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

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. (m

m)

1340

1360

1380

1400

1420

1440

1460

1480

1500

1520ThiessenKrigingIDWSplineRegression

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)

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

Net

hyd

rolo

gic

flux

(kg

ha-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 h

ydro

logi

c flu

x (k

g/ha

./yr)

-25

-20

-15

-10

-5

0

Contributions to uncertainty

• Stream chemistry sampling interval• Rating curve at high flow

Other sources of Uncertainty

Source of excess Ca in W5

• Dissolution of calcium oxalate, which is common in plant tissue and is known to accumulate in forest soils (Bailey et al. 2002).

• Dissolution of nonsilicate minerals, such as calcite and apatite, which are more rapidly weathered than silicate minerals (Hamburg et al. 2003).