W. McNair Bostick, Oumarou Badini, James W. Jones, Russell S. Yost, Claudio O. Stockle, and

Amadou Kodio

Ensemble Kalman Filter Estimation of Soil Carbon in a Semi-Arid

Rotational Grazing System

Roles of Crop-Soil Models

• Improve understanding of soil C in West African conditions, combined with field experiments

• Explore management options; interactions with climate and soil

• Monitoring and verification of soil C - Prediction of soil C changes- Integrate with Remote Sensing and In-Situ

measurements to optimally estimate soil C changes

- Scale-up estimates over space

Contributions to SM CRSP & SANREM-SM CRSP Projects in West Africa (NASA and USAID funding)

Carbon from Communities:A Satellite View

Objectives of Today’s Paper

• Analysis of potential for rotational grazing to increase soil C in a large Rotational Grazing area

• Evaluate use of Ensemble Kalman Filter for estimation of aggregate soil C and its uncertainty

• Identify role of remote sensing

i. can be used with the non-linear models that characterize cropping systems and soil C dynamics,

ii. can be used to estimate both system states and parameters,

iii. can use data from multiple sources, e.g. in situ and remote measurements and simulations,

iv. accounts for the uncertainty in information provided to the filter and provides estimates of uncertainty in filtered results, and

v. utilizes spatial correlation to interpolate estimates over space.

Ensemble Kalman Filter (EnKF) Data Assimilation

Biomass is an input (from remote sensing of LAI, computing biomass)

Fresh Mass vs. LAI

y = 784.76x1.4208

R2 = 0.9384

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0 0.5 1 1.5 2 2.5 3 3.5

LAI

Fre

sh

Ma

ss

(g

/m^

2)

Millet & Sorghum

Fresh Mass vs. LAI

y = 507.93x0.9639

R2 = 0.7814

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LAI

Fre

sh M

ass

(g/m

^2)

Cotton

Soil Carbon Model

Crop Biomass,Two Soil C Pools, One Uncertain Parameter

Bi,t = Bi,t(meas) + εB [1]

Mi,t = (1 – RM) Mi,t-1 + FB Bi,t-1 + εM [2]

Si,t = (1 – RS) Si,t-1 + RM FM Mi,t-1 + εS [3]

RM = RM0 + η [4]

EnKF with three fields (f1, f2, f3) each with 3 state variables (M, S, R). Measurements (Z) in f1 and f3

mtt

mt

mt V*K)(X̂)(X̂

3,3,3

,1,1,1

)(

)(

ZSM

ZSMV

tt

tttmt

mtX̂

vector of estimates of state variables and/or parameters for the mth realization (Mi,t, Si,t, and Ri,t)

mtV residual vector of differences between measured and

simulated values of the mth ensemble realization

tK Kalman gain matrix at time t

Computation of Kalman Gain Matrix (3 fields, measurements in 2)

1)()(

WHPHHPK T

tttTttt

2

2

3

1

0

0

Z

ZW

011000000

000000011tH

M1 S1 R1 M2 S2 R2 M3 S3 R3

Pt (-) = Covariance matrix among state variables for all fields before updating

Framework for Monitoring Soil Carbon Sequestration

How Does the Ensemble Kalman Filter Work?

Analysis

• Demonstrate the performance of the EnKF in estimating aggregate soil C in the Torokoro grazing site– Rotational grazing vs. conventional grazing– Different estimates of initial parameters

Nov. 2002 image of the site with grazing parcels and 2002 sample sites

Implementation of EnKF• Initial Conditions

– Initial soil C, all fields• Sample subset of fields (cells in this example) • Use geostatistics to estimate initial C & uncertainty in all other fields

– Initial estimates of model parameters, also uncertainty in decomposition rate

• To Operate over Time– Annual measurements of crop biomass added to field – Measurements of soil C over time and space

• Outputs (each year)– Soil C mean and variance estimates over space– Aggregated soil C, its variance– Crop yield (if using crop model; this example does not)

Measurements

• Remote sensing to estimate biomass in each field unit, each year

• Field samples from subset of fields at specified years

• For this example, we generated a set of biomass and field measurements by – Generating “true” soil C vs. time for each field unit– Generating measurements by perturbing “true” values

with random deviates from the distribution of sampling errors

EnKF Outputs, Annually

• Soil C estimates in each field in study area• Estimate of Variance of soil C, each field• Estimate of aggregate soil C• Estimate of aggregate soil C change• Variance of aggregate estimates• Refined parameter estimate for each field• Updated estimate of parameter uncertainty• Aggregate crop biomass, its uncertainty

Remote Sensing

• Identify fields

• Measure field areas

• Identify land management (i.e., ridge tillage)

• Estimate LAI, biomass in each field

• Estimate residue remaining on field

Grazing Simplifications

• Goal is to link the CROPSYST pasture model (Badini et al., this conference) with the EnKF

• Assumed that soil C was at steady state under conventional grazing, with biomass estimates based on measurements made by Badini et al.

• Assumed 50% increase in biomass production under rotational grazing, for this example

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ge in

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Rotational GrazingConventional Grazing

EnKF estimates of changes in soil C

~0.2%C gain)

Initial C Sequestration Rate = 286 kg[C] ha-1 yr-1

Average C Sequestration Rate = 167 kg[C] ha-1 yr-1

Variance of predict C for 82 measurements in alternate years, and 596 measurements yearly.

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C V

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nes2 )

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tonnessc 7ˆ

tonnessc 24ˆ

Total Change in soil C

Rotational Grazing – RM biased low

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err

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EnKF: 82 - alternate year

EnKF: all - yearly

Figure 3.2 Error in estimation of change in C relative to reference C for the 150 ha site under rotational grazing and the RM biased low case.

Figure 3.1 Estimated and reference change in C for the 150 ha site under rotational grazing for the RM biased low case. The three estimations were made using Monte-Carlo simulation, EnKF with 82 measurements in alternate years, and EnKF with measurements in all model cells in all years.

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EnKF: 82 - alternate year

EnKF: all - yearly

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EnKF: 82 - alternate year

EnKF: all - yearly

Figure 3.2 Error in estimation of change in C relative to reference C for the 150 ha site under rotational grazing and the RM biased low case.

Figure 3.1 Estimated and reference change in C for the 150 ha site under rotational grazing for the RM biased low case. The three estimations were made using Monte-Carlo simulation, EnKF with 82 measurements in alternate years, and EnKF with measurements in all model cells in all years.

year

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EnKF: 82 - alternate year

EnKF: all - yearly

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esti

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Monte Carlo

EnKF: 82 - alternate year

EnKF: all - yearly

Figure 3.2 Error in estimation of change in C relative to reference C for the 150 ha site under rotational grazing and the RM biased low case.

Figure 3.1 Estimated and reference change in C for the 150 ha site under rotational grazing for the RM biased low case. The three estimations were made using Monte-Carlo simulation, EnKF with 82 measurements in alternate years, and EnKF with measurements in all model cells in all years.

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EnKF: 82 - alternate year

EnKF: all - yearly

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Monte Carlo

EnKF: 82 - alternate year

EnKF: all - yearly

Figure 3.2 Error in estimation of change in C relative to reference C for the 150 ha site under rotational grazing and the RM biased low case.

Figure 3.1 Estimated and reference change in C for the 150 ha site under rotational grazing for the RM biased low case. The three estimations were made using Monte-Carlo simulation, EnKF with 82 measurements in alternate years, and EnKF with measurements in all model cells in all years.

year

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0 5 10 15 20 25 30

es

tim

ati

on

err

or

(%)

Monte Carlo

EnKF: 82 - alternate year

EnKF: all - yearly

Figure 3.2 Error in estimation of change in C relative to reference C for the 150 ha site under rotational grazing and the RM biased low case.

Figure 3.1 Estimated and reference change in C for the 150 ha site under rotational grazing for the RM biased low case. The three estimations were made using Monte-Carlo simulation, EnKF with 82 measurements in alternate years, and EnKF with measurements in all model cells in all years.

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EnKF: 82 - alternate year

EnKF: all - yearly

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EnKF: 82 - alternate year

EnKF: all - yearly

Figure 3.2 Error in estimation of change in C relative to reference C for the 150 ha site under rotational grazing and the RM biased low case.

Figure 3.1 Estimated and reference change in C for the 150 ha site under rotational grazing for the RM biased low case. The three estimations were made using Monte-Carlo simulation, EnKF with 82 measurements in alternate years, and EnKF with measurements in all model cells in all years.

year-25

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Monte Carlo

EnKF: 82 - alternate year

EnKF: all - yearly

Figure 3.2 Error in estimation of change in C relative to reference C for the 150 ha site under rotational grazing and the RM biased low case.

Figure 3.1 Estimated and reference change in C for the 150 ha site under rotational grazing for the RM biased low case. The three estimations were made using Monte-Carlo simulation, EnKF with 82 measurements in alternate years, and EnKF with measurements in all model cells in all years.

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EnKF: 82 - alternate year

EnKF: all - yearly

Figure 3.2 Error in estimation of change in C relative to reference C for the 150 ha site under rotational grazing and the RM biased low case.

Figure 3.1 Estimated and reference change in C for the 150 ha site under rotational grazing for the RM biased low case. The three estimations were made using Monte-Carlo simulation, EnKF with 82 measurements in alternate years, and EnKF with measurements in all model cells in all years.

yearyear

%Estimation Error

Rotational Grazing – RM biased low

Conclusions

• Method can estimate aggregate soil C values and uncertainties in those estimates

• Adaptive, but good estimates are needed for initial soil C, model parameters, and their uncertainties

• More work is needed to refine method and provide inputs– Remote sensing estimates of biomass– Scale up to larger areas– Sensitivity analysis– Compare with measurements alone, kriging– Etc.

Nov. 2002 image of the site with grazing parcels and 2002 sample sites

Adapt DSSAT-CENTURY Crop-Soil Model to Conditions in Mali

Grain Yield, kg/ha

2000

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2000 4000 6000 8000

Observed

Sim

ula

ted

Maize Grain Yield

Data of M. Coulibaly, Sotuba, Mali (IER)

Simulated maize yield (kg/ha)under CT and RT compared with

results from Gigou et al. (2000) CT RT % Increase

Simulated, 2651 3565 34 10-yr AvgGigou et al., 2603 3599 38 2000

Framework for Monitoring Soil Carbon Sequestration

Compare RT vs. CT for Increasing Soil C using DSSAT Crop-Soil Model

Treatment

(10 years) kg ha-1 %

Beginning C 7016 0.244CT 6961 0.242RT + F 7053 0.245RT + F & M 8248 0.286Rt + F,M & R 10317 0.358

Organic C in Soil

Soil Carbon Changes over

10 Years, 5 Different Management Systems:Simulated Results for

Omarbougou, Mali

CT – Conventional TillageRT – Ridge TillageF – Nitrogen Fertilizer (40 kg/ha)M – Manure Added (3 t/ha)R – Return 90% Crop Residue to Soil

Soil Organic Carbon 0 - 20 cm

0.37

0.24

0.2

0.25

0.3

0.35

0.4

0 2 4 6 8 10

Time, Yrs

SO

C, t

ons

ha-1

RTAllCT

Framework for Monitoring Soil Carbon Sequestration

(a) Measured ( * )and filtered means of total C for various values

of measurement error. (b) error in soil C estimate

Estimates of soil C for the Rothamsted bare soil treatment (Ensemble Kalman Filter data assimilation using simple soil C

model with uncertain parameters and inputs (Bostick et al., 2003)

0

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Framework for Monitoring Soil Carbon Sequestration

Figure 4.1 Estimated and reference change in C for the 150 ha site under rotational grazing for the RM biased high case. The three estimations were made using Monte-Carlo simulation, EnKF with 82 measurements in alternate years, and EnKF with measurements in all model cells in all years.

Figure 4.2 Error in estimation of change in C relative to reference C for the 150 ha site under rotational grazing and the RM biased high case.

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E n K F : a ll - ye a r ly

Figure 4.1 Estimated and reference change in C for the 150 ha site under rotational grazing for the RM biased high case. The three estimations were made using Monte-Carlo simulation, EnKF with 82 measurements in alternate years, and EnKF with measurements in all model cells in all years.

Figure 4.2 Error in estimation of change in C relative to reference C for the 150 ha site under rotational grazing and the RM biased high case.

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%Estimation Error

Rotational Grazing – RM biased high

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Figure 5. Estimated and reference change in C for the 150 ha site under conventional grazing for the RM biased low case. The three estimations were made using Monte-Carlo simulation, EnKF with 82 measurements in alternate years, and EnKF with measurements in all model cells in all years.

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Figure 5. Estimated and reference change in C for the 150 ha site under conventional grazing for the RM biased low case. The three estimations were made using Monte-Carlo simulation, EnKF with 82 measurements in alternate years, and EnKF with measurements in all model cells in all years.

year

Total Change in soil C

Conventional Grazing – RM biased low

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EnKF: all - yearly

Figure 6. Estimated and reference change in C for the 150 ha site under conventional grazing for the RM biased low case. The three estimations were made using Monte-Carlo simulation, EnKF with 82 measurements in alternate years, and EnKF with measurements in all model cells in all years.

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Figure 6. Estimated and reference change in C for the 150 ha site under conventional grazing for the RM biased low case. The three estimations were made using Monte-Carlo simulation, EnKF with 82 measurements in alternate years, and EnKF with measurements in all model cells in all years.

year

Total Change in soil C

Conventional Grazing – RM biased high

y = 9.5096x + 0.0151

R2 = 0.609

0

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NDVI

LA

I

Y = 9.51x + 0.02 R2 = 0.61

cotton

y = 8.0394x + 0.6465

R2 = 0.5993

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millet

LAI vs. Landsat-derived NDVI for Oumarbougou Sept., 2002

Landsat has a 30 m spatial resolution.

Figure 4.1 Estimated and reference change in C for the 150 ha site under rotational grazing for the RM biased high case. The three estimations were made using Monte-Carlo simulation, EnKF with 82 measurements in alternate years, and EnKF with measurements in all model cells in all years.

Figure 4.2 Error in estimation of change in C relative to reference C for the 150 ha site under rotational grazing and the RM biased high case.

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Figure 4.1 Estimated and reference change in C for the 150 ha site under rotational grazing for the RM biased high case. The three estimations were made using Monte-Carlo simulation, EnKF with 82 measurements in alternate years, and EnKF with measurements in all model cells in all years.

Figure 4.2 Error in estimation of change in C relative to reference C for the 150 ha site under rotational grazing and the RM biased high case.

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Total Change in soil C

Rotational Grazing – RM biased high