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