Recursive Calibration of Ecosystem Models Using Sequential Data Assimilation

1
Recursive Calibration of Ecosystem Models Using
Sequential Data Assimilation
Mingshi Chen¹, Shuguang Liu¹, Larry L. Tieszen²,
and David Y. Hollinger3 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.

• Goal
• Developing a smoothed ensemble Kalman filter
  (SEnKF) to simultaneously estimate system states
  and model parameters when observations are
  progressively available in time.

• 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

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.
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.
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.
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.

• 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.

U. S. Department of the Interior U. S.
Geological Survey
Feb. 22, 2007