Campbell, Quantifying uncertainty in ecology: Examples from small watershed studies.

Quantifying Uncertainty in Ecology: Examples from Small Watershed Studies

Ecological Society of America Meeting

Minneapolis, MN - August 2013

John Campbell – US Forest ServiceRuth Yanai – SUNY-ESF

Mark Green – Plymouth State Univ.

LTER Workshop Participants

Campbell, J.L., Yanai, R.D., Green, M.B., Levine, C. R, Adams, M.B., Burns, D.A., Buso, D.C., Harmon, M.E., LaDeau, S.L., McDowell, W.H., Parman, J.N., Sebestyen, S.D., Shanley, J.B., Vose, J.M.

Fernow - WVBiscuit Brook - NY HJ Andrews - ORLuquillo - PR Niwot Ridge – COMarcell - MNSleepers River – VTCoweeta – NC

Sites

QUEST is a NSF funded Research Coordination Network (PI: Ruth Yanai)

The goal is to improve understanding and facilitate use of uncertainty analyses in ecosystem studies.

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Paired watershed studies

• Watersheds are unreplicated

• It’s difficult to find suitable replicate watersheds and expensive to treat them

• Uncertainty analysis can be used to report statistical confidence Andréassian 2004 Journal of

Hydrology 29:1-27

Easier said than done…

• Difficult to identify sources of uncertainty

• Difficult to quantify sources

• Multiple approaches to uncertainty analysis

• No single answer

W6W5

• Net hydrologic flux = precipitation inputs minus stream outputs

• W5 - whole tree harvest during winter of 1983-1984

• All trees >5 cm dbh were removed (boles and branches)

• Purpose: evaluate impact of this more intensive management practice on nutrient removals and site productivity

Uncertainty in the flux of Ca

Water year (June 1)

1960 1970 1980 1990 2000 2010

Net

hyd

rolo

gic

flux

(kg

ha-1

yr-

1)

-24

-21

-18

-15

-12

-9

-6

-3

0

W6 (reference)W5 (harvested)

Ca response to harvesting

Harvest

Calcium data courtesy G.E. Likens

Sources of uncertainty

Precipitation • Interpolation model

• Collector undercatch

• Chemical analysis

• Gaps in chemistry

Stream water• Watershed area

• Rating curve

• Gaps in discharge

• Chemical analysis

• Streamwater

interpolation model

Precipitation interpolation method

0 1000 m

1000 1600 mm

Precip. gageWatershed

Precip.

W6 W5 W4W2

W3

W7W8

W9

W1 W6 W5 W4W2

W3

W7W8

W9

W1

W6 W5 W4W2

W3

W7W8

W9

W1

W6 W5 W4W2

W3

W7W8

W9

W1

Kriging

W6 W5 W4W2

W3

W7W8

W9

W1Inverse distanceweighting

Thiessen polygon

Spline

Regression

Precipitation interpolation method

W1 W2 W3 W4 W5 W6 W7 W8 W9

Ann

ual p

reci

p. (

mm

)

1340

1360

1380

1400

1420

1440

1460

1480

1500

1520

ThiessenKrigingIDWSplineRegression

Uncertainty = 0.6%

Chemical analyses

Uncertainty = 1.0%

• Precision describes the variation in replicate analysis of the same sample

• At Hubbard Brook, one sample of every 40 is analyzed four times 

Watershed area

Watershed area

W6

Uncertainty = 2.3%

Gaps in streamflow

• 7% of streamflow record is gaps• 65% due to the chart recorder (53% clock)

Gaps in streamflow

Uncertainty = 3.3%

• Randomly generate fake gaps

• Fill the gaps based on regression from the reference watershed

• Calculate the different between the predicted and actual value

• Repeat thousands of times

• More detail to follow

What is Monte Carlo analysis?

1) Select a distribution to describe possible values (not necessary to assume a normal distribution)

2) Generate data from this distribution

3) Use the generated data as possible values in the calculation to produce output

Monte Carlo simulations use repeated, random sampling to compute results.

Streamflow

Monte Carlo approach

Watershed Area

Net Hydrologic Flux

Etc.

Calculation

Ca response to harvesting

Harvest

Water year (June 1)

1960 1970 1980 1990 2000 2010

Ne

t hyd

rolo

gic

flu

x (k

g h

a-1

yr-

1)

-24

-21

-18

-15

-12

-9

-6

-3

0

W6 (reference)W5 (harvested)

Harvest

Ca response to harvesting

W6 Ca Net hydrologic flux (kg/ha/yr)

-25 -20 -15 -10 -5 0

W5

Ca

net

hydr

olog

ic f

lux

(kg/

ha./

yr)

-25

-20

-15

-10

-5

0

Contributions to uncertainty

Conclusions

• Uncertainty analysis can be used in cases where replication is not possible

• Monte Carlo is just one of many possible approaches

• There’s no such thing as a perfect uncertainty analysis

• It’s important to report how the uncertainty was calculated

Acknowledgments

Funding was provided by the NSF and LTER Network Office. Calcium data were obtained through funding from the A.W. Mellon Foundation and the NSF, including LTER and LTREB.

LTER Workshop Participants

Craig SeeBrannon Barr

Gene Likens

Amey BaileyIan HalmNick GrantTammy WoosterBrenda Minicucci

www.quantifyinguncertainty.org