Estimating Uncertainty

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Estimating Uncertainty in Ecosystem Budgets
Ruth Yanai, SUNY-ESF, Syracuse Ed 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
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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 the product 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 the product is the
product of the means times the sum of the
variance of the factors
wood mass wood N concentration But
log (Mass) a blog(PV) error And PV 1/2
r2 Height log(Height) a blog(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 Simulation Tree Height
log (Height) a blog(Diameter) error
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Monte Carlo Simulation Tissue Mass
log (Mass) a blog(PV) error PV 1/2 r2
Height
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Monte Carlo Simulation Tissue Concentration
N concentration constant error
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Monte Carlo Simulation
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Monte Carlo Simulation
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
IMPORTANT Random selection of parameters
values happens HERE, not separately for each tree
Height 10(a blog(Diameter) log(E))
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Biomass Parameters
Lookup
Lookup
Lookup
Biomass 10(a blog(PV) log(E))
PV 1/2 r2 Height
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Biomass Parameters
Lookup
Lookup
Lookup
Biomass 10(a blog(PV) log(E))
PV 1/2 r2 Height
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Biomass Parameters
Lookup
Lookup
Lookup
Biomass 10(a blog(PV) log(E))
PV 1/2 r2 Height
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Concentration Parameters
Lookup
Lookup
Concentration constant error
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COPY THIS ROW--gt
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After enough interations, analyze your results
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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
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Repeated Calculations of N in Biomass Hubbard
Brook Watershed 6
Uncertainty in Biomass N 110 kg/ha Coefficient
of Variation 18
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Approaches to Estimating Uncertainty Replicate
Measurements
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Replicate Samples
Variation across plots 16 Mg/ha, or 5
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Replicate Samples
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 doesnt 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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The N budget for Hubbard Brook published in 1977
was missing 14.2 kg/ha/yr
Borrmann et al. (1977) Science
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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 cant 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?
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What is the greatest source of uncertainty to my
answer?
Better than the uncertainty in the parameter
estimates--we can tolerate a large uncertainty in
an unimportant parameter.
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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.