Estimating Uncertainty in Ecosystem Budgets
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Estimating Uncertainty
in Ecosystem Budgets
Ruth Yanai, SUNY-ESF, SyracuseEd Rastetter, Ecosystems Center, MBL
Dusty Wood, SUNY-ESF, Syracuse
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Ecosystem Budgets have No Error
Hubbard Brook P Budget
Yanai (1992) Biogeochemistry
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Replicate Measurements
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Disparate measurements, all with errors?
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How can we estimate the uncertainty in ecosystem budget calculations from the uncertainty in the component measurements?
Try it with biomass N in Hubbard Brook Watershed 6.
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Mathematical Error Propagation
When adding, the variance of the total (T) is the sum of the variances of the addends (x):
For independent errors. If they’re correlated, use the sum of covariances.
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Mathematical Error Propagation
When adding, the variance of the total (T) is the sum of the variances of the addends (x):
Biomass N content = wood N content+ bark N content+ branch N content+ foliar N content+ twig N content+ root N content
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Mathematical Error Propagation
When adding, the variance of the total (T) is the sum of the variances of the addends (x):
Biomass N content = wood mass · wood N concentration+ bark mass · bark N concentration+ branch mass · branch N concentration+ foliar mass · foliar N concentration+ twig mass · twig N concentration+ root mass · root N concentration
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Mathematical Error Propagation
When multiplying, variance of theproduct is the product of the means times the sum of
the variance of the factors:
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Mathematical Error Propagation
When multiplying, variance of theproduct is the product of the means times the sum of
the variance of the factors:
wood mass · wood N concentration
But
log (Mass) = a + b*log(PV) + error
AndPV = 1/2 r2 * Height
log(Height) = a + b*log(Diameter) + error
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Mathematical Error Propagation
“The problem of confidence limits for treatment of forest samples by logarithmic regression is unsolved.” --Whittaker et al. (1974)
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Monte Carlo Simulation
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Monte Carlo SimulationTree Height
log (Height) = a + b*log(Diameter) + error
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Monte Carlo SimulationTissue Mass
log (Mass) = a + b*log(PV) + errorPV = 1/2 r2 * Height
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Monte Carlo SimulationTissue Concentration
N concentration = constant + error
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Monte Carlo Simulation
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Monte Carlo Simulation
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Calculate the nutrient contents of wood, branches, twigs, leaves and roots, using species- and element-specific parameters, sampling these parameters with known error.After many iterations, analyze the variance of the results.
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A Monte-Carlo approach could be implemented using specialized software or almost any programming language.
This illustration uses a spreadsheet model.
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Height Parameters
Height = 10^(a + b*log(Diameter) + log(E))
LookupLookup
Lookup
***IMPORTANT***Random selection of parameters values happens HERE, not separately for each tree
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Biomass Parameters
Biomass = 10^(a + b*log(PV) + log(E))
LookupLookup
Lookup
PV = 1/2 r2 * Height
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Biomass Parameters
Biomass = 10^(a + b*log(PV) + log(E))
Lookup
Lookup Lookup
PV = 1/2 r2 * Height
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Biomass Parameters
Biomass = 10^(a + b*log(PV) + log(E))
Lookup
Lookup Lookup
PV = 1/2 r2 * Height
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Concentration Parameters
Concentration = constant + error
LookupLookup
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COPY THIS ROW-->
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After enough interations, analyze
your results
Paste Values button
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total N, kg/ha
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Repeated Calculations of N in Biomass
Hubbard Brook Watershed 6
How many iterations is enough?
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Repeated Calculations of N in Biomass
Hubbard Brook Watershed 6
Two different sets of 250 iterations:Mean settles down over many iterations
Mean estimate of Biomass of N
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Number of Iterations
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Uncertainty in Biomass N: 110 kg/haCoefficient of Variation: 18%
Repeated Calculations of N in Biomass
Hubbard Brook Watershed 6 Standard Deviation of Biomass of N
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Hubbard Brook W6 is surveyed in 208 25m x 25m plots.
How much variation is there from one part of this watershed to another?
This is a more common way to represent uncertainty in budgets.
Approaches to Estimating Uncertainty:
Replicate Measurements
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Replicate Samples
Variation across plots: 16 Mg/ha, or 5%
Biomass for 50 m x 50 m Plots
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Plot Cluster2
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Bio
mass (
Mg
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RS
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STM
YB
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SM
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Replicate Samples
Biomass for 25 m x 25 m Plots
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Plot
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Variance across plots: 30 Mg/ha, or 10%with smaller plots
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Which is More Uncertain?
Total biomass
CV
Nitrogen content
CV
Multiple Plots 5%, 10% 6%, 10%
Uncertainty in Calculations
18% 18%
Parameter uncertainty doesn’t affect comparisons across space. But it matters when you take your number and go.
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The Value of Ecosystem Error
Quantify uncertainty in our results
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Borrmann 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 fixation (14.2 kg/ha/yr) = hydrologic export+ N accretion in the forest floor + N accretion in mineral soil + N accretion in living biomass- precipitation N input- weathering N input- change in soil N stores
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We can’t detect a difference of 1000 kg N/ha in the mineral soil…
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The Value of Ecosystem Error
Quantify uncertainty in our results
Identify ways to reduce uncertainty
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“What is the greatest source of uncertainty in my answer?”
Better than the sensitivity estimates that vary everything by the same amount--they don’t all vary by the same amount!
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Better than the uncertainty in the parameter estimates--we can tolerate a large uncertainty in an unimportant parameter.
“What is the greatest source of uncertainty to my answer?”
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Tissue
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Other Considerations
Independence of error (covariance)
Distribution of errors (normal or not)
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Additional Sources of Error
Bias in measurements
Errors of omission
Conceptual errors
Measurement errors
Spatial and temporal variation
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The Value of Ecosystem Error
Quantify uncertainty in our results
Identify ways to reduce uncertainty
Advice
One way or another, find a way to calculate ecosystem errors, and report them.
This is not possible unless researchers also report error with parameters.