uncertainty analysis for a us inventory of soil organic carbon stock changes f. jay breidt...
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Uncertainty Analysis for a US Inventory of Soil Organic Carbon Stock Changes
F. Jay BreidtDepartment of StatisticsColorado State University
Stephen M. Ogle and Keith PaustianNatural Resources Ecology Laboratory
Colorado State University
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
Atmosphere
Surface
Reflected 25% 5%
Absorbed 25% 45%
Carbon Sequestration
Lithosphere: fossil fuels, limestone, dolomite, chalk
Oceans: shells, dissolved CO2
Biosphere: organic molecules in living and dead organisms
Soils: organic matter
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 kkc 1,zx
Carbon Dynamics in Century
Metherell, Harding, Cole, & Parton 1993
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
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 (PSUs=quarter 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”
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
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
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: doesn’t use tillage; all crop residues
left on surface
Tillage Input Distribution Conservation
Technology Information Center (CTIC) collects county-level information
construct discrete distributions for Monte Carlo (CTCT, CTRT, CTNT, RTRT, RTNT, etc.)
draw from these distributions to reflect uncertain inputs
Photo courtesy of USDA
Organic Amendments and Fertilizer
Organic amendments and fertilizer not included in NRI
Use USDA Manure Management Database
county-level dataconstruct distributions for
Monte Carlocombine with USDA-ERS
cropping survey information to account for negative correlation with fertilizer
Artwork courtesy of the Wisconsin Department of Natural Resources
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
Measured Carbon Stock at Long-Term Experiment Sites
Measured vs. Modeled
Organic Amendments
25 35 45 55 65 75 85 95
25
35
45
55
65
75
85
95
Hay/Pasture in
Annual Cropping Rotation
Sq
rt M
easu
red
So
il O
rgan
ic C
Sto
ck (
g/m
2 )
25
35
45
55
65
75
85
95
Bare-Summer
Fallow
25
35
45
55
65
75
85
95
Other Cropping
Practices
25 35 45 55 65 75 85 95
Hay/Pasture in
Annual Cropping Rotation
w/ Organic Amendments
Sqrt Modeled Soil Organic C Stock (g/m2)
No-Till Set-Aside Lands (CRP)
25 35 45 55 65 75 85 95
Adjusted Century Output Experiment sites
No attempt to estimate Century rate parameters from these data (very high dimension)
kkkkk cfy θzzx ,,, 21
known covariates
estimated from data
measured carbon stock
error with dependence from repeated measures
Expansion to National Total Ideal expansion estimator
Feasible
rkkrk
k kr cf θzzX ˆ,,,
1ˆ 21
NRI
MC from sampling distribution
MC from modeled distribution
known covariates
r th replicate estimate of national total
θzzx ,,,1~
21NRI
kkkk k
cf
Complete Uncertainty Analysis Framework
(sampling)
correlated
Cropping History
Combining Design and Monte Carlo Uncertainties Define
second-order inclusion prob:
design covariance: MC expectation: MC covariance:
Unconditional variance
Uk lk
klkl
Uk lk
lkklkkk
k k
cf V:ˆ,,,1
Var 21NRI
θzzX
NRI,Pr lkkl
lkklkl θzzX ˆ,,,E 21 kkkk cf
θzzXθzzX ˆ,,,,ˆ,,,Cov 2121 lllkkkkl cfcf
sampling uncertainty
model uncertainty input uncertainty
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)
NRI,
'
'21
'212
2
ˆ,,,ˆ,,,
1ˆ
lk lk
r
rll
rl
r
rkk
rk
kl
kl
RcfRcf
RR
RV
θzzXθzzX
1
ˆˆˆ
2
11
2
1
R
R
V
R
rr
R
rr
R
r lk lk
rll
rl
rkk
rk
kl
kl cfcf
RRV
1 NRI,
21213
ˆ,,,ˆ,,,
1
1ˆ
θzzXθzzX
Variance Estimation, Continued
Unbiased estimator of V is then
But note that
Simpler (saves R variance computations), conservative estimator
Rn
NOV
n
NOV
n
NOV
2
3
2
2
2
1ˆE,ˆE,ˆE
21* ˆˆˆ VVV
321ˆˆˆˆ VVVV
Implementation
n=123K NRI superpoints in cropland, from almost 1M total NRI points
R=100 MC reps for each NRI superpoint
12.3M Century runs Compute estimates and
uncertainties at national level as well as for interesting domains
National-Scale Century Inventory Results (Tg CO2 Eq.)
Soil Type 1990-1994 1995-2004
Mineral Soils
Croplands Remaining Croplands
(71.24) (62.52)
95% C.I. (69.7) to (73.0) (60.9) to (64.2)
Lands Converted to Croplands
1.47 (2.82)
95% C.I. 0.7 to 2.2 (2.2) to (3.3)
Grasslands Remaining Grasslands
(8.25) 3.96
95% C.I. (6.2) to (10.3) 2.2 to 5.5
Lands Converted to Grasslands
(12.80) (15.99)
95% C.I. (12.5) to (13.2) (15.8) to (16.1)
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