the 300-year
reconstructed record, and 2) the investigation of alternative types of hydrologic
reconstructions.
GAGE
PHOTO BY JEFF LUKAS2. CLEAR CREEK RECONSTRUCTED STREAMFLOW
Total annual streamflow for Clear Creek at Welch Ditch gage ( ) was
reconstructed using a least-squares stepwise regression technique (Woodhouse
2000). The period of time common to both the gage record and the tree-ring
chronologies was 1912-1980. The stepwise regression was run on the full time period.
Four predictor variables, out of 28 possible variables, were selected
). Together, they explain 61% of the variance in the
streamflow ( ).
The reconstruction was validated using a split-sample technique in which regression
models with the same predictor variables were calibrated on the years 1912-1946
and verified on the years 1947-1980, and then
map above
(see map above
for chronology locations
left, top
calibrated on the years 1947-1980
and verified on the years 1912-1946. The variances explained in the full model and
both calibration and verification periods for split models were similar and averaged
about 60%. The regression model was then used to reconstruct Clear Creek
streamflow from 1685 to 1987 ( )left, bottom
3. QUANTIFYING DROUGHT -- LOW FLOW EVENTS
Drought can be quantified in terms of duration, severity, and
magnitude ( ). Individual water resource systems respond
differently to these factors. For example, a lengthy but moderately
dry period may be devastating to one system, while another may
be sensitive to short-term, severe droughts. It is important to analyze
drought in terms of all three measures.
Low-flow events in the 303-year Clear Creek reconstruction were
evaluated in terms of 1) number of consecutive years below
average, 2) cumulative negative departures (CND) for those years
(calculated from standardized values), and 3) an annual severity
index (CND divided by number of years) ( ). In the 20th
century, the most extreme low flow periods coincided with the
droughts of the 1930s and 1950s. In the 1930s, annual flow was
below average for eight consecutive years (1929-1936). The CND
for these years is -4.541. In contrast, the 1950’s low flow event lasted
only four years (1953-1956) but the CND is similar to the 1930’s
event, at -4.485. Accordingly, the annual severity of the 1950’s
event is much greater ( -1.121 vs. -0.568) (
The full reconstruction permits evaluation of the 1930s and 1950s
events in a broader temporal context ( ). The
19th century is especially notable for the frequency of low flow
events, some of which were quite severe. The eight-year event of
1845-1852 matched the length of the 1930’s event, but the annual
severity exceeds that of the 1950s event. In addition, this event is
separated by only two years from the three-year event of 1840-
1842, with the most extreme annual severity on record. The four
year 1885-1888 event was similar in magnitude to the 1950s event.
figure, right
figure, right
figure, bottom right).
figure, bottom right
5. DAILY FLOWS
For some purposes, such as fish survival or
recreation, the flow variable of interest might not be
the annual total flow, but the lowest daily flow
averaged over a few days or weeks each year. The
recurrence interval of such low flows can be used by
planners. The 10-year 7-day low flow, or the annual
minimum 7-day average flow with an average
recurrence interval of 10 years, is one example
(Dunne and Leopold 1978).
As a pilot study of the weekly or monthly low-flow
signal in tree rings, we analyzed the -day low flows
for Clear Creek using the daily gage data for the
period 1947-1995. To avoid the low flows that
commonly occur on this stream in late winter and
early spring, we restricted the search window for
defining annual low flows to the months July-
September. The interannual variation in -day low
flow on Clear Creek is clearly coupled with that of
total annual (water-year) flow even at the shortest
periods -- the 1-day average ( ).
A correlation analysis of the 7-day low flows against
fourteen nearby standard tree-ring chronologies of
varied species and site-type indicates that the
relationship between tree rings and annual 7-day
flow is weaker than that between tree rings and total
annual flow ( ). Sites with the strongest
signal for 7-day low flow also have the strongest
signal for annual flow. If the 7-day low flow is viewed
conceptually as a baseflow component, we might
expect that annual flow minus this component
would have an amplified signal in tree growth. For all
sites tested, however, subtraction of the ‘baseflow’
component resulted in a reduction of the correlation
with tree rings. For Clear Creek, it appears therefore
that little would be gained by attempting to directly
reconstruct 7-day low flows from tree-ring data; a
better alternative might be to reconstruct annual
flow and use the relationship between gaged
annual flow and 7-day low flow to infer 7-day low
flows prior to the gaged record. We emphasize that
a different conclusion might be reached for other
streams, depending on climatic regime, basin size,
hydrogeology and available tree-ring data.
n
n
right, top
right, bottom
REFERENCES CITEDCleaveland, M. K., 2000. A 963-year reconstruction of summer (JJA)
streamflow for the White River, Arkansas. 10,33-41
Dunne, T. and Leopold, L. B., 1978.
W. H. Freeman and Co., New York, 818 pp.
Loaciga, H. A., L. Haston, and J. Michaelsen, 1993. Dendrohydrology
and long-term hydrologic phenomena. 31,151-171.
Meko, D. and D. A. Graybill, 1995. Tree-ring reconstructions of upper Gila
River discharge. 31,605-615.
Stockton, C. W. and G. C. Jacoby, 1976. Long-term surface water supply
and streamflow levels in the upper Colorado River basin.
, Inst. of Geophysics and
Planetary Physics, University of California, Los Angeles, 70 pp.
Woodhouse, C. A., 2000. Extending hydrologic records with tree rings.
, 2,25-27.
This Research was supported by NSF awards ATM-972957, ATM-0080834
The Holocene
Water in environmental planning.
Rev. Geophys.
Water Res. Bull.
Lake
Powell Research Project Bulletin No. 18
Water Res. Impacts
4. NEW APPROACHES TO STREAMFLOW RECONSTRUCTION - MEDIAN AND QUANTILE REGRESSION
One shortcoming of traditional reconstructions based on least-squares regression, is that the extreme values are
underestimated. a consequence of the least squares process. For the City of Westminster, over- or under-estimated
low flow can have costly results. We investigated the use of median and quantile regression to estimate values at
given quantiles and to establish a range of probable values. The characteristics of median and quantile regression,
and their differences from ordinary least squares (OLS) regression, are outlined in the table, .below
Results from quantile regressions for the
10th and 90th percentiles are shown
along with the observed streamflow
record ( ). To validate the
regression results, split sample analysis
was carried out on each of the quantile
regressions, calibrating on half the years,
testing on the other half, then reversing
the halves. Residuals generally fell into
the appropriate negative/positive splits
expected according to the quantile. In
comparing the observed record and
the 90th and 10th percentile
regressions, only five of the observed
cases fall outside the two regression
lines (and only slightly so). Full
reconstructions (1685-1987) based on
the regression coefficients for these two
percentiles and the median regression
will result in an extended record that
includes a range of probable values for
each year.
figure at right
The same four predictor variables
defined in the stepwise regression were
used as the variables predicting Clear
Creek streamflow in the median and
quantile regressions. Results for the
median regression, compared to the
observed values, and values obtained
from the OLS regression ( )
show that while the OLS regression tends
to underpredict extreme values, the
median regresssion tends to overpredict
them. However, the median
reconstruction also does a better job of
duplicating observed values in some
years, such as the 1930s.
figure at left
0
1
-1
-2
2
Magnitude
Severity
Duration0
1
-1
-2
2
Interval
MEASURES
of
DROUGHT
(1/interval = frequency)National Archives and Records Administration