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Quantifying Uncertainty in Ecosystem Studies

QUEST is a NSF-funded Research Coordination Network with the goal of improving understanding and facilitating the use of uncertainty analyses in ecosystem studies.

First, a quick survey…• Which of you make measurements of

• Precipitation• Streamflow• Vegetation (biomass)• Soils• Other

• Which of you reports• Measurement Uncertainty • Natural Variation• Model Error• Model Selection Error

First, a quick survey…• Which of you deals with:

• Deciding when data are unusable• Filling gaps in datasets• Analytical values at or below detection limit

About this Working Group

Brief Presentations, each followed by discussion• Ruth Yanai: intro to QUEST: uncertainty in ecosystem budgets• Craig See: Streamflow Gaps: Why they occur and what we can do about it• John Campbell: Uncertainty in net hydrologic flux of calcium • Melissa Slater: Spatial patterns of precipitation in complex terrain• Josh Roberti: Connecting uncertainty estimates and QA/QC methods• Carrie Levine: Bayesian hierarchical analysis of demographic processes

Discussion of more general issues

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A Brief History of QUEST1983 Yanai started at HBR: Ecosystem Budgets have no Error

2008 Yanai commits to addressing error in a symposium. Ed Rastetter helps.

2009 Battles and Richardson join in publication of “Error for Dummies” paper in Ecosystems (Yanai et al. 2010)

2010 Hubbard Brook Committee of Scientists addresses uncertainty. Mark Green and John Campbell join.

2011 John Campbell names QUEST. Carrie Levine designs the logo

2011, 2012 LTER Working Groups address streamflow, precipitation

2013 QUEST funded by NSF as an RCN for 5 years

2012 - Sessions at LTER ASM, ESA, AGU, ESA, IUFRO, ASM…

UNCERTAINTY

Natural Variability

Spatial Variability

Temporal Variability

Knowledge Uncertainty

Measurement Error

Model Error

Types of uncertainty commonly encountered in ecosystem studies

Adapted from Harmon et al. (2007)

Bormann et al. (1977) Science

How can we assign confidence in ecosystem nutrient fluxes?

Bormann et al. (1977) Science

The N budget for Hubbard Brook published in 1977 was “missing” 14.2 kg/ha/yr

Net N gas exchange = sinks – sources = - precipitation N input+ hydrologic export+ N accretion in living biomass+ N accretion in the forest floor ± gain or loss in soil N stores- weathering N input

The N budget for Hubbard Brook published in 1977 was “missing” 14.2 kg/ha/yr

14.2 ± ?? kg/ha/yr

Net N gas exchange = sinks – sources = - precipitation N input+ hydrologic export+ N accretion in living biomass + N accretion in the forest floor± gain or loss in soil N stores

The N budget for Hubbard Brook published in 1977 was “missing” 14.2 kg/ha/yr

14.2 ± ?? kg/ha/yr

Measurement Uncertainty Sampling UncertaintySpatial and Temporal Variability

Model Uncertainty

Error within models Error between models

Volume = f(elevation, aspect): 3.4 mm

Undercatch: 3.5%Chemical analysis: 0-3%

Model selection: <1%

Across catchments:

3%

Across years:

14%

We tested the effect of sampling intensity by sequentially omitting individual precipitation gauges.

Estimates of annual precipitation volume varied little until five or more of the eleven precipitation gauges were ignored.

Net N gas exchange = sinks – sources = - precipitation N input (± 1.3)+ hydrologic export+ N accretion in living biomass + N accretion in the forest floor± gain or loss in soil N stores

The N budget for Hubbard Brook published in 1977 was “missing” 14.2 kg/ha/yr

14.2 ± ?? kg/ha/yr

Net N gas exchange = sinks – sources = - precipitation N input (± 1.3)+ hydrologic export+ N accretion in living biomass + N accretion in the forest floor± gain or loss in soil N stores

The N budget for Hubbard Brook published in 1977 was “missing” 14.2 kg/ha/yr

14.2 ± ?? kg/ha/yr

Net N gas exchange = sinks – sources = - precipitation N input (± 1.3)+ hydrologic export (± 0.5)+ N accretion in living biomass + N accretion in the forest floor± gain or loss in soil N stores

The N budget for Hubbard Brook published in 1977 was “missing” 14.2 kg/ha/yr

14.2 ± ?? kg/ha/yr

Net N gas exchange = sinks – sources = - precipitation N input (± 1.3)+ hydrologic export (± 0.5)+ N accretion in living biomass + N accretion in the forest floor± gain or loss in soil N stores

The N budget for Hubbard Brook published in 1977 was “missing” 14.2 kg/ha/yr

14.2 ± ?? kg/ha/yr

Monte Carlo

Simulation

Yanai, Battles, Richardson, Rastetter, Wood, and Blodgett (2010) Ecosystems

Monte Carlo simulations use random sampling of the distribution of the inputs to a calculation. After many iterations, the distribution of the output is analyzed.

0

50

100

150

200

250

300

350

400

LeavesBranchesBarkWood

Biom

ass

(Mg/

ha)

C1 C2 C3 C4 C5 C6 HB-Mid JB-Mid C7 C8 C9 HB- Old JB-Old

Young Mid-Age Old

Biomass of thirteen standsof different ages

0

50

100

150

200

250

300

350

LeavesBranchesBarkWood

Biom

ass

(Mg/

ha)

C1 C2 C3 C4 C5 C6 HB-Mid JB-Mid C7 C8 C9 HB- Old JB-Old

3% 7% 3%

4% 4% 3% 3% 3%

3% 2% 4% 4% 5%

Coefficient of variation (standard deviation / mean)of error in allometric equations

Young Mid-Age Old

0

50

100

150

200

250

300

350

LeavesBranchesBarkWood

Biom

ass

(Mg/

ha)

C1 C2 C3 C4 C5 C6 HB-Mid JB-Mid C7 C8 C9 HB- Old JB-Old

Young Mid-Age Old

3% 7% 3%

4% 4% 3% 3% 3%

3% 2% 4% 4% 5%

CV across plots within stands (spatial variation)Is greater than the uncertainty in the equatsions

6% 15% 11%

12% 12% 18% 13% 14%

16% 10% 19% 3% 11%

Net N gas exchange = sinks – sources = - precipitation N input (± 1.3)+ hydrologic export (± 0.5)+ N accretion in living biomass (± 1)+ N accretion in the forest floor± gain or loss in soil N stores

The N budget for Hubbard Brook published in 1977 was “missing” 14.2 kg/ha/yr

14.2 ± ?? kg/ha/yr

Net N gas exchange = sinks – sources = - precipitation N input (± 1.3)+ hydrologic export (± 0.5)+ N accretion in living biomass (± 1)+ N accretion in the forest floor± gain or loss in soil N stores

The N budget for Hubbard Brook published in 1977 was “missing” 14.2 kg/ha/yr

14.2 ± ?? kg/ha/yr

Oi

Oe

Oa

E

Bh

Bs

ForestFloor

MineralSoil

Excavation of a forest floor block (10

x 10 cm)

Nitrogen in the Forest FloorHubbard Brook Experimental Forest

Nitrogen in the Forest FloorHubbard Brook Experimental Forest

The change is insignificant (P = 0.84).The uncertainty in the slope is ± 22 kg/ha/yr.

Net N gas exchange = sinks – sources = - precipitation N input (± 1.3)+ hydrologic export (± 0.5)+ N accretion in living biomass (± 1)+ N accretion in the forest floor (± 22)± gain or loss in soil N stores

The N budget for Hubbard Brook published in 1977 was “missing” 14.2 kg/ha/yr

14.2 ± ?? kg/ha/yr

Net N gas exchange = sinks – sources = - precipitation N input (± 1.3)+ hydrologic export (± 0.5)+ N accretion in living biomass (± 1)+ N accretion in the forest floor (± 22)± gain or loss in soil N stores

The N budget for Hubbard Brook published in 1977 was “missing” 14.2 kg/ha/yr

14.2 ± ?? kg/ha/yr

Nitrogen Pools (kg/ha)Hubbard Brook Experimental Forest

Forest Floor

Live Vegetation

Coarse Woody Debris

Mineral Soil10 cm-C

Dead Vegetation

Mineral Soil0-10 cm

Quantitative Soil Pits0.5 m2 frame

Excavate Forest Floor by horizonMineral Soil by depth increment

We can’t detect a difference of 730 kg N/ha in the mineral soil.

From 1983 to 1998, 15 years post-harvest, there was an insignificant decline of 54 ± 53 kg N ha-1 y-1

Huntington et al. (1988)

Net N gas exchange = sinks – sources = - precipitation N input (± 1.3)+ hydrologic export (± 0.5)+ N accretion in living biomass (± 1)+ N accretion in the forest floor (± 22)± gain or loss in soil N stores (± 53)

The N budget for Hubbard Brook published in 1977 was “missing” 14.2 kg/ha/yr

14.2 ± ?? kg/ha/yr

Net N gas exchange = sinks – sources = - precipitation N input (± 1.3)+ hydrologic export (± 0.5)+ N accretion in living biomass (± 1)+ N accretion in the forest floor (± 22)± gain or loss in soil N stores (± 53)

The N budget for Hubbard Brook published in 1977 was “missing” 14.2 kg/ha/yr

14.2 ± 57 kg/ha/yr

The Value of Uncertainty Analysis

Quantify uncertainty in our resultsUncertainty in regressionMonte Carlo samplingDetectable differences

Identify ways to reduce uncertaintyDevote effort to the greatest unknowns

Improve efficiency of monitoring efforts

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QUANTIFYING UNCERTAINTY IN ECOSYSTEM STUDIES