Melissa Martin and Julia Jones, PhD. Oregon State University.

Melissa Martin and Julia Jones, PhD.Oregon State University

O R E G O N

study basinsstreams

44°N

5 km

LookoutCreek

climate stationAndrews stream gage

Primet CS-2

WS 2

WS 8

WS 9

Vanmet

Hi-15

boundaries ofLookout Creek

WS 2 WS 8 WS 9

Gradient > 50% 25% > 60%

Slope length Median 150 m Median 90 m Median 60 m

Size 60 ha 15 ha 9 ha

Snow presence 6 mo. at high elev 6 mo. 1-2 weeks

Order Second order basin First order basin First order basin

Storm events 67 WR, 32 DR, 113 WRS (212)

14 WR, 7 DR, 23 WRS (44)

226 WR, 109 DR, 34 WRS (369)

peak discharge

precipitationbeforehydrographrise

event precipitation

centroid lag

start lag time to peak

event duration

maximum 15-minute precipitation intensity

baseflowat beginning

of hydrographrise

peak dischargedepth

time

Fig. 4

Compare peak discharge and precipitation for WR, DR, WRS events for each watershed

Examine relationship of hydrograph variables to intensity/timing of precipitation, under the three soil conditions listed above for each watershed

How are these different across the watersheds?

Why consider PCA? What is PCA?

- Explains variance-covariance structure

- Good for data reduction The ith PC is given by

Proportion of total population variance due to the kth PC is equal to

1 1 2 2' ...i i i i ip pY e X e X e X e X

( ) ' 1, 2,...,

( , ) ' 0i i i i

i k i k

Var Y i p

Cov Y Y i k

e Σe

e Σe

1 2 ...k

p

Examine the 10 hydrograph variables for normality

Chi-square plot for WS2 (untransformed variables)

sort(d)

Qch

i

0 20 40 60

51

01

52

02

5

Chi-square plot for WS2 (log transformed variables)

sort(d2)

Qch

i2

0 20 40 60 80 100

51

01

52

02

5

Obtain the coefficients of the PC’sVariable

ltotalprecip 0.400 0.028 -0.436 0.144

lmaxprecip -0.058 0.162 -0.465 -0.833

lprerunoff 0.172 -0.623 -0.166 -0.190

lstartlag 0.135 -0.652 -0.037 0.023

lcentroidlag 0.287 -0.221 0.330 -0.185

ltimetopeak 0.372 0.054 0.015 0.081

leventdur 0.445 0.124 -0.055 0.070

lqbase 0.215 0.062 0.599 -0.440

lqpeak 0.400 0.173 -0.244 0.077

lrunoffratio 0.406 0.243 0.183 -0.051

Variance 4.198 1.868 1.217 0.941

cum % of total var.

42.0 61.2 73.4 82.8

1e 2e 3e 4e

]734.1)[ln(406.0...]644.2))[ln(max058.0(]616.4)[ln(400.0ˆ1 orunoffratiprecipptotalpreciy

]734.1)[ln(243.0...]644.2)[ln(max162.0]616.4)[ln(028.0ˆ 2 orunoffratiprecipptotalpreciy

How many PC’s to choose?

Four PC’s are included in all principal component analyses

i

pro

p

2 4 6 8 10

0.0

0.2

0.4

0.6

0.8

1.0

Screeplot for WS2

Biplots: A 2-dimensional representation

Comp.1

Co

mp

.2

-0.2 -0.1 0.0 0.1 0.2

-0.2

-0.1

0.0

0.1

0.2

1

2

3

4

5

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8

910

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1213

14 1516

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-10 -5 0 5 10

-10

-50

51

0

ltotalprecip

lmaxprecip

lprerunofflstartlag

lcentroidlag

ltimetopeakleventdur

lqbase

lqpeaklrunoffratio

Biplot for storm events for WS2

-4 -2 0 2 4

y2hat

-20

24

y1h

atScatterplot of (y2hat,y1hat) for WS2

wrdrwrs

Storm event type for WS2

WS2 (60 ha) WS8 (15 ha) WS9 (9 ha)Gradient > 50% 25% > 60%

Slope length Median 150m Median 90m Median 60m

Snow presence 6 mo. at high elev 6 mo. 1-2 weeks

PC1 Magnitude of storm (no maxprecip)

Magnitude with maxprecip, no qbase

Magnitude, no qbase

PC2 Timing Antecedent vs. timing “Full” timing

PC3 Antecedent wetness vs. totalprecip and maxprecip

Centroidlag, qbase vs. maxprecip

Antecedent wetness

Event type PCA Fairly consistent-for DR events, PC3 is measure of maxprecip

Not consistent, but sample sizes are small

Fairly consistent-for WR events, PC3 is measure of peak discharge (instead of qbase)

Not good for WS9 Not good for WS8

Chi-square plot for WS9 (log transformed variables)

sort(d2)

Qch

i2

10 20 30 40

51

01

52

02

5

Chi-square plot for WR events in WS8

sort(d3)

Qch

i3

7 8 9 10 11 12

51

01

52

0

Statistical models: Factor analysis, two-way MANOVA, blocking, restricted date ranges, PCA regression

Hydrograph properties: Getting more storm events for WS8 (GetPQ), creating software for HJA

Slide 1: Photograph courtesy of Julia Jones. Slide 3: HJ Andrews Experimental Forest figure

from Perkins and Jones, Snow and physiographic controls, 1997.

- Information about the watersheds and event classification: Perkins and Jones, Snow and physiographic controls, 1997.

Slide 4: Hydrograph figure from Perkins and Jones, Snow and physiographic controls, 1997.

Slide 6: The result quoted is Result 8.1, found in Johnson, Richard A. and Wichern, Dean W. Applied Multivariate Statistical Analysis, 2002. Fifth edition, Prentice Hall, Upper Saddle River, New Jersey. Page 428.

Desiree Tullos for creating the EISI program Julia Jones and Tom Dietterich for

mentoring help on this research project Reed Perkins for running GetPQ to create

the hydrograph data set The entire HJA staff Fellow EISI participants