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Uncertainty in Forest Carbon and Nutrient Budgets
Ruth D. Yanai
State University of New YorkCollege of Environmental Science and Forestry
Syracuse NY 13210, USA
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Quantifying uncertainty in ecosystem budgetsPrecipitation (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
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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)
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Bormann et al. (1977) Science
How can we assign confidence in ecosystem nutrient fluxes?
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Bormann et al. (1977) Science
The N budget for Hubbard Brook published in 1977 was “missing” 14.2 kg/ha/yr
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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
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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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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%
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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.
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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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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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Yanai, Levine, Green, and Campbell (2012) Journal of Forestry
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Don Buso HBES
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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
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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
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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
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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
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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.
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Repeated Calculations of N in Biomass
Hubbard Brook Watershed 6
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611 ± 54 kg N/ha
Nitrogen Content of Biomasswith Uncertainty
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***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!
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100 Simultaneous Calculations of N in Biomass in 1997 and 2002
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100 Simultaneous Calculations of N in Biomass in 1997 and 2002
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Accumulation Rate of N in Biomass
Distribution of Estimates
18 ± 5 kg N/ha over 5 yr
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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
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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
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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%
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Yanai, Levine, Green, and Campbell (2012) Journal of Forestry
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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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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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Oi
Oe
Oa
E
Bh
Bs
ForestFloor
MineralSoil
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Nitrogen in the Forest FloorHubbard Brook Experimental Forest
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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.
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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
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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
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Power analysis can be used to determine the difference detectable with known confidence
Yanai et al. (2003) SSSAJ
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Sampling the same experimental units over time permits detection of smaller changes
Yanai et al. (2003) SSSAJ
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In this analysis of forest floor studies, few could detect small changes
Yanai et al. (2003) SSSAJ
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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
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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
Yanai et al. (2013) ES&T
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Quantitative Soil Pits0.5 m2 frame
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Excavate Forest Floor by horizonMineral Soil by depth increment
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Sieve and weigh in the fieldSubsample for laboratory analysis
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In some studies, we excavate in the C horizon!
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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
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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
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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
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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!
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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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Be a part of QUEST!• Find more information at: www.quantifyinguncertainty.org
• Read papers, share sample code, stay updated with QUEST News• Email us at [email protected]• Follow us on LinkedIn and Twitter: @QUEST_RCN
QUANTIFYING UNCERTAINTY IN ECOSYSTEM STUDIES
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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)
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Alternative spatial models for precipitation in the Hubbard Brook Valley
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Alternative spatial models for precipitation in the Hubbard Brook Valley
0.36%
0.58%
0.24%
0.77%
0.83%