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