This study implements a Bayesian statistical framework to calibrate the SCOPE process-based simulator for simulating gross primary production (GPP) and top-of-canopy reflectance at a spruce flux tower site in the Czech Republic. Markov chain Monte Carlo simulation is used to quantify the uncertainty in SCOPE input parameters by comparing simulated and measured reflectance and GPP data. The results show the posterior parameter distributions have lower uncertainty than the prior distributions. Simulated half-hourly GPP over the growing season using maximum a posteriori parameter estimates matches the measured data. Future work will estimate seasonal parameter variations to improve GPP simulation accuracy.

1. Integration of flux tower data and remotely
sensed data into the SCOPE simulator: A
Bayesian approach
Rahul Raj1, Petr Lukeš1, Lucie Homolová1, Olga Brovkina1, Ladislav Šigut1, Bagher Bayat2
1 Global Change Research Institute CAS, Belidla 986/4a, 603 00, Brno, Czech Republic
2 Faculty of Geo-Information Science and Earth Observation , University of Twente,
Enschede, the Netherlands
1

2. Introduction
 Forest ecosystems play an important role in the global carbon
cycle by controlling atmospheric CO2 level.
 Forest gross primary production (GPP) is a crucial measures of
vegetation dynamics, as it determines carbon storage and
biomass.
“GPP refers to the total photosynthesis of a stand, expressed either
as moles or as mass of gross CO2 uptake per unit of soil surface
and per unit of time”
2

3.  Quantification of GPP:
 process-based simulator (PBS)
 flux tower measurements of the net ecosystem exchange (NEE)
of CO2
 Remotely sensed optical data also carry valuable information to
express canopy photosynthesis (i.e., GPP).
 Process-based simulator (PBS) evaluates GPP by simulating
different physiological plant responses to climatic conditions,
atmospheric properties and plant structures.
3

4.  A PBS can be run at temporal and spatial scales beyond the limit
of direct measurements.
 PBS requires input parameters, difficult to measure and often
taken from the literature.
 Systematic adjustment (i.e., calibration) of PBS parameters are
required.
4

5.  Calibration needs data on the output variable:
 At flux tower sites, NEE/partitioned GPP data can serve the
purpose.
 Flux tower data is limited at the spatial scale. Remote sensing of
spectral reflectance can play an important role here.
 To utilize both reflectance and flux tower data, a PBS is required
that links remotely sensed reflectance with land surface process.
 SCOPE (Soil-Canopy-Observation of Photosynthesis and
Energy balance) (van der Tol et al., 2009) simulator fulfills this
requirement, and therefore is adopted in the current study.
5van der Tol, C., Verhoef, W., Timmermans, J., Verhoef, A., and Su, Z.: An integrated model of soil-canopy spectral radiances, photosynthesis,
fluorescence, temperature and energy balance, Biogeosciences, 6, 3109-3129, 2009.

6.  Calibration is often performed to obtain single optimized values of
the parameters without the quantification of uncertainty in the
parameters and the simulated outputs.
 Quantification of uncertainty is important for both scientific and
practical purposes.
 A Bayesian approach provides a coherent method for calibrating
PBS.
6

7. Objective
This study implements Bayesian statistical framework to calibrate
process-based simulator SCOPE in simulating gross primary
production (and top of the canopy reflectance) at the spruce
dominated flux tower site Bílý Kříž, Czech Republic. This study
quantifies the uncertainty in SCOPE input parameters.
7

8. Methods
Bayesian calibration begins with Bayes rule (Gelman et al., 2013):
𝑝 𝜽 𝐳 ∝ 𝑝 𝐳 𝜽 × 𝑝 𝜽
Posterior distribution
Likelihood: mismatch between
simulator output & data
Prior distribution
Simulator
(f)
Simulated output
f(θ)
Input parameters
𝑝 𝜽
Data z: measured data
on the output variableCalibration =
find 𝑝 𝜽 𝐳
8Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., and Rubin, D. B.: Bayesian Data Analysis, CRC press, Boca Raton, 2013.

9.  Inference on 𝑝 𝜽 𝐳 was performed using Markov chain Monte Carlo
(MCMC) simulation that was implemented by DREAM (DiffeRential
Evolution Adaptive Metropolis) algorithm (Vrugt et al., 2016).
 𝑁 Markov chains for each parameter evolve in parallel for 𝑇 times.
 Converged part of Markov chains to a stationary distribution is the
posterior probability distribution function (pdf).
 Unconverged part of Markov chains is discarded as ”burn-in”.
Markov chains for a parameter 𝜃1
Converged partBurn-in
Sample
from
posterior
pdf
In this study
𝑁 = 10
𝑇 = 20000
Burn-in = 10000
1
2
𝑁-1
𝑁
9Vrugt, J. A.: Markov chain Monte Carlo simulation using the DREAM software package: Theory, concepts, and MATLAB implementation,
Environmental Modelling & Software, 75, 273–316, 2016.

10. Proposed methodological flow chart to
implement Bayesian framework for
calibrating SCOPE:
Prior distribution
of SCOPE
parameters*
MCMC (DREAM algorithm)
TOC
reflectance
Half-hourly
GPP
partitioned
from NEE
Time series of
meteorological
data
Generate parameter sample
Calculate combined likelihood
Run SCOPE at each parameter vector
Posterior
distribution of
SCOPE
parameters
Simulated half-
hourly GPP and
TOC reflectance
with uncertainty
Comparison
What could be implemented till now:
Prior distribution
of SCOPE
parameters
#
MCMC (DREAM algorithm)
TOC
reflectance
Generate parameter sample
Likelihood calculation
Run radiative transfer module of SCOPE
at each parameter vector
Posterior
distribution of
SCOPE
parameters
Simulated TOC
reflectance with
uncertainty
Estimating maximum a
posteriori probability
(MAP) of each parameter
Vcmax and m
parameter from
the expert
opinion
Time series of
meteorological
data
Run SCOPE model
Simulated half-
hourly GPP
Half-hourly
GPP
partitioned
from NEE
Validation
* Cab, Cdm, Cw, Cs, Cca, N, LAI, Vcmax, and m
# Cab, Cdm, Cw, Cs, Cca, N, LAI
TOC: Top of the canopy
10

11. 11© Lucie Homolová
Spruce forest (Bílý Kříž, Czech Republic)
Species Picea abies
Age 35 years
Height 15 m
DBH 17 cm
Density 1 500 trees/ha
LAI 8.5 m2 m-2
In-situ measurements (Data Z):
Canopy reflectance:
 Average canopy reflectance extracted from merged CASI-SASI airborne
hyperspectral images (acquired on 31.8.2016) with 2.5m pixel size.
 Average reflectance was computed for a circular plot (50m2 in diameter)
around the flux tower.
GPP Ecosystem respiration
Lasslop, G., et al.: Separation of net ecosystem exchange into assimilation and respiration using a light response curve approach: critical
issues and global evaluation, Global Change Biology, 16(1), 187-208, 2010.
Partitioned GPP:
Flux partitioning model (Lasslop et al. 2010) were used to partition half-hourly NEE
(April to September 2016 at the Bílý Kříž site, CZ) into the component fluxes:

12. Parameter Symbol Unit pdf
Chlorophyll content Cab µg cm-2 N(37, 10.5)
Dry matter content Cdm g cm-2 U(0,0.035)
Leaf water Cw g cm-2 U(0, 0.03)
Scenecent material fraction Cs U(0,0.4)
Carotenoid content Cca µg cm-2 U(2,15)
leaf thickness parameters N U(1,2.5)
Leaf area index LAI m-2 m-2 U(5,10)
maximum carboxylation capacity Vcmax µmoles m-2 s-1 --
Ball-Berry stomatal conductance
parameter
m --
Prior distributions 𝒑 𝜽 :
Prior probability distribution functions (pdfs) of the input parameters were based
on the literature search, expert opinion, and available field data related to a
particular parameter.
12

13. Results
Fig1: Trace plots of the posterior distributions of the parameters
after burn-in period of 10000
Convergence of Markov chains:
Statistical evidence
Convergence of Markov chains: Visual evidence
Output of Bayesian calibration of radiative transfer module
13

14. Fig 2: Histogram, empirical density and normal fit of the
posterior distributions:
Posterior distribution Prior distribution
Parameter MAP Mean Std
Cab 40.65 41.05 4.329 N(37, 10.5)
Cdm 0.025 0.025 0.001 U(0,0.035)
Cw 0.020 0.021 0.001 U(0, 0.03)
Cs 0.133 0.146 0.070 U(0,0.4)
Cca 10.38 10.36 1.875 U(2,15)
N 2.499 2.447 0.050 U(1,2.5)
LAI 8.274 8.202 0.549 U(5,10)
Estimates of MAP (maximum a posteriori probability),
mean, and standard deviation of the posterir distributions
14

15. Fig 3: 95% credible intervals of the posterior simulated canopy reflectance
15

16. Simulation of half-hourly GPP (Apr to Sep 2016) by SCOPE using MAP
estimates obtained from the Bayesian calibration of radiative transfer module:
Fig 5: Half-hourly GPP from 20th June (172) to 29th June (181)
Fig 6: Daily mean of half-hourly GPP from 1st April (92) to 30th Sep
(274)
Fig 4: Half-hourly GPP from 1st April (92) to 10th April
(101)
Vcmax = 50 µmoles m-2 s-1
m = 8
16

17. Conclusions
 The Bayesian framework allowed quantification of uncertainty in both
the estimated parameters and the posterior (predictive) canopy
reflectance.
 The Bayesian framework should be extended to calibrate full SCOPE
simulator: that needs the construction of SCOPE emulator (Verrelst et
al. 2017) due to high computational cost of SCOPE.
 Future work will estimate the seasonality in the parameters (particularly
Vcmax and stomatal conductance) to improve the accuracy of GPP
simulations. The Bayesian framework can provide an effective tool for
this (Raj et al. 2018).
17
Raj, R., van der Tol, C., Hamm, N.A.S., & Stein, A.: Bayesian integration of flux tower data into a process-based simulator for
quantifying uncertainty in simulated output, Geosci. Model Dev., 11, 83-101, 2018.
Verrelst, J., et al.: SCOPE-Based Emulators for Fast Generation of Synthetic Canopy Reflectance and Sun-Induced Fluorescence
Spectra, Remote Sensing, 9(9), 927, 2017.

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