Low Flow R² = 0.767 Peak Flow

R² = 0.8498

-6.0

-4.0

-2.0

0.0

2.0

4.0

6.0

-6.0 -4.0 -2.0 0.0 2.0 4.0 6.0

Pred

icte

d

Observed

B. RANK ALL UNITS BY AREA WEIGHTED Dd AND AGGREGATE For Shitike Creek example, the initial 75 units (including edges) are ranked by area weighted Dd and progressively summed to create 58 1km2 units, accurately accounting for edge cells without over-or under-weighting.

REVISITING WATERSHED DRAINAGE DENSITY: New considerations for hydrologic prediction

Sarah L. Lewis, Mohammad Safeeq College of Earth Ocean & Atmospheric Sciences

Oregon State University, Corvallis, Oregon 97331

Anne Jefferson Department of Geology, Kent State University, Kent, Ohio 44242

Gordon E. Grant USDA Forest Service, PNW Research Station, Corvallis, Oregon 97331

5 – Predicting Peak and Low Flows

2 – Probability Distribution Functions & Statistics

3 – A Unique Example: The McKenzie River 4 – Scaling up to a regional view

80 watersheds along the length of the Oregon Cascades, with varying proportions of High Cascade geology, a proxy for low Dd. Watersheds on the drier, east side of the Cascade crest are limited by gage availability. Gage records range from 30 to 100 years, and were QAQC for diversion and regulation.

How to represent heterogeneity within a watershed? Grid method captures average watershed behavior and provides additional information about distribution of Dd within the watershed. Is this sensitive to grid size? 2km grid under-estimates Dd, especially in elongate basins; 0.5km grid doesn’t improve estimates and is computationally heavy.

Stepwise regression with p>0.05 stopping rule

A. OVERLAY A GRID ON NHD FLOWLINES AND CALCULATE Dd FOR EACH 1 KM2 UNIT.

Dd = Stream Length (km) Basin Area (km2)

(inverse of spacing btwn streams)

3rd Skewness asymmetry

Kurtosis = 2.71

Landscape level variation in standard descriptive statistics

% HC mean stdev skew kurtosis 0 3.15 1.33 0.04 0.06

21 3.07 1.37 0.08 -0.24 46 2.64 1.50 0.22 -0.38 75 2.04 1.36 0.52 -0.07

100 1.18 0.93 0.88 0.81

C. GENERATE PDFs AND DESCRIPTIVE STATISTICS

The Upper McKenzie River is a landscape of strong geologic contrasts. Sourced from the

young volcanic High Cascades, the upper streams are groundwater dominated and

rarely flood. Joined downstream by flashy tributaries running through the older, steep and highly-dissected Western Cascades, the

larger watersheds are a hybrid of the two distinct geologic and hydrologic regimes.

Dd:mean

•There is a strong theoretical basis for drainage density (Dd) as a landscape level predictor of flow, but its application has been met with mixed success.

•Dd, traditionally represented as a single average value, can also be represented as a probability distribution function (PDF) of a range of values, reflecting Dd heterogeneity within a watershed.

• In single watersheds and within nested systems, PDFs and L-moment statistics describing their shapes explain flow behavior better than average Dd.

• In some landscapes, PDF metrics can greatly improve our process-based understanding of how drainage density influences peak and low flows.

PDF for Shitike Creek is positively skewed to lower Dd values and mesokurtic (normal).

Western High Cascades Signpost

1 – Why Drainage Density (Dd)?

Normal distributions & standard descriptive (L-moment) statistics

y = 2.7024x1.5905

R2 = 0.8154

y = 3.0368x-0.9864

R2 = 0.1267

0.01

0.1

1

10

100

1000

1 10Drainage Density

Uni

t Dis

char

ge

2DdflowFlood ∝

21

DdBaseflow∝

HORTON + DARCY = CARLSTON, 1963

• Directly applicable to flow routing • Measurable at a landscape scale and in ungaged basins • Reflects interaction between geology & climate • Represents underlying geology (lithology, structure, age and history) • Theoretically related to key hydrologic properties

R² = 0.01 R² = 0.15

R² = 0.05

R² = 0.04

0.01

0.1

1

10

0.1 1.0 10.0 100.0

2 yr

Pea

k F

low

(m

3 /s/

km2 )

Dd (km/km2)

North Central Utah

Southern California

Indiana

Appalachian Plateau

Data from Patton and Baker, 1976 ; as discussed by Dingman, 1984.

BUT IT DIDN’T WORK SO WELL IN OTHER PLACES…INCLUDING OUR STUDY AREA IN OREGON High Cascades

Western Cascades

IN THEORY…

Dd:Mean= 1.209

Watershed Ave Dd= 1.219

Shitike Creek USGS #14082750

Mean: 4.5 Stdev: 1.7 Skew: 0.01 Kurtosis: 0.09 DA: 409km2

Mean: 2.5 Stdev: 1.9 Skew: 0.5 Kurtosis: -0.2 DA: 2409km2

Mean: 3.0 Stdev: 1.2 Skew: -0.4 Kurtosis: -0.3 DA: 117km2

Mean: 2.2 Stdev: 1.4 Skew: 0.1 Kurtosis: -1.2 DA: 62km2

Mean: 2.7 Stdev: 1.3 Skew: -0.4 Kurtosis: -0.7 DA: 194km2

Mean: 1.5 Stdev: 1.3 Skew: 0.8 Kurtosis: 0.1 DA: 238km2

Mean: 2.1 Stdev: 0.9 Skew: -0.1 Kurtosis: -0.7 DA: 40km2

Mean: 1.3 Stdev: 1.3 Skew: 0.9 Kurtosis: 0.2 DA: 901km2

Dd:stdev Dd:skew Dd:kurtosis

SUMMARY STATISTICS FOR 80 STUDY WATERSHEDS

Dd:mean Dd:stdev Dd:skew Dd:kurtosis

Low Dd:range Dd:mean Dd:skew

Precip Slope

logMaxEl

Peak Dd:mean Elev:mean Precip Slope

High Dd (4.8 km/ km2) Low Dd (1.6 km/km2)

This study, 80 watersheds in Oregon (see site figure, Panel 4, for USGS gage locations)

1st Mean equivalent to traditional watershed ave Dd

2nd Standard deviation variation

4th Kurtosis shape of peak, weight of tails

+ =

S. Fork Vida abv.Blue Lookout blw. Blue Clear Smith Bridge

Dd

Rela

tive

Freq

uenc

y (%

)

Mean = 1.21

Skew = 1.18

Stdev = 1.03

moment moment moment moment

Drainage Density (km/km2)

Rela

tive

Freq

uenc

y (%

)

Vida S. Fork blw.Blue Lookout abv.Blue Bridge Smith Clear

R² = 0.25

R² = 0.14

0

0.5

1

1.5

2

2.5

3

0

20

40

60

80

100

0.5 0.75 1 1.25 1.5 1.75 2

R² = 0.05

R² = 0.16 0

0.5

1

1.5

2

2.5

3

0

20

40

60

80

100

0 1 2 3 4 5

R² = 0.81

R² = 0.87

-0.5 0 0.5 1 1.5 2 2.5 3

0

20

40

60

80

100

-0.6 -0.1 0.4 0.9 1.4

R² = 0.57

R² = 0.59 -0.5 0 0.5 1 1.5 2 2.5 3

0

20

40

60

80

100

-1.5 -1 -0.5 0 0.5

2yr P

eak

Flow

7 day 2 yr Low Flow

1:24,000-scale NHD flowlines

To get a sense of how these statistics play out across the landscape, we rank them by

High Cascade geology. High Cascade dominated watersheds have lower

Dd:mean and are also positively skewed.

CROSS CORRELATION OF L-MOMENT

STATISTICS FROM PDFS

PDFs help us understand how Dd works with respect to flow, but do

not necessarily improve models where landscape properties

(slope, relief) and climate (precip, snow) are incorporated

The ungaged upper McKenzie has very low Dd; this is reflected by the downstream most (Vida) PDF

mean stdev skew kurtosis area (km2) mean 1 stdev 0.60 1 skew -0.75 -0.37 1

kurtosis -0.16 -0.27 0.63 1 area (km2) 0.08 0.33 0.00 -0.11 1

PRELIMINARY MODELING RESULTS

R² = 0.23

R² = 0.20 0

2

4

6

8

10

12

14

0

20

40

60

80

100

120

140

0.000 1.000 2.000 3.000 4.000 5.000 6.000

2yr 7

-day

Low

Flo

w (m

m/d

ay)

2yr P

eak

Flow

(mm

/day

)

Watershed Average Dd (km/km2)