Uncertainty Analysis for a US Inventory of Soil Organic Carbon Stock Changes

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Uncertainty Analysis for a US Inventory of Soil
Organic Carbon Stock Changes

• F. Jay Breidt
• Department of Statistics
• Colorado State University
• Stephen M. Ogle and Keith Paustian
• Natural Resources Ecology Laboratory
• Colorado State University

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Why Inventory Soil Carbon Stocks?

• Solar energy transmitted to earth as visible and
  ultraviolet radiation
• Radiation absorbed by surface gets re-radiated as
  infrared
• Greenhouse Gases (GHGs)
• pass visible and UV, but trap infrared
  greenhouse effect
• include (among others) water vapor, methane,
  nitrous oxide, CO2

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Carbon Sequestration

• Lithosphere fossil fuels, limestone, dolomite,
  chalk
• Oceans shells, dissolved CO2
• Biosphere organic molecules in living and dead
  organisms
• Soils organic matter

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Agricultural Management and Carbon Storage

• Tillage, fertilization, irrigation, etc. all
  affect carbon storage
• Century, a biogeophysical process model,
  describes site-specific dynamics in an
  agricultural system
• tracks carbon, water, nutrient cycling over long
  time scales (centuries to millennia)
• requires inputs on soils, weather, agricultural
  management
• deterministic output for given inputs

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Carbon Dynamics in Century
Metherell, Harding, Cole, Parton 1993
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Inventory Goal

• Estimate total carbon stock change for US
  agricultural soils, 1990-2004
• Report to United Nations Framework Convention on
  Climate Change
• pre-Kyoto agreement nearly universal
• Use Century to model carbon stock change across
  US
• need Century inputs on nationally-representative
  set of sites in US agricultural lands

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USDA National Resources Inventory (NRI)

• Nationally-representative set of sites in US
  agricultural lands
• Stratified two-stage area sample
• Fine stratification with two primary sampling
  units (PSUsquarter sections) for every 1/3
  township
• Three secondary sampling units (points) per PSU
• Many points have
• same county, MLRA, weather
• same categorical values of cropping history,
  soil, etc.
• Run Century at NRI superpoints

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NRI Handles Sampling Uncertainty

• NRI is a nationally-representative probability
  sample
• straightforward and unbiased expansion of
  point-level data to national total carbon stock
  change
• consistent design-based variance estimation and
  valid confidence intervals
• NRI contains many key Century inputs
• site-level cropping history, soil properties

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Input Uncertainty

• Not all needed Century inputs are in NRI
• Weather (but treat as known from PRISM local
  interpolation of station data)
• Tillage use county-level Conservation Technology
  Information Center data
• Organic amendments use county-level USDA Manure
  Management Database
• Fertilizer use county-level USDA-ERS Cropping
  Surveys

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Tillage

• Traditional Tillage
• after harvest, field contains crop residues
• tillage turns over the soil to bury residues
• often repeated several times prior to planting
• Conservation Tillage
• Reduced-Till limited tillage substantial crop
  residues on surface
• No-Till doesnt use tillage all crop residues
  left on surface

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Tillage Input Distribution

• Conservation Technology Information Center (CTIC)
  collects county-level information
• construct discrete distributions for Monte Carlo
  (CT?CT, CT?RT, CT?NT, RT?RT, RT?NT, etc.)
• draw from these distributions to reflect
  uncertain inputs

Photo courtesy of USDA
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Organic Amendments and Fertilizer

• Organic amendments and fertilizer not included in
  NRI
• Use USDA Manure Management Database
• county-level data
• construct distributions for Monte Carlo
• combine with USDA-ERS cropping survey information
  to account for negative correlation with
  fertilizer

Artwork courtesy of the Wisconsin Department of
Natural Resources
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Model Uncertainty

• Century is imperfect
• For some long-term experimental sites, have
• measured carbon stock changes
• modeled carbon stock changes from Century
• complete set of inputs, plus additional
  covariates
• Adjust using regression of measured on modeled

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Measured Carbon Stock at Long-Term Experiment
Sites
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Measured vs. Modeled
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Adjusted Century Output

• Experiment sites
• No attempt to estimate Century rate parameters
  from these data (very high dimension)

estimated from data
error with dependence from repeated measures
measured carbon stock
known covariates
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Expansion to National Total

• Ideal expansion estimator
• Feasible

known covariates
MC from sampling distribution
MC from modeled distribution
r th replicate estimate of national total
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Complete Uncertainty Analysis Framework
correlated
(sampling)
Cropping History
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Combining Design and Monte Carlo Uncertainties

• Define
• second-order inclusion prob
• design covariance
• MC expectation
• MC covariance
• Unconditional variance

• model uncertainty

• input uncertainty

• sampling uncertainty

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Variance Estimation

• Combination of MC replication and design-based
  methods for (unreplicated) sample
• usual MC variance estimate
• usual design-based variance estimate for MC
  averages (SAS proc surveymeans or PCCARP once)
• average of design-based variance estimates across
  MC reps (SAS proc surveymeans or PCCARPR times)

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Variance Estimation, Continued

• Unbiased estimator of V is then
• But note that
• Simpler (saves R variance computations),
  conservative estimator

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Implementation

• n123K NRI superpoints in cropland, from almost
  1M total NRI points
• R100 MC reps for each NRI superpoint
• 12.3M Century runs
• Compute estimates and uncertainties at national
  level as well as for interesting domains

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National-Scale Century Inventory Results (Tg CO2
Eq.)
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Summary

• National inventory of carbon stock changes, using
  variety of data sources
• Combine Monte Carlo and design-based methods to
  account for
• sampling uncertainty
• input uncertainty
• model uncertainty
• First phase in ongoing study
• Future improvements
• Incorporate remote sensing data for estimating
  crop and forage production
• Account for emissions of N2O associated with
  agricultural management