estimating uncertainty in ecosystem budgets ruth yanai, suny-esf, syracuse ed rastetter, ecosystems...
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Estimating Uncertainty
in Ecosystem Budgets
Ruth Yanai, SUNY-ESF, SyracuseEd Rastetter, Ecosystems Center, MBL
Dusty Wood, SUNY-ESF, Syracuse
Ecosystem Budgets have No Error
Hubbard Brook P Budget
Yanai (1992) Biogeochemistry
Replicate Measurements
Disparate measurements, all with errors?
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.
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.
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
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
Mathematical Error Propagation
When multiplying, variance of theproduct is the product of the means times the sum of
the variance of the factors:
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
Mathematical Error Propagation
“The problem of confidence limits for treatment of forest samples by logarithmic regression is unsolved.” --Whittaker et al. (1974)
Monte Carlo Simulation
Monte Carlo SimulationTree Height
log (Height) = a + b*log(Diameter) + error
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Sugar Maple Diameter (cm)
He
igh
t (c
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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.
A Monte-Carlo approach could be implemented using specialized software or almost any programming language.
This illustration uses a spreadsheet model.
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
Biomass Parameters
Biomass = 10^(a + b*log(PV) + log(E))
LookupLookup
Lookup
PV = 1/2 r2 * Height
Biomass Parameters
Biomass = 10^(a + b*log(PV) + log(E))
Lookup
Lookup Lookup
PV = 1/2 r2 * Height
Biomass Parameters
Biomass = 10^(a + b*log(PV) + log(E))
Lookup
Lookup Lookup
PV = 1/2 r2 * Height
Concentration Parameters
Concentration = constant + error
LookupLookup
COPY THIS ROW-->
After enough interations, analyze
your results
Paste Values button
total N, kg/ha
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Repeated Calculations of N in Biomass
Hubbard Brook Watershed 6
How many iterations is enough?
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
kg
N/h
a
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
Replicate Samples
Variation across plots: 16 Mg/ha, or 5%
Biomass for 50 m x 50 m Plots
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Plot Cluster1
Plot Cluster2
Plot Cluster3
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Bio
mass (
Mg
/ha)
RS
WA
STM
YB
BE
SM
Replicate Samples
Biomass for 25 m x 25 m Plots
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75 108 142 181 204
Plot
Bio
mass (
Mg
/ha)
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STM
YB
BE
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Variance across plots: 30 Mg/ha, or 10%with smaller plots
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.
The Value of Ecosystem Error
Quantify uncertainty in our results
Borrmann et al. (1977) Science
The N budget for Hubbard Brook published in 1977 was “missing” 14.2 kg/ha/yr
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
We can’t detect a difference of 1000 kg N/ha in the mineral soil…
The Value of Ecosystem Error
Quantify uncertainty in our results
Identify ways to reduce uncertainty
“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!
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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StemWood
StemBark
Branches Leaves Twigs Roots LightWood
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Tissue
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(M
g/h
a)
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Other Considerations
Independence of error (covariance)
Distribution of errors (normal or not)
Additional Sources of Error
Bias in measurements
Errors of omission
Conceptual errors
Measurement errors
Spatial and temporal variation
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.
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