Uncertainty in Forest Carbon and Nutrient Budgets

Ruth D. Yanai

State University of New YorkCollege of Environmental Science and Forestry

Syracuse NY 13210, USA

Quantifying uncertainty in ecosystem budgets

Precipitation (evaluating monitoring intensity)

Streamflow (filling gaps with minimal uncertainty)

Forest biomass (identifying the greatest sources of uncertainty)

Soil stores (detectable differences)

QUANTIFYING UNCERTAINTY IN ECOSYSTEM STUDIES

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

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.

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

14.2 ± ?? kg/ha/yr

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

14.2 ± ?? kg/ha/yr

Yanai, Levine, Green, and Campbell (2012) Journal of Forestry

Don Buso HBES

Gaps in the discharge record are filled by comparison to other streams at the site, using linear regression.

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Cross-validation: Create fake gaps and compare observed and predicted discharge

Gaps of 1-3 days: <0.5%Gaps of 1-2 weeks: ~1%

2-3 months: 7-8%Yanai et al. (2014) Hydrological Processes

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

Tree Inventory

log(Height) = a + b*log(Diameter) ± errorlog (Mass) = a + b*log(1/2 r2 *Height) ± error

Nutrient content = Mass * (Concentration ± error)Sum all trees and all tissue types

Allometric Equations

and Nutrient Concentrations

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.

Repeated Calculations of N in BiomassHubbard Brook Watershed 6

611 ± 54 kg N/ha

Nitrogen Content of Biomasswith Uncertainty

***IMPORTANT***

Random selection of parameter values applies across all the trees and all the time periods in each iteration.

The uncertainty between two measurements can be less than in a single measurement!

100 Simultaneous Calculations of N in Biomass in 1997 and 2002

100 Simultaneous Calculations of N in Biomass in 1997 and 2002

Accumulation Rate of N in BiomassDistribution of Estimates

18 ± 5 kg N/ha over 5 yr

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

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

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%

Yanai, Levine, Green, and Campbell (2012) Journal of Forestry

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

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Nitrogen in the Forest FloorHubbard Brook Experimental Forest

y = 0 . 0 0 0 2 x - 0 . 1 6 1 9R 2 = 0 . 0 1 0 9

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Nitrogen in the Forest FloorHubbard Brook Experimental Forest

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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

Studies of soil change over time often fail to detect a difference.We should always report how large a difference is detectable.

Yanai et al. (2003) SSSAJ

Power analysis can be used to determine the difference detectable with known confidence

Yanai et al. (2003) SSSAJ

Sampling the same experimental units over time permits detection of smaller changes

Yanai et al. (2003) SSSAJ

In this analysis of forest floor studies, few could detect small changes

Yanai et al. (2003) SSSAJ

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

1796

29

10

1260

750

3080

Forest Floor

Live Vegetation

Coarse Woody Debris

Mineral Soil10 cm-C

Dead Vegetation

Mineral Soil0-10 cm

Yanai et al. (2013) ES&T

Quantitative Soil Pits

0.5 m2 frame

Excavate Forest Floor by horizon

Mineral Soil by depth increment

Sieve and weigh in the field

Subsample for laboratory analysis

In some studies, we excavate in the C horizon!

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)

Yanai et al. (2013) ES&T

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

Net N gas exchange = sinks – sources = - precipitation N input (± 1.3)+ hydrologic export (± 0.5)+ N accretion in living biomass (± 1)

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

14.2 ± 2.6 kg/ha/yr

Draw your budget boundaries to ask questions that can be answered with confidence!

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

ReferencesYanai, R.D.,  N. Tokuchi, J.L. Campbell, M.B. Green, E. Matsuzaki, S.N. Laseter, C.L. Brown, A.S. Bailey, P. Lyons, C.R. Levine, D.C. Buso,  G.E. Likens, J. Knoepp, K. Fukushima. 2014. Sources of uncertainty in estimating stream solute export from headwater catchments at three sites.   Hydrological Processes. DOI: 10.1002/hyp.10265

Yanai, R.D., M.A. Vadeboncoeur, S.P. Hamburg, M.A. Arthur, M.A. Fuss, P.M.Groffman, T.G. Siccama, and C.T. Driscoll.  2013.  From Missing Source to Missing Sink: Long-Term Changes in a Forest Nitrogen Budget.  Environmental Science & Technology. 47(20):11440-11448.  

Yanai, R.D., C.R. Levine, M.B. Green, and J.L. Campbell. 2012. Quantifying uncertainty in forest nutrient budgets,  J. For.  110:  448-456

Yanai, R.D., J.J. Battles, A.D. Richardson, E.B. Rastetter, D.M. Wood, and C. Blodgett. 2010. Estimating uncertainty in ecosystem budget calculations. Ecosystems 13: 239-248

Wielopolski, L, R.D. Yanai, C.R. Levine, S. Mitra, and M.A Vadeboncoeur. 2010. Rapid, non-destructive carbon analysis of forest soils using neutron-induced gamma-ray spectroscopy. For. Ecol. Manag. 260: 1132-1137

Yanai, R.D., S.V. Stehman, M.A. Arthur, C.E. Prescott, A.J. Friedland, T.G. Siccama, and D. Binkley. 2003. Detecting change in forest floor carbon. Soil Sci. Soc. Am. J. 67:1583-1593

My web site: www.esf.edu/faculty/yanai (Download any papers)

Alternative spatial models for precipitation in the Hubbard Brook Valley

Alternative spatial models for precipitation in the Hubbard Brook Valley

0.36%

0.58%

0.24%

0.77% 0.83%