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)

Soil Carbon Model Crop Biomass,Two Soil C Pools, One Uncertain Parameter B i,t = B i,t (meas) + ε B [1] M i,t = (1 – R M ) M i,t-1 + F B B i,t-1 + ε M [2] S i,t = (1 – R S ) S i,t-1 + R M F M M i,t-1 + ε S [3] R M =R M0 + η[4]

EnKF with three fields (f 1, f 2, f 3 ) each with 3 state variables (M, S, R). Measurements (Z) in f 1 and f 3 vector of estimates of state variables and/or parameters for the m th realization (M i,t, S i,t, and R i,t ) residual vector of differences between measured and simulated values of the m th ensemble realization Kalman gain matrix at time t

Computation of Kalman Gain Matrix (3 fields, measurements in 2) M 1 S 1 R 1 M 2 S 2 R 2 M 3 S 3 R 3 P t (-) = 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 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

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.

Total Change in soil C Rotational Grazing – R M biased low

year %Estimation Error Rotational Grazing – R M 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 image of the site with grazing parcels and 2002 sample sites

Adapt DSSAT-CENTURY Crop-Soil Model to Conditions in Mali 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, yr Avg Gigou et al., Framework for Monitoring Soil Carbon Sequestration

Compare RT vs. CT for Increasing Soil C using DSSAT Crop-Soil Model Soil Carbon Changes over 10 Years, 5 Different Management Systems: Simulated Results for Omarbougou, Mali CT – Conventional Tillage RT – Ridge Tillage F – Nitrogen Fertilizer (40 kg/ha) M – Manure Added (3 t/ha) R – Return 90% Crop Residue to Soil 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) Framework for Monitoring Soil Carbon Sequestration

%Estimation Error Rotational Grazing – R M biased high

year Total Change in soil C Conventional Grazing – R M biased low

year Total Change in soil C Conventional Grazing – R M biased high

Y = 9.51x R 2 = 0.61 cotton Y = 8.03x R 2 = 0.60 millet LAI vs. Landsat-derived NDVI for Oumarbougou Sept., 2002 Landsat has a 30 m spatial resolution.

year Total Change in soil C Rotational Grazing – R M biased high