recursive calibration of ecosystem models using sequential data assimilation mingshi chen¹,...
TRANSCRIPT
Recursive Calibration of Ecosystem Models Using Sequential Data Assimilation
Mingshi Chen¹, Shuguang Liu¹, Larry L. Tieszen², and David Y. Hollinger 3
¹ SAIC, contractor to the USGS Center for Earth Resources Observation and Science (EROS), Sioux Falls, South Dakota 57198, USA. Work performed under USGS contract 03CRCN0001, ² USGS Center for EROS, Sioux Falls, South Dakota 57198, USA, 3USDA Forest Service, Northern Research Station, Durham, New Hampshire,03824 USA
Introduction
The specification of model parameter values to characterize a system is a fundamental issue in contemporary ecosystem science. The conventional inversion methods that treat observations as a whole lack the flexibility to investigate possible temporal evolution of the model parameters. Their main weakness is that all errors from input, output, and model structure are attributed solely to model parameter uncertainties. Sequential data assimilation procedures such as the ensemble Kalman filter (EnKF) have the potential to overcome this drawback by explicitly taking all sources of uncertainty into account step by step.
Figure 1. Temporal variations of two key parameters in the flux partition model: (a) light use efficiency (lue) and (b) reference respiration (Rref). The grey vertical lines indicate the standard deviation around the mean of ensembles. The SEnKF reveals the strong seasonality of the key parameters.
Approach
Model: We use a flux partition model as our test dynamic model for the SEnKF method. The flux partition model divides net ecosystem exchange (NEE) into gross primary production (GPP) and total ecosystem respiration (RESP) as follows:
where subscript t denotes time-dependent, LUEt is light use efficiency, PARt is photosysnthetically active radiation, NDVIt is the normalized difference vegetation index, Rref,t is respiration when air temperature (Tair,t) equals reference temperature (Tref,t, usually specified as 10 oC), E0 is temperature sensitivity, and T0 is a datum of temperature to avoid a denominator of zero in the model, kept constant at –46.02 oC. Dtemp determines the effect of temperature on photosynthesis, and DVPD expresses the decrease in leaf exchange from both photosynthesis and transpiration caused by vapour pressure deficit (VPD), according to
where Tmin, Topt, and Tmax denote minimum, optimal, and maximum temperatures for photosynthesis, respectively, VPD is vapour pressure deficit, and v0 and v1 are two unknown coefficients.
Data:
• Net Ecosystem Exchange (NEE) of carbon, PAR, Ta, and VPD were from Ameriflux tower station in Howland (Maine, USA). RESP data were calculated from the temperature dependence curve of ecosystem respiration derived from nighttime NEE, GPP data were pseudo-observations as a total of NEE and RESP.
• NDVI: from MODIS. Time: from 2000 to 2004
Data Assimilation:
• All unknown parameters were treated as state variables. Evolution models of the parameters similar to that of the state variables were built by applying a Kernel smoothing technique on parameter samples . The initial values of parameters are optimally determined by a nonlinear inverse procedure.
• An Ensemble Kalman Filter (EnKF) was used to sequentially assimilate measurements into the dynamic model described above, and into evolution models of parameters to improve estimates of GPP, R, NEE and the parameter values.
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Conclusion
• The SEnKF revealed that the parameter values (e.g., light efficiency and reference respiration) possessed strong seasonality or temporal variability (Fig.1). The SEnKF can quickly stabilize the parameter values regardless of their initial values (Fig.2). These demonstrate that the SEnKF can be used to perform recursive model calibration to diagnose the adequacy of the model structure.
• Figure 3 shows that the SEnKF can significantly improve the estimate of GPP, RESP and NEE (left panel) and reduce up to 70 percent of the variation of the ensemble without data assimilation (right panel).
• Figure 4 shows that the estimates of GPP, RESP, and NEE using the parameter values modified by the SEnKF had less bias against the observation than the estimates using the base model. This indicates that the SEnKF can extend the model parameter values to predictions when the observations are not available. This capability could be valuable for filling data gaps caused by instrument failure.
Goal Developing a smoothed ensemble Kalman filter (SEnKF) to simultaneously estimate system states and model parameters when observations are progressively available in time.
Figure 2. Regardless of initial values of parameters, the SEnKF can quickly stabilize the variation of parameters. The temporal variation of parameters is relatively smooth because a smoothing procedure was implemented in the SEnKF to control the over-dispersion of parameter sampling.
y = 0.9017x + 0.2651R2 = 0.88
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0 2 4 6 8 10 12 14observed gpp(gC/m 2/d)
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y = 0.9543x + 0.0226R2 = 0.9406
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0 2 4 6 8 10 12observed resp(gC/m 2/d)
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y = 0.8214x + 1.3419R2 = 0.8282
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0 2 4 6 8 10 12 14observed gpp(gC/m 2/d)
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y = 0.5157x + 1.0909R2 = 0.8037
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Figure 3. The left panel compares estimates of GPP, RESP, and NEE generated by the SEnKF and the base model against 20 percent of the assimilated data. Data assimilation accounted for more than 99 percent of the variation in the observations of GPP, REPS, and NEE, The right panel shows reduced ratio of ensemble variances of GPP, RESP, and NEE generated by the SEnKF against that by the base model alone. The results show the SEnKF can more dramatically reduce variances of state variables than the ensemble based only on the Monte Carlo technique.
Figure 4. The left panel shows the forecasted values of three state variables (GPP, RESP and NEE) of the model modified by the SEnKF against unassimilated data (80 percent of total observations). The right panel displays the simulation results by the base model against the same unassimilated data. Comparing three pairs of corresponding linear fitting regression equations for GPP, RESP and NEE and their corresponding coefficients of determination (R2), we see that the estimates of the three flux variables using the parameters modified by the SEnKF had less bias against observations than estimates using the base model.
Daily variation of light use efficiency
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Daily variation of Rref
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U. S. Department of the InteriorU. S. Geological Survey
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VPDtemptttt
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DDNDVIPARLUEGPP
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Effect of Initial l ight use efficiency
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Effect of initial Rref
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___SEnKF eq.y = 0.9814x + 0.0111
R2 = 0.9929
…... Model eq.y = 0.5279x + 1.0494
R2 = 0.8278
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observed resp(gC/m2/d)
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___ SEnKF eq.y = 0.9946x + 0.001
R2 = 0.9927
…... Model eq.y = 0.6351x + 1.3768
R2 = 0.3263-6
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…... Model eq.y = 0.8011x + 1.4346
R2 = 0.8085
___SEnKF eq.y = 0.9735x - 0.0085
R2 = 0.9956
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0 2 4 6 8 10 12 14observed gpp(gC/m2/d)
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Feb. 22, 2007