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Addressing the Ability of a Land Biosphere Model to Predict Key
Biophysical Vegetation Characterisation Parameters with a GSA study
Gareth Ireland1, George P. Petropoulos1*, Toby N. Carlson2, Sarah Purdy3
1Department
of Geography and Earth Sciences, University of Aberystwyth, SY23 2EJ, UK
of Meteorology, Pennsylvania State University, University Park, PA 16802, USA
3Institute of Biological Environmental and Rural Sciences, University of Aberystwyth, SY23 3EE, UK
2Department
*Author of correspondence: E-mail:george.petropoulos@aber.ac.uk, Tel: +44-0-1970-621861
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ABSTRACT
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Sensitivity Analysis (SA) of the SimSphere Soil Vegetation Atmosphere Transfer
(SVAT) model has been performed in our research using a cutting edge and robust Global
Sensitivity Analysis (GSA) approach, based on the use of the Gaussian Emulation Machine
for Sensitivity Analysis (GEM-SA) tool. The sensitivity of the following model outputs was
evaluated: the ambient CO2 concentration and the rate of CO2 uptake by the plant, the
ambient O3 concentration, the flux of O3 from the air to the plant/soil boundary and the
flux of O3 taken up by the plant alone. The most sensitive model inputs for the majority of
outputs were: The Leaf Area Index (LAI), Fractional Vegetation Cover (Fr), Cuticle
Resistance (CR) and Vegetation Height (VH). The influence of the external CO2 on the leaf
and O3 concentration in the air as input parameters was also significant. Our study
provides a step forward in the global efforts towards SimSphere model verification which
is important given the increasing interest in the use of SimSphere as an independent
modelling or educational tool. Results of this study are also timely given the ongoing
global efforts focused on deriving, at an operational level, the spatio-temporal estimates
of energy fluxes and soil moisture content using SimSphere synergistically with Earth
Observation data.
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Keywords: Sensitivity Analysis, CO2 flux, ambient CO2, O3 flux, SimSphere, Gaussian process
emulators, BACCO GEM-SA.
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1. INTRODUCTION
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The complex interplay between the different facets of land-surface interactions
play a fundamental role in the spatio-temporal variations of carbon dioxide (CO2) and
ozone (O3) fluxes within the Earth system. Within the atmospheric boundary layer, the
exchange of CO2 at the surface is primarily the result of complex vegetation processes
(Boussetta et al, 2013). CO2 is assimilated in vegetation by photosynthesis (expressed as
gross primary productivity) and is returned to the atmosphere by a variety of above-and
below- ground metabolic processes (Bloemen et al., 2013). Stomatal behaviour provides
the main short-term control of both transpiration and CO2 assimilation. Crops grown
under CO2 enrichment usually exhibit increased mass, which is attributed to greater
photosynthetic capacity and enhanced water use efficiency (Olvera et al., 2013). Carbon
assimilation and water dynamics are inherently linked to crop yield and so an
understanding of these relationships is fundamental to our ability to understand, or
predict, plant productivity. The Intergovernmental Panel on Climate Change (IPCC)
predicts concentrations of atmospheric CO2 to continue rising from their current
concentrations of ~395ppmv to > 420ppmv by 2050 (IPCC, 2001). Therefore,
understanding the interactions between plants and environment is a central requirement
when forecasting the effects of future climate change and variability (Williams et al.,
2012).
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Tropospheric ozone is a phytotoxic air pollutant responsible for crop and forest
damage worldwide (Panek, 2004). The impact of O3 exposure usually manifests as
necrotic lesions, decreased photosynthesis and accelerated senescence (Pell et al., 1997;
Wiese and Pell, 1997). The exact mechanism by which O3 stress is imposed is unclear but
probably occurs through the formation of reactive oxygen species such as superoxide and
hydrogen peroxide (Pell et al., 1997). Furthermore, stomatal control may be reduced
following exposure to O3 which causes greater susceptibility to drought stress
(McLaughlin et al., 2007). This has major implications for tree and crop performance in
the future climate as temperatures are predicted to increase (thus increasing
transpiration) along with a greater areas affected by more frequent drought (IPCC, 2014).
The effect of O3 stress on stomatal regulation and implications for drought susceptibility
has been found to offset much of the projected benefit of rising CO2 for plant growth in
some biogeochemical models (Ollinger et al., 2002). The direct reduction in forest
productivity currently caused by O3 stress is estimated to be 1-10% for forests in Europe
and North America (Broadmeadow, 1998). Thus O3 is clearly an important economic
factor in biomass production and there is a need to understand its influence on plant
processes (Ainsworth et al., 2012; Konovalov, et al., 2012). To this end, an improved
quantification of the effect of atmosphere-land-surface interactions on the spatiotemporal distribution of CO2 and O3 fluxes will enable the development of coherent plans
to manage ecosystems for future climate mitigation and agricultural production (Pitman
et al., 2012; Williams et al., 2012).
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In this context, a representative description of land surface-atmosphere
interaction requires mathematical models able to accurately describe interdependent
physical and biological processes in vegetation and soil, as well as physical processes
within the atmospheric boundary layer (Marras et al., 2011). Several modelling
approaches have been developed to represent the terrestrial carbon cycle depending on
the main goals of the modelling effort. Aggregated ‘big leaf’ models for instance, act to
simulate selected mass, water and energy transfers from a representative leaf surface
which is scaled up to the whole canopy, either based on simple linear scaling or on a
non‐linear scaling by partitioning between sunlight and shaded leaves (Ganzeveld et al.,
2012). Generally, these models are widely regarded as the simplest group of models, but
behold vast application value such as data gap filling and tracing gas fluxes (Baldocchi,
2010). SVAT models are more complex ‘distributed multilayer models’ which differ in
their approach to estimate surface exchanges. These embedded modelling efforts are
numerical representations of the multifarious interactions of energy and mass transfers
through the soil/vegetation/atmospheric 1-dimensional vertical column (Marras et al.,
2011). They require an application context constrained by input variables (atmospheric
forcing and vegetation variables) and input parameters (soil and vegetation properties,
initialisation) to simulate the water and energy budget at the surface. The number of
parameters is generally related to the complexity of the model and their calibration
requires the development of optimisation methodologies (Coudert and Ottle, 2007).
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A variation on the SVAT model architecture, termed SimSphere, was originally
developed by Carlson and Boland (1978) within the Department of Meteorology of
Pennsylvania State University, USA, and has continued to be developing over a period of
more than two decades. Notably, during this period the model has undergone significant
modifications by a number of contributors, most recently by Petropoulos et al. (2013a).
Briefly, it is a one-dimensional boundary layer model with a plant component implicitly
referring to a horizontal area of undefined size that can be composed of a mixture of bare
soil and vegetation. In addition to its use as a stand-alone modelling tool, it is also
integrated synergistically with Earth Observation (EO) data, via a method termed the
“triangle” method (Carlson, 2007; Petropoulos & Carlson, 2011). This method interprets
the relationship between a Vegetation Index (VI) and surface radiative temperature (Ts)
derived from a satellite-derived scatter plot, linked with a SVAT model to deduce
evaporative fraction (EF) over large areas (Long and Singh, 2013). Variants of this
method are at present being considered for the development of operational products
from EO data, some anticipated to be delivered on a global scale (Chauhan et al., 2003;
ESA STSE, 2012). However, being a mathematical representation of natural processes,
such modelling approaches require a considerable number of assumptions on model
structure, model parameter values and model input variables. These input parameters
can lead to output uncertainty and inaccuracy (Cosenza et al., 2014; Vanuytrecht et al.,
2014). Thus, Sensitivity Analysis (SA) is an essential and well-established tool that has
been used in evaluating robustness of model based results (Feyissa et al., 2012; Ratto et
al., 2012). In particular, SA quantifies the influence of each uncertain factor (parameter or
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driving variable) on the model’s output variability (Gan et al., 2014). It can help to
determine the relationship between independent and dependent variables to get a better
understanding of the model performance. Reasons for performing SA are diverse; it
allows for Factor Fixing (FF), where factors that are non-influential can be set to a fixed
value anywhere in their uncertainty range and it would not affect model output variance.
Factor Prioritisation (FP) on the other hand, is where the modeller focuses on the
parameters that have the potential to maximally reduce model output variance if
determined. For the case of FP, SA allows for better estimation of the actual factor value
and distribution (Nossent et al., 2011; Gamerith et al., 2013).
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SA methods are generally classified as either Local Sensitivity Analysis (LSA) or
Global Sensitivity Analysis (GSA). In LSA methods each factor is perturbed in turn from
randomly generated reference parameter sets, whilst holding all others to their central
value and computing the difference in the outputs (Wainwright et al., 2013; Baroni and
Tarantola, 2014). Although a computationally frugal method, LSA can be criticised for
being inadequate for analysing complex biophysical process models which may have
many parameters, and may be high-dimensional and/or non-linear (Song et al., 2012;
Wainwright et al., 2013). Compared with LSA, GSA provides quantitative importance
measures that relate the variance of the output with each input dependent variable on
different sources of variation over the entire parameter space (Wei et al., 2013).
Furthermore, GSA approaches are not limited by model complexity and provide robust
sensitivity measures in the presence of non-linearity and interactions amongst
parameters. However, the model complexity and high number of parameters can be
computationally intensive and inefficient (Gatelli et al., 2009; Wainwright et al., 2013; Gan
et al., 2014). Given the intricacy of the physical interconnections involved in modelling
land surface-atmosphere interactions, GSA has become popular in the environmental
modelling field in recent years. The complexity of such models and their ability to
incorporate parameter interactions can be a significant advantage when deriving
simulation outputs that are fully analogous of the real world system in terms of accuracy,
generality and realism (Anderson et al., 2008). A number of studies have thus performed
advanced GSA on SimSphere based on a Gaussian process emulator (Petropoulos et al.
2009b, 2010, 2013b–d). These allowed, for the first time, an insight into the model
architecture and the mapping of the sensitivity between the model inputs and outputs.
However, SA studies on SimSphere have been limited to only a small number of output
parameters, and the effect of different simulation times on model sensitivity has yet to be
explored.
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In this context, the objective of this study is two-fold: i) To perform a GSA to
explore the sensitivity of target quantities simulated by SimSphere for the model
inputs/outputs, which have not been previously investigated. These parameters are
namely; the ambient CO2 concentration [ppmv], the rate of uptake of CO2 by the plant
[µmol m-2 s-1], the ambient O3 concentration [ppmv x 10-3], the flux of O3 from the air to the
plant/soil boundary [mg m-2 s-1], the flux of O3 taken up by the plant alone [mg m-2 s-1].
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ii) To extend the GSA on SimSphere and to explore the sensitivity of the same target
quantities at different simulation times (9:30/11:30/13:30), which coincide closely to the
satellite overpass times of different satellite sensors. These objectives will allow us to
foster our understanding of the model structure and further establish its coherence.
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2. SimSphere SA Studies
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SimSphere is a one-dimensional boundary layer model with a plant component
implicitly referring to a horizontal area of undefined size that can be composed of a
mixture of bare soil and vegetation. An overview of the model use was recently provided
by Petropoulos et al. (2009a). An excellent systematic overview of the SimSphere model
architecture and its initialisation process is available in Gillies (1993); The model is able
to simulate the various physical processes and interactions that take place in a column
that extends from the root zone below the soil surface up to the surface mixing layer over
a 24-h cycle at a chosen time step (typically 3 minutes), starting from a set of initial
conditions given in the early morning (at 06.00 h local time). The model simulates a
number outputs including the surface energy (H, LE and soil heat) fluxes at the soil
surface and in, around and above the vegetation canopy, the transfer of water in the soil
and in the plants, the flux of CO2 between the atmosphere and the plants (the carbon
assimilation rate), the surface O3 flux, a number of other parameters. SimSphere is
globally distributed and maintained from Aberystwyth University, UK
(http://www.aber.ac.uk/simsphere).
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A number of studies based essentially on relatively basic empirical or LSA
methods have been performed on the SimSphere model (Lynn and Carlson, 1990; Olioso
et al., 1996). However, Petropoulos et al (2009b) demonstrated for the first time, the use
of a GSA method using the Bayesian Analysis of Computer Code Outputs (BACCO) method
for performing SA on SimSphere to identify the most responsive model inputs to the
simulation of key model outputs. GSA methods, despite their often high computational
demands, have become popular in environmental modelling due to their ability to
incorporate parameter interactions and their relatively straightforward interpretation
(Makler-Pick et al., 2011). Results by these investigators showed that the method was
able to detect interactions between model parameters and derive absolute sensitivity
measures concerning the model structure. Furthermore, in this initial study, the
dominant input parameters were found to consistently control the predictions of the
considered outputs by the model, namely, the topography parameters (slope, aspect), as
well as the Fractional Vegetation Cover (Fr) and surface moisture. Petropoulos et al.
(2010) expanded on this work by performing a comparative study of various emulator
types including BACCO GEM, investigating the effect of sampling method and size on the
sensitivity of key target quantities simulated by SimSphere. Their results showed that the
sampling size and method did affect the SA results in terms of absolute values, but had no
bearing in identifying the most sensitive model inputs and their interactions for model
outputs on which SA was performed. Petropoulos et al., (2013c-d) also used the BACCO
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method in performing SA on SimSphere, aiming to further understand model structure
and establish its coherence. Authors examined the effect of assuming uniform Probability
Distribution Functions (PDFs) for the model inputs/outputs on the sensitivity of key
quantities simulated by SimSphere. Furthermore, authors also explored the sensitivity of
new, previously unexplored variables simulated by the model, namely of the Daily
Evaporative, Non-Evaporative Fractions and Radiometric Temperature. Findings
reinforced the conclusions of previous SA works on SimSphere that, regardless of the PDF
assumption, only a small number of model input parameters exerted a significant
influence on the model outputs, with the majority of parameters inconsequential.
Petropoulos et al., (2013c) also examined the effect of assuming different PDFs for the
model’s inputs/outputs on the sensitivity of key quantities simulated by SimSphere. Their
results suggested that the assumption of different PDFs for the model inputs/outputs did
not have significant bearing on mapping the most responsive model inputs and
interactions, but only the absolute SA measures. However, they subsequently expanded
the study to also examine the effect of changing the atmospheric sounding profile to the
sensitivity of key variables predicted by the model. Notably, results did not show
dramatic changes in the nature or ranking of influential model inputs using an
atmospheric sounding derived from a different region to previous studies. Consequently,
the previous work conducted on the BACCO method of SA on SimSphere represents a
significant step forward in the global efforts on the model verification, especially given
that its use is explored at present towards the development of global operational
products from its synergy with EO data (Chauhan et al., 2003; Piles et al., 2011; ESA STSE,
2012). Our study anticipates to expand on these previous studies to enhance our
knowledge of SimSphere model structure and establish further its coherence and
correspondence to that of a natural system’s behaviour.
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3. GLOBAL SENSITIVITY ANALYSIS
Herein we employed a sophisticated, cutting edge meta-modelling GSA method
adopting a Bayesian analysis of computer code outputs (BACCO) SA on the model using the
freely available software tool GEM SA (Kennedy, 2005). The theory related to the BACCO
method of GSA is presented by Oakley and O’Hagan (2004), while the statistical theory
and mathematical principles dominating the Gaussian Process (GP) emulation are
documented by Kennedy and O’Hagan (2001) and Kennedy (2004).
Initially, BACCO SA implementation uses an efficient space-filling design of
training input points and fits a Gaussian process model to the corresponding code runs to
yield an emulator of the model (O’Hagan, 2006). The emulator is a mathematical function
built from SimSphere to quantify the relationships between the model output and the
model input, specifically the sensitivity of the former to the latter. Following this, the
emulator itself is used to compute a number of statistical parameters to characterise the
sensitivity of the targeted model output in respect to its inputs (Kennedy and O’Hagan,
2001).
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For implementation of the BACCO SA, initially, a prior belief based on a Gaussian
processes model about the actual model is inferred. The Bayes' theorem and a set of the
model runs are considered together to refine the prior information to yield the posterior
distribution of the output (Qin et al., 2013). On this basis, the emulator is used to calculate
a mean function, which passes through the observed runs and the same time it quantifies
the remaining uncertainty due to the emulator being an approximation to the true code
(O’Hagan, 2006). Within BACCO, various measures of sensitivity, each of which requires
integration of the model output with respect to probability distributions on the inputs,
are generated. These include the main effects or first order sensitivity indices (Si). The main
effect of a single input parameter component (Xi) measures the expected change in the
output f(X) as Xi is varied, averaged with respect to the distribution of the remaining
parameters (Parry et al., 2013). Thus, in other words this statistical measure quantifies
the relative importance of an individual input variable Xi, in driving the total output
uncertainty, indicating where to direct future efforts to reduce that uncertainty.
Similarly, using the same approach, higher order interactions (joint effect indices)
of a group of input components (e.g. Xi, Xj) are generated to calculate the expected change
in model output as a function of those inputs. Additionally, subsequent measures based
on variations in the input parameters together induce a total variation in the output.
These total effects can therefore be used as a measure of the combined influence of an
input (Saltelli et al, 2000; Oakley and O’Hagan, 2004), where the sum of all inputs' total
effects with respect to each model outcome will be greater than 100% (Parry et al., 2013;
Qin et al., 2013). Use of the BACCO method has already been demonstrated in a large
number of environmental modelling problems, providing useful insights in various
disciplines and in various SA studies (Kennedy and O’Hagan, 2001; Kennedy et al., 2012;
Parry et al., 2013; Petropoulos et al., 2009b).
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Figure 1: Overview of the SA implementation in this study
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4. SA EXPERIMENT IMPLEMENTATION
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The BACCO GEM-SA was implemented along the lines of GSA studies applied previously
to SimSphere (Petropoulos et al., 2009b, 2010, 2013b–d). However, differently to
previous studies, the sensitivity of several new, yet to be studied, model outputs were
studied herein (Table 1). In addition, the sensitivity of the SA results to the time of the
model simulation output was also explored, specifically here for the model output times
9:30/11:30/13:30. Again, effect of simulation times on model sensitivity is yet to be
explored. These particular times were selected because they are close to the overpass
times of most of the polar-orbiting satellites which provide data suitable for the
“triangle” technique implementation on which SimSphere is also used. In particular, the
sensitivity of the SimSphere outputs exhibited in Table 1 were examined primarily due to
their importance in studies related to vegetation:
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Table 1: Summary and description of the SimSphere outputs examined in this study.
Parameter
Description
CO2 Canopy ( CO2canopy )
the ambient CO2 concentration [ppmv]
CO2 Flux ( CO2 flux )
the rate of uptake of CO2 by the plant [µmol m-2 s-1]
O3 Canopy ( O3canopy )
the ambient O3 concentration [ppmv x 10-3]
Global O3 Flux ( O3 flux
GLOBAL
O3 Flux in Plant ( O3 flux
PLANT
)
)
the flux of O3 from the air to the plant/soil boundary [mg
m-2 s-1]
the flux of O3 taken up by the plant alone [mg m-2 s-1]
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To ensure consistency, comparability and a continuation of this study to previous SA
experiments on SimSphere, the same implementation setting and dataset was used to that
previously adopted (Petropoulos et al., 2009b; 2013b-d). In summary, a design space of
400 SimSphere simulations was developed using the LP-tau sampling method. All
SimSphere inputs (Table 2) were allowed to vary across their full range of variation. An
exemption to this was the geographical location (latitude/longitude) and atmospheric
profile, for which a priori real observations for August 2002 were used from the Loobos
CarboEurope site, located in The Netherlands (52° 10' 04.29" N, 05° 44' 38.25" E). Both
cases of normal and uniform probability distribution functions for the inputs/outputs
from the model were explored. For all variables, the theoretical ranges of values were
defined from the entire possible theoretical range which they could take in SimSphere
parameterisation and each of the model outputs were exported on three occasions
relating to the different simulation output times. In addition, the emulator performance
was evaluated based on the “leave final 20% out” method offered in GEM-SA, again in
accordance to previous studies conducted to the model.
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Table 2: Summary of the SimSphere inputs considered in the GSA implementation using the BACCO GEM SA method.
In parentheses are also provided the units of each of the model inputs.
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Model input
short name
X1
X2
X3
X4
X5
X6
X7
X8
X9
X10
X11
X12
X13
X14
X15
X16
X17
X18
X19
X20
X21
X22
X23
X24
X25
X26
X27
X28
X29
X30
Actual name of the model input
Slope (degrees)
Aspect (degrees)
Station Height (meters)
Fractional Vegetation Cover (%)
LAI ( m2m-2)
Foliage emissivity (unitless)
[Ca] (external [CO2] on the leaf) (ppmv)
[Ci] (internal [CO2 ] of the leaf) (ppmv)
[03] (ozone concentration in the air) (ppmv)
Vegetation height (meters)
Leaf width (meters)
Minimum Stomatal Resistance ( sm-1)
Cuticle Resistance ( sm-1)
Critical leaf water potential ( bar)
Critical solar parameter (Wm-2)
Stem resistance ( sm-1)
Surface Moisture Availability (vol/vol)
Root Zone Moisture Availability ( vol/vol)
Substrate Max. Volum. Water Content (vol/vol)
Substrate climatol. mean temperature ( oC )
Thermal inertia ( Wm-2K-1)
Ground emissivity (unitless)
Atmospheric Precipitable water (cm)
Surface roughness (meters)
Obstacle height (meters)
Fractional Cloud Cover (%)
RKS (satur. thermal conduct.(Cosby et al., 1984)
Cosby B (see Cosby et al., 1984)
THM (satur.vol. water cont.) (Cosby et al., 1984)
PSI (satur. water potential) (Cosby et al., 1984)
Process in which
each parameter is
involved
time & location
time & location
time & location
vegetation
vegetation
vegetation
vegetation
vegetation
vegetation
vegetation
vegetation
plant
plant
plant
plant
plant
hydrological
hydrological
hydrological
surface
surface
surface
meteorological
meteorological
meteorological
meteorological
soil
soil
soil
soil
Min
value
0
0
0
0
0
0.951
250
110
0.0
0.021
0.012
10
200
-30
25
0.011
0
0
0.01
20
3.5
0.951
0.05
0.02
0.02
1
0
2.0
0.3
1
Max
value
45
360
4.92
100
10
0.990
710
400
0.25
20.0
1.0
500
2000
-5
300
0.150
1
1
1
30
30
0.980
5
2.0
2.0
10
10
12.0
0.5
7
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5. RESULTS
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5.1 Emulator Performance
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Emulator performance was initially assessed using the self-test mechanism of the
BACCO approach, based upon the quantitative evaluation of a series of statistical
measures calculated by GEM-SA (Table 3). In addition, the roughness value of each input
parameter, a unitless value, was computed internally by GEM-SA to specify the
relationship that exist between model output and input (linearity or nonlinear) (Kennedy,
2004; Qin et al., 2013). A comprehensive description of the statistical measures computed
by GEM SA is available in Kennedy and O’Hagan (2001) and O’Hagan (2006).
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Table 3: Emulator performance statistics for the SA tests conducted in this study under normal PDF
assumptions for the model inputs/outputs at each different time scenario.
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EMULATOR STATISTICS
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O3 fluxPLANT
354
Sigma-squared
-2 -1
09:30
11:30
13:30
1.826
2.847
1.462
Cross- validation root mean squared-error (mg m s ):
4.745
8.158
7.389
355
Cross-validation root mean squared relative error (%):
2.054
1.369
8.752
356
Cross-validation root mean squared standardised error:
1.656
2.372
1.409
2.864
3.532
2.192
Cross- validation root mean squared-error (mg m s ):
4.228
4.613
7.764
Cross-validation root mean squared relative error (%):
4.841
9.664
1.260
Cross-validation root mean squared standardised error:
1.150
0.154
1.381
1.650
0.855
1.688
Cross- validation root mean squared-error (ppmv x 10 ):
4.956
3.652
4.285
Cross-validation root mean squared relative error (%):
2.225
6.536
2.567
Cross-validation root mean squared standardised error:
1.401
2.014
2.321
Sigma-squared
0.013
0.029
0.144
Cross- validation root mean squared-error (ppmv):
3.383
4.555
4.807
Cross-validation root mean squared relative error (%):
1.483
1.815
2.509
Cross-validation root mean squared standardised error:
1.970
1.640
2.206
357
358
O3 fluxGLOBAL
Sigma-squared
-2 -1
359
360
361
362
363
364
O3canopy
Sigma-squared
-3
365
366
367
368
369
CO2canopy
370
CO2 flux
371
Sigma-squared
-2 -1
Cross- validation root mean squared-error (µmol m s ):
Cross-validation root mean squared relative error (%):
0.709
1.053
0.788
4.163
3.100
3.822
2.031
1.215
3.087
Cross-validation root mean squared standardised error:
1.769
1.242
1.841
372
Page | 11
373
As can be observed from Table 3, sigma-squared values for the CO2canopy and
374
CO2 flux parameters were low, ranging from 0.01 to 1.05, indicating only moderate
375
deviations from linearity. However, sigma-squared values for the O3 flux
376
O3canopy parameters were all relatively high. The majority of values ranged from 1.46 to
377
3.53, where only the O3canopy 11:30 scenario displayed a value below 1 (0.86), suggesting a
378
high degree of non-linearity.
379
The cross- validation RMSD also displayed a variation in accuracy dependent on
model output and simulation time. For the O3 flux
, O3 flux
, and CO2 flux model outputs
380
PLANT
GLOBAL
, O3 flux
GLOBAL
and
PLANT
382
the range of error was relatively low for all simulated time periods ranging from 3.10 (
– 13:30). The error range for the O3canopy and
CO2 flux – 11:30) to 8.16 mg m-2 s-1 ( O3 flux
383
CO2canopy model outputs was on average slightly lower, ranging from 3.38 ppvm to 4.96
384
385
ppvm x 10-3. The cross-validation root mean squared standardised error values were all
moderately close to 1 for all model outputs and simulation times, with the majority of
values ranging from 0.15 ( O3 flux
– 11:30) to 1.97 ( CO2canopy – 9:30). Notably, a number
381
386
PLANT
GLOBAL
388
of model outputs exhibited lesser accuracy at certain simulation times where values
reached above 2, ranging from 2.01 ( O3canopy – 11:30) to 2.37 ( O3 flux
– 11:30). The
389
390
391
392
393
394
395
majority of values for the cross-validation root mean square relative error were below
5%, ranging from 1.22% to 4.84%. Three of the 15 scenarios exhibited values above 5%
(ranging from 6.54% to 9.66%). However, these values are still relatively low, indicating a
good overall emulator performance able to provide simulations of the target quantities
examined with an accuracy ranging between 1.21% and 9.66%. The overall emulator
accuracy results obtained herein were largely comparable to previous GSA studies on
SimSphere (Petropoulos et al., 2009b, 2010, 2013b–d).
396
397
398
399
400
401
402
403
404
For each of the model outputs, roughness value of 30 input parameters was
calculated for the three different simulation times (9:30h/11:30h/13:30h). Any values of
below 1 suggested a generally smooth response from the emulator to variations in its
inputs, an important requirement for effective emulator build (Petropoulos et al.,
2013c,d). Notably, roughness values for the majority of the model inputs were low, below
1, with few exceptions based on certain model outputs and time scenarios. For example,
the 9:30 Leaf Width, Surface Moisture Availability, Substrate Max. Volume Water Content,
Thermal Inertia, and Surface Roughness input parameters showed roughness values
ranging from 0 to 0.05 for all model outputs, where 17 of the 25 roughness values for the
5 model outputs was 0. On the other hand, LAI for the O3 flux
model output exhibited
387
405
PLANT
PLANT
409
roughness values exceeding 1. Variations were also visible within the individual input
parameters dependent on simulation time. For example, the Critical Leaf Water Potential
input parameter for the 09:30 and 11:30 scenarios exhibited roughness values of 0 for
the O3canopy output, adverse to the 2.03 roughness value exhibited at the 13:30 time
410
scenario, indicating that simulation time can have a major effect on model parameter
406
407
408
Page | 12
411
412
413
414
415
relationships. In summary, roughness values above were relatively rare and indicated
some degree of non-linearity between model inputs and outputs; however, apart from
some exceptions, in the majority of cases these were not significant enough to suggest an
extreme level of non-linear relationships. Overall, results indicate that the model output
can be an approximate linearity function of the inputs.
416
417
5.2 SA Results
418
419
420
421
422
423
424
The sensitivity of the model input parameters with respect to the decomposition
of the examined model outputs for the cases of all the 3 different time scenarios (i.e.
9:30/11:30/13:30) has been summarised in Table 4. Figure 3 displays the input
parameter sensitivity rankings with regards to each model output. Table 5 summarise the
highly sensitive and moderately sensitive input parameters. Figure 2, exemplifies the
main and total effects for each model output, for the case of the 3 different times at which
SA was examined.
425
426
427
428
429
430
431
432
433
434
435
436
Page | 13
437
438
439
440
441
Table 4: Summarised results from the implementation of the BACCO GEM SA method on the different outputs simulated by SimSphere. Computed main
(Main) and total effect (Total) indices by the GEM tool (expressed as %) for each of the model parameters are shown, whereas the last three lines
summarise the percentages of the explained total output variance of the main effects alone (ME), the 1st order interactions only (1st) and the 2nd or
higher order interactions only (2nd). Input parameters with a variance decomposition of greater than 1% are highlighted. The tables below show the
summarised results for a) The 9:30 scenario b) The 11:30 scenario and c) the 13:30 scenario.
(a)
442
(b)
9:30 Scenario
Model Input
O3 Canopy
Global O3 Flux
(c)
11:30 Scenario
O3 Flux in Plant
CO2 Canopy
CO2 Flux
Main
Total
Main
Total
Main
Total
Main
Total
Main
Total
X1
0.101
0.626
0.465
1.105
0.105
0.107
0.002
0.002
0.025
0.500
X2
0.736
5.268
0.092
0.096
0.320
3.632
0.001
0.003
0.016
X3
1.042
8.904
0.108
0.112
0.399
6.865
0.001
0.002
0.127
X4
0.183
0.444
2.169
16.080
0.025
0.039
0.002
0.002
X5
2.791
16.171
4.103
34.038
8.921
32.035
0.004
X6
0.235
0.823
0.081
0.085
0.064
0.066
0.001
X7
0.132
0.795
0.129
0.271
0.022
0.023
Model Input
O3 Canopy
Global O3 Flux
13:30 Scenario
O3 Flux in Plant
CO2 Canopy
CO2 Flux
Main
Total
Main
Total
Main
Total
Main
Total
Main
Total
X1
0.276
1.181
0.059
0.175
0.061
0.064
0.004
0.008
0.135
2.267
0.017
X2
0.264
0.371
0.014
0.016
0.108
0.249
0.002
0.003
0.064
1.558
X3
0.052
0.053
0.023
0.101
0.056
0.399
0.002
0.002
0.041
17.130
31.710
X4
0.114
0.412
0.652
1.399
0.023
0.259
0.006
0.006
0.004
3.704
6.994
X5
0.074
1.246
4.093
46.103
7.578
29.940
0.001
0.001
0.014
0.015
X6
0.217
1.574
0.030
0.340
0.036
0.039
0.001
99.706
99.824
14.160
27.130
X7
0.044
0.258
0.016
0.018
0.026
0.029
Model Input
O3 Canopy
Global O3 Flux
O3 Flux in Plant
CO2 Canopy
CO2 Flux
Main
Total
Main
Total
Main
Total
Main
Total
Main
Total
X1
0.115
1.069
1.789
10.657
0.096
0.097
0.003
0.113
0.103
1.872
0.860
X2
0.922
14.377
0.436
7.057
0.836
3.838
0.011
0.180
0.023
0.294
0.200
X3
0.251
0.329
0.073
0.076
0.093
0.094
0.007
0.067
0.036
0.065
16.088
30.058
X4
0.072
0.075
4.478
23.228
0.057
0.058
0.096
0.152
14.741
30.199
0.004
4.545
9.702
X5
2.001
26.278
2.314
4.280
14.196
40.571
0.011
0.105
5.096
12.080
0.001
0.012
0.040
X6
0.681
13.238
0.120
0.123
0.084
0.371
0.007
0.012
0.019
0.122
99.499
99.727
15.728
28.732
X7
0.162
0.165
0.077
0.079
0.061
0.062
97.221
98.583
14.561
26.596
X8
0.080
0.081
0.223
0.226
0.023
0.025
0.001
0.001
6.827
12.450
X8
0.063
0.125
0.020
0.057
0.093
1.282
0.002
0.003
6.695
11.854
X8
0.093
0.095
0.959
7.267
0.603
6.860
0.074
0.220
6.381
13.414
X9
31.798
44.021
9.780
16.264
6.153
21.861
0.000
0.000
0.021
0.116
X9
32.584
68.480
4.920
22.176
2.776
4.747
0.000
0.000
0.028
0.029
X9
17.533
63.959
4.932
8.906
9.141
20.912
0.021
0.182
0.022
0.023
X10
10.454
31.556
2.721
10.100
3.619
25.735
0.024
0.024
0.156
0.521
X10
12.796
32.067
0.867
10.019
3.655
6.831
0.044
0.049
0.204
0.596
X10
6.721
26.765
2.226
4.528
7.935
34.431
0.371
0.540
0.695
4.340
X11
0.027
0.028
0.081
0.084
0.017
0.019
0.000
0.000
0.045
0.273
X11
0.058
0.135
0.127
0.711
0.139
0.245
0.001
0.001
0.032
0.033
X11
0.079
0.081
0.182
0.185
0.050
0.051
0.005
0.006
0.061
0.256
X12
0.050
0.185
0.082
1.388
0.038
0.333
0.001
0.001
1.532
5.083
X12
0.055
0.056
0.061
0.064
0.046
0.493
0.002
0.002
1.189
4.205
X12
0.203
0.206
0.555
14.691
0.047
0.048
0.006
0.018
1.005
3.790
X13
10.544
30.982
11.008
31.356
27.376
67.835
0.001
0.001
26.300
42.700
X13
8.249
21.930
32.792
79.954
35.830
75.963
0.002
0.008
26.102
40.467
X13
0.160
0.162
4.592
13.159
9.430
26.872
0.071
0.110
25.103
42.390
X14
0.032
0.033
0.081
0.084
0.012
0.014
0.002
0.002
0.041
0.725
X14
0.048
0.049
0.026
0.170
0.083
0.800
0.003
0.003
0.097
0.432
X14
1.461
22.855
0.403
2.195
0.305
1.522
0.003
0.014
0.138
0.530
X15
0.181
4.462
0.139
1.599
0.058
0.073
0.001
0.001
0.105
1.088
X15
0.105
3.909
0.103
0.105
0.056
0.058
0.000
0.006
0.057
0.798
X15
0.163
0.404
0.332
1.051
0.102
0.103
0.003
0.003
0.080
0.713
X16
0.147
1.599
0.190
0.334
0.073
0.166
0.000
0.001
0.065
0.381
X16
0.077
0.077
0.015
0.018
0.039
0.041
0.000
0.000
0.118
0.443
X16
0.097
0.099
0.065
0.067
0.046
0.047
0.008
0.015
0.164
0.548
X17
0.052
0.054
0.138
1.558
0.075
0.077
0.000
0.000
0.038
0.039
X17
0.140
0.141
0.109
0.111
0.037
0.039
0.001
0.006
0.020
0.021
X17
0.133
0.136
0.173
0.176
0.115
0.116
0.003
0.003
0.029
0.138
X18
0.057
0.059
0.097
0.101
0.045
0.047
0.001
0.001
0.291
1.065
X18
0.146
4.228
0.031
0.034
0.048
0.051
0.003
0.005
0.305
1.524
X18
0.260
0.263
1.211
3.680
0.106
0.107
0.004
0.009
0.072
0.073
X19
0.088
0.089
0.158
0.162
0.042
0.135
0.001
0.001
0.078
0.136
X19
0.222
0.463
0.075
0.302
0.031
0.048
0.000
0.001
0.036
0.265
X19
0.138
0.422
0.396
0.398
0.167
3.422
0.003
0.003
0.027
0.401
X20
0.075
0.864
0.093
0.097
0.028
0.030
0.000
0.000
0.023
0.023
X20
0.307
4.244
0.014
0.109
1.123
21.379
0.001
0.001
0.017
0.018
X20
0.200
0.202
0.330
2.140
0.043
0.044
0.034
0.103
0.021
0.062
X21
0.050
0.052
0.089
0.093
0.090
0.313
0.001
0.001
0.025
0.057
X21
0.042
0.043
0.063
0.076
0.037
0.039
0.001
0.002
0.043
1.082
X21
0.192
0.350
8.899
46.828
1.071
11.041
0.012
0.031
0.023
0.177
X22
0.579
1.096
0.771
3.260
0.707
4.336
0.000
0.000
0.019
0.020
X22
0.182
0.537
0.313
7.288
0.153
0.307
0.000
0.005
0.027
0.058
X22
0.425
11.518
0.091
0.093
0.126
0.127
0.003
0.003
0.036
0.062
X23
0.251
1.259
5.009
34.569
0.079
0.333
0.003
0.003
0.245
0.542
X23
0.062
0.063
0.049
0.051
0.025
0.073
0.002
0.002
0.095
0.159
X23
0.094
0.096
1.310
13.294
0.550
3.478
0.025
0.208
0.088
0.244
X24
0.324
0.753
0.077
0.081
0.090
0.091
0.006
0.006
0.106
0.271
X24
1.599
10.675
0.031
0.034
0.394
1.577
0.005
0.009
0.091
0.092
X24
0.443
1.234
0.170
0.410
0.394
1.238
0.006
0.014
0.112
0.237
X25
0.034
0.035
0.134
2.174
0.030
0.031
0.001
0.001
0.028
0.167
X25
0.055
0.056
0.037
0.079
0.714
17.566
0.001
0.001
0.014
0.015
X25
0.144
0.147
0.147
0.149
0.097
0.410
0.007
0.067
0.028
0.029
X26
0.134
0.250
1.098
13.459
0.190
1.019
0.005
0.097
0.018
0.066
X26
0.156
0.280
0.029
0.031
0.049
0.629
0.001
0.051
0.028
0.029
X26
0.118
0.120
0.100
0.103
0.083
1.311
0.004
0.004
0.043
0.065
X27
0.138
1.283
0.877
11.808
0.380
7.046
0.004
0.101
0.020
0.021
X27
0.145
2.116
0.218
4.989
0.136
2.068
0.007
0.189
0.016
0.017
X27
0.817
18.509
1.227
15.802
1.104
18.619
0.004
0.005
0.093
0.521
X28
0.183
2.193
0.333
7.404
0.207
1.127
0.004
0.111
0.041
0.042
X28
0.038
0.039
0.014
0.016
0.027
0.030
0.012
0.190
0.017
0.018
X28
0.135
3.101
0.581
12.969
0.036
0.037
0.038
0.825
0.040
0.041
X29
0.087
2.827
0.152
0.525
0.041
0.043
0.006
0.112
0.038
1.332
X29
0.047
0.687
0.021
0.074
0.028
0.912
0.011
0.195
0.019
0.726
X29
0.168
5.344
0.109
0.111
0.060
0.061
0.010
0.446
0.035
1.287
X30
0.040
0.041
0.351
2.140
0.053
0.055
0.003
0.104
0.082
1.539
X30
0.247
9.281
0.053
0.108
0.021
0.024
0.005
0.171
0.045
0.116
X30
0.156
0.158
0.190
0.520
0.650
4.609
0.074
0.794
0.030
0.031
ME
60.628
40.828
49.280
99.783
71.320
ME
58.462
44.876
53.429
99.621
71.908
ME
34.134
38.468
47.683
98.145
68.907
1st
25.397
34.087
32.025
0.083
22.120
1st
23.637
38.271
29.778
0.171
22.312
1st
31.295
35.167
30.831
1.025
23.230
443
13.975
25.085
18.695
0.134
0.208
2nd or Higher
17.901
16.853
16.793
0.208
5.780
2nd or Higher
34.571
26.365
21.486
0.830
7.863
2nd or Higher
444
Page | 14
445
Table 5: Summary of the most sensitive SimSphere inputs with respect to each of the model outputs
446
of which their sensitivity was examined in our study. O3canopy is the ambient O3 concentration [ppmv
447
x 10-3], O3 fluxGLOBAL is the flux of O3 from the air to the plant/soil boundary [mg m-2 s-1], O3 fluxPLANT is the
448
flux of O3 taken up by the plant alone [mg m-2 s-1], CO2canopy is the ambient CO2 concentration
449
[ppmv], CO2 flux is the rate of uptake of CO2 by the plant [µmol m-2 s-1].
450
451
452
MODEL
OUTPUTS
O3canopy
453
454
455
456
457
458
O3 fluxGLOBAL
459
460
461
462
463
464
O3 fluxPLANT
465
466
467
HIGHLY SENSITIVE MODEL INPUTS
(total sensitivity index > 10%)
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
[O3] in the Air
Vegetation Height
LAI
Cuticle Resistance
Critical Leaf Water Potential
Foliage Emissivity
RKS
Aspect
Ground Emissivity
Surface Roughness
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
Stem Resistance
Root Zone Moisture Availability
Slope
THM
Station height
Critical Solar Parameter
Atmospheric Precipitable Water
CosyB
Substrate Climatological Mean Temperature
PSI
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
Cuticle Resistance
Thermal Inertia
LAI
Fractional Vegetation Cover
[O3] in the Air
RKS
Vegetation Height
Atmospheric Precipitable Water
Minimum Stomatal Resistance
Fractional Cloud Cover
CosyB
Slope
1.
2.
3.
4.
5.
6.
7.
8.
9.
Ground Emissivity
Aspect
Obstacle Height
[Ci]
PSI
Critical Solar Parameter
Surface Moisture Availability
Critical leaf Water Potential
Root Zone Moisture Availability
1.
2.
3.
4.
5.
6.
7.
8.
Cuticle Resistance
LAI
Vegetation Height
[O3] in the Air
Substrate Climatological Mean Temperature
Obstacle Height
Thermal Inertia
RKS
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
[Ci]
PSI
Aspect
Station Height
Substrate Maximum Volume Water Content
Atmospheric Precipitable Water
Ground Emissivity
Surface Roughness
Fractional Cloud Cover
Critical leaf Water potential
CosyB
RKS
468
469
470
471
472
473
474
475
CO 2 canopy
CO 2 flux
MODERADLY SENSITIVE MODEL INPUTS
(total sensitivity index < 10%)
1. [Ca]
1.
2.
3.
4.
5.
Cuticle Resistance
Fractional Vegetation Cover
[Ca]
[Ci]
LAI
1.
2.
3.
4.
5.
6.
7.
8.
9.
Minimum Stomatal Resistance
Vegetation Height
PSI
Slope
THM
Root Zone Moisture Availability
Critical Solar Parameter
Station Height
Thermal Inertia
Page | 15
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5.2.1 Sensitivity for CO2canopy
477
The CO2canopy SA results showed that the percentage variance contribution of each
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input parameter’s main and total effects for this parameter were significantly higher
compared to all other model output results, ranging from 0% to 99.71% and 0% to
99.82% for the main and total effects respectively. Although these ranges are
considerably greater than all other model outputs, there is only one significant input
parameter contributing to the main effects for all time scenarios. The external CO2 on the
leaf [Ca] parameter’s individual contributions dominate the total variance with ranges
from 97.22% to 99.71%, followed by negligible contributions for all other input
parameters (<1%). Main effects results also shows that first order interactions for the
CO2canopy parameter range between 98.15% and 99.78%, being the only significant
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contribution to variance decomposition. This is also reinforced by the considerably low
percentage influence of 2nd order (or higher) interactions which range from 0.13% to
0.83%. These trends are mirrored in the total effects where [Ca] ranges from 98.58% to
99.82%, with all other parameters again negligible (<1%). Furthermore, no significant
(>1%) first order interaction were recorded (Table 4 and Figure 2d).
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5.2.2 Sensitivity for CO2 flux
494
Percentage contributions from each input parameter to the total CO2 flux variance
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ranged from 0.01% to 26.10%, and 0.02% and 42.70% for the main and total effects
respectively (Table 4 and Figure 2e). The summarised percentages of the main effects
alone were relatively high, exhibiting comparable ranges for all three time scenarios,
ranging between 68.91% and 71.91%. Highest individual contributions to first order
main effects is given by Cuticle Resistance, followed by Fr and [Ca], which together
contribute to ~50% of all first order main effects, suggesting that there are significant
higher order interactions between these parameters. Second order interactions are less
significant ranging from 5.78% to 7.86%. The same parameters were also important in
terms of total effects, yet with increased percentage contributions. In addition many other
factors also became important in the case of total effects, the most significant being
internal CO2 of the leaf [Ci] and LAI. Six significant first order interactions (joint effects
higher than 1%) were found for all three time scenarios. These included; Fr and Cuticle
Resistance, Fr and [Ca], [Ca] and Cuticle Resistance, LAI and Cuticle Resistance, Fr and
[Ci], and [Ci] and Cuticle Resistance. Although all three time scenarios shared the same six
significant first order interactions, the percentage contribution and order of significance
varied between different simulation times.
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5.2.3 Sensitivity for O3canopy
Page | 16
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The input parameter’s main and total effect variance contribution to the
simulation of the O3canopy output by SimSphere showed relatively wide variations in range
529
dependent on computation time (Table 4, and Figure 2a). Main effects ranged from 0.03%
to 32.58%, and total effects ranged from 0.63% to 68.48% respectively for all time
scenarios. The model input with the lowest main effect of 0.03% (Leaf Width) was
included within the 9:30 scenario, whereas the 11:30 scenario included the model input
with the highest main effect of 32.58% ([03] in the Air). With regards to the total effects,
the 9:30 and 11:30 scenarios again included the same model inputs with the lowest and
highest total effect of 0.03% (Leaf Width) and 68.48% ([03] in the Air) respectively. The
summarised percentages of the explained total output variance of the main effects alone,
show that model output was mainly affected by the variance decomposition of input
parameters during the 9:30 and 11:30 scenarios, which displayed main effects of 60.63%
and 58.45% respectively. As Table 3 shows, the Cuticle Resistance, VH and [03] in the Air
parameters had the largest percentage variance contributions for all time scenarios,
suggesting significant first order interactions between these parameters. In terms of the
total effects, Cuticle Resistance, VH and [03] in the Air were again the most important
parameters for the simulation of O3canopy in all time scenarios, although there were a
530
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533
number of other significant contributors (e.g. LAI, Saturated Water Potential (PSI),
Saturated Thermal Conductivity (RKS) and Surface Roughness) (Table 4). It should be
noted that the 2nd order interactions are also significant here as they account for
between 13.98% and 34.57% of variance.
534
535
536
537
538
Significant first order interactions (higher than 1% joint effects) varied with
simulation times; however, all time scenarios exhibited at least a minimum of 5
interactions. The most important interactions were i) 9:30 - VH and CR (5.95%) ii) 11:30
- [03] in the Air and VH (7.19%) iii) 13:30 – LAI and [03] in the Air (4.37%). Notably, VH,
CR and [03] in the Air were incorporated in some part in the majority of interactions.
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5.2.4 Sensitivity for O3 flux
541
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Main effects and total effects ranged from 0.01% to 32.79% and 0.02% to 79.95%
respectively for all time scenarios (Table 4 and Figure 2b), where Main Effects (ME)
results suggested all simulation times exhibited comparable ranges between 38.47% and
44.88%. The input parameters with the largest percentage variance contribution were
similar to that of the O3canopy , where [03] in the Air and CR were significant contributors.
546
Higher than first order interactions for the O3 flux
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550
and 26.37% dependent on time scenario, contributing to significant variance
decomposition. In terms of the individual total effects, as well as mirroring the main
effects, several other significant parameters exhibited high percentage variance (e.g.
Thermal Inertia, LAI, VH) which were important contributors to total effects (>10%).
GLOBAL
GLOBAL
parameter range between 16.85%
Page | 17
554
Over thirty significant first order interactions were found for this output with the
most important being i) 9:30 - LAI and Atmospheric Precipitable Water (3.58%) ii) 11:30
- LAI and CR (21.67%) iii) 13:30 – Fr and Thermal Inertia (2.13%) As was seen for the
first order interactions of the O3canopy , vegetative input parameters contributed
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significantly to the percentage variance, where interactions between Fr and LAI, [03] in
the Air and Cuticle Resistance, LAI and VH, and LAI and [O3] in the Air also had significant
contribution above 1%. Notably the first two time periods shared a number of significant
first order interactions which were not deemed significant for the 13:30 scenario,
suggesting that simulation time has a considerable effect on the performance of certain
model inputs.
551
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5.2.5 Sensitivity for O3 flux
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Values of percentage contributions from each parameter to the main and total
variance again vary for the different simulation times. SA results showed ranges in main
effects and total effects for all time scenarios ranged from 0.01% to 35.83% and 0.01% to
75.96% respectively (Table 4 and Figure 2c). The percentages of the explained total
output variance of the main effects alone again showed comparable ranges with minimal
variance, ranging from 47.68% to 53.43%. Parameters with the highest individual
contributions were Cuticle Resistance, LAI and [03] in the Air which, with lesser
contributions by VH, Thermal Inertia, and RKS amongst others (Table 4). Contributions
by other parameters were negligible (<1%). Together the contributions from the three
most significant parameters amount to over 60%, suggesting significant first order
interactions between these model input parameters. This was also mirrored in the total
effects results obtained, yet at higher percentage contributions (e.g. 11:30 – 35.83%
increases to 75.96% for Cuticle Resistance), where a large number of additional
parameters contributed > 1% to the total effects also (e.g. Station Height, Critical Solar
Parameter, Surface Roughness) (Table 3).
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For the 29 significant first order interactions (>1%) the most important were i)
9:30 - VH and CR (7.58%) ii) 11:30 - CR and Substrate Climatological Mean Temperature
(8.37%) iii) 13:30 – LAI and CR (3.63%). Similarly to the most significant first order
interactions for both the O3canopy and O3 flux
, the most important interactions included
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some contribution from vegetative input parameters, and the majority of the highest
percentage contributions correlated between the three model outputs. Several other
significant first order interactions were also recorded including [03] in the Air and CR, LAI
and [03] in the Air, LAI and VH, and CR and Obstacle Height amongst others. Again the
first two time scenarios shared a considerable number of first order interactions which
were not deemed significant at the later simulation time. This again suggests the
important effect of simulation time on model input contributions.
PLANT
GLOBAL
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Page | 18
CO2 Canopy Main Effects
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Main Effects - 13:30 Scenario
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Main Effects - 11:30 Scenario
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Page | 19
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CO2 Flux Main Effects
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Main Effects - 09:30
Scenario
Main Effects - 11:30
Scenario
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Scenario
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CO2 Flux Total Effects
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Page | 20
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O3 Canopy Main Effects
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Main Effects - 11:30 Scenario
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Total Effects - 09:30 Scenario
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Total Effects - 11:30 Scenario
Total Effects - 13:30 Scenario
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Page | 21
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Global O3 Flux Main Effects
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Total Effects - 09:30 Scenario
Total Effects - 11:30 Scenario
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Total Effects - 13:30 Scenario
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Page | 22
O3 Flux in Plant Main Effects
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Main Effects - 09:30 Scenario
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O3 Flux in Plant Total Effects
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Total Effects - 09:30 Scenario
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Total Effects - 11:30 Scenario
Total Effects - 13:30 Scenario
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Figure 2: Bar graphs displaying the results from the implementation of the BACCO GEM SA method
on the different outputs simulated by SimSphere. The values on the x axis show the 30 input
parameters examined in our study and the y axis displays the percentage contribution of each input
parameter to the model output. Contributions of the input parameters to main effects and total
effects variance decomposition, for each of the three time scenarios are displayed a) SA results for
the O3 Canopy model output b) SA results for the Global O3 Flux model output c) SA results for the O3
Flux in Plant model output d) SA results for the CO2 canopy model output e) SA results for the CO2
flux model output.
Page | 23
a)
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Main Effects 09:30 Scenario
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Low
Medium
X30
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O3 Canopy
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Total Effects 09:30 Scenario
X1
Global O3 Flux
O3 Flux in Plant
CO2 Canopy
CO2 Flux
High
O3 Canopy
Main Effects 11:30 Scenario
b)
Global O3 Flux
O3 Flux in Plant
CO2 Canopy
CO2 Flux
Total Effects 11:30 Scenario
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Low
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Medium
Page | High
24
X30
O3 Canopy
Global O3 Flux
O3 Flux in Plant
CO2 Canopy
CO2 Flux
O3 Canopy
Global O3 Flux
O3 Flux in Plant
CO2 Canopy
CO2 Flux
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c)
Main Effects 13:30 Scenario
Total Effects 11:30 Scenario
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Low
Medium
X30
O3 Canopy
Global O3 Flux
O3 Flux in Plant
CO2 Canopy
CO2 Flux
High
O3 Canopy
Global O3 Flux
O3 Flux in Plant
CO2 Canopy
CO2 Flux
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Figure 3: Input parameter sensitivity rankings for the different model outputs for both main and total effects a) Input parameter sensitivity rankings for
the 09:30 scenario main and total effects b) Input parameter sensitivity rankings for the 11:30 scenario main and total effects c) Input parameter
sensitivity rankings for the 13:30 scenario main and total effects.
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Page | 25
790
6. DISCUSSION
791
In terms of the CO2canopy simulation, it is clear that this parameter within
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798
SimSphere is dominated by the [Ca] and [Ci] input parameters (internal leaf CO2 and
external, ambient, CO2). This is logical due to the fact that both components will be
inherently linked in regards to the processes and feedbacks associated with
photosynthesis. In essence, [Ca] represents the ambient concentration of CO2 in the
atmosphere within, and above the canopy. Therefore [Ca], directly affects the carbon
assimilation rates through the formation of concentration gradients that promote the
diffusion of CO2 through the stomata and into the mesophyll. The significant influences of
[Ca], as well as several vegetative parameters, are again apparent for the CO2 flux model
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output. This is due to the integrated effect of carbon assimilation rates within the plant
structures and CO2 uptake by plant canopies affecting the diffusive flux of CO2 (Fernández
et al., 2013). The effect of vegetative parameters on the CO2 flux model output can be
explained by the process of CO2 diffusion by plants for use in photosynthetic carbon
assimilation. Within a plant structure, stomatal behaviour directly affects assimilation by
being able to regulate when to open if photosynthetic demand for CO2 is high or close if
water supply becomes inadequate (Gordon and Olsen, 2013). In Pinus ponderosa, water
potential alone explains 82% of the day-to-day variation in stomatal conductance (Panek,
2004). Fr and LAI were also identified as important determinants of CO2 flux . Fr is an
823
input parameter to scale the vegetation cover on the ground, i.e. it determines the size of
the vegetated portion of the land surface that will be communicating with the
atmosphere. LAI is the total one‐sided area of leaf tissue per unit ground surface area
characterising the canopy of an ecosystem, which is inherently linked to stomatal density
and aperture (Bréda, 2003; Barlage and Zeng, 2004). Fr and LAI in essence determine the
amount of biomass available for assimilation and transpiration, as well as being
inherently linked to stomatal density and aperture (Bréda, 2003; Barlage and Zeng,
2004). Furthermore, the LAI, for example, determines canopy photosynthesis and plant
productivity by providing the potential for light interception (Levis, 2010; Oikawa et al,
2013). Thus, given these plant physiological traits, these parameters determine the
amount of CO2 uptake into a canopy for photosynthesis and transpiration (through the
amounts and rates of CO2 diffusion through the stomata), as well as the amount of CO2
produced within a leaf structure through respiration (e.g. the higher the values of Fr and
LAI, the greater the amount of CO2 uptake, diffusion and production), thus explaining the
influence of these parameters on the CO2 flux output.
824
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829
CO2 diffusion through the cuticle can be up to 100 times less intensive than
through the stomata (due to the cuticle on the epidermis being almost impermeable to
CO2. However, this varies with leaf age and thickness, and is still an important influence
on the dynamics of CO2 flux within the troposphere (Kvesitadze et al., 2006; Kirkham,
2011). The cuticle controls water loss from the leaf and the permeability of cuticles
depends upon their evolutionary origin (Riederer and Schreiber, 2001). As properties of
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Page | 26
830
the cuticle are responsible for the loss of water, the effect of the leaf cuticle on CO2 flux may
831
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be the influence of water dynamics affecting stomatal conductance which explains the
significance of the CR parameter on the CO2 flux model output. In addition, stomatal
833
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836
conductance has been shown to decline in taller trees due to hydraulic limitation, which
may reduce intercellular CO2 concentrations within leaves and result in declines in
assimilation, explaining the significance of VH on this output parameter (Sendall and
Reich, 2013).
837
838
It is clear from the results obtained that vegetative parameters have a significant
influence on several of the model outputs relating to O3 (CR, LAI, Fr, and VH). In terms of
the modelled O3canopy , O3 flux
and O3 flux
simulation by the SimSphere model, the
839
GLOBAL
PLANT
855
influence of these vegetative parameters can be explained by the fact that ozone has a
sink at the ground surface as well as in the leaves, and since the cuticular resistance is
typically many times that of the stomatal resistance, most of the ozone ingested by the
leaf is through the stomates. However, an approximately equal flux is deposited at the
ground surface in and around a plant canopy (Tuzet et al., 2011; Ganzeveld et al., 2012).
In the case of full vegetation cover or dense canopies (large percentages of LAI, VH and
Fr) this is mainly governed by stomatal aperture where O3 uptake is a function of both
ambient O3 levels and stomatal conductance (Mauzerall and Wang, 2001). Quantified as
stomatal resistance against the diffusion of O3 molecules into the sub‐stomatal cavities
(Emberson et al., 2000), uptake increases with stomatal pore number or density (Eichert
and Burkhardt, 2001). This is directly linked to the structural properties of a plant or
plant canopy which is in turn represented by Fr and LAI. Essentially, the specific leaf area
on a dry weight basis, or the area of assimilatory leaf material per dry weight unit thus
becomes the main determining factor of amount of O3 uptake (WHO, 2006). This link
between Fr, LAI and stomatal uptake of O3 explains the significant influence of the Fr and
LAI input parameters on the O3canopy , O3 flux
and O3 flux
model outputs. Furthermore,
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vegetation height can play a role in the amount of available O3 for uptake due to possible
vertical variations in mean O3 concentration within the canopy air space, with some
experiments recording it to be as large as 10–30 ppb within forests and grasslands
(Utiyama et al., 2004; Jäggi et al., 2006; Launiainen et al. 2013). Variations in canopy or
plant height can thus affect the amount of O3 available for deposition which explains the
influence of the VH parameter on these model outputs.
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The conventionally termed non-stomatal O3 removal pathways can also have some
effect on O3 plant uptake, these include external plant parts (e.g. cuticles, bark, twigs etc.)
the ground surface underlying the vegetative canopy (including soil, litter moss etc.) and
the associated in-canopy aerodynamic resistance to O3 transfer to the ground surface.
Non-stomatal O3 flux has been attributed mainly to physical and chemical O3 depletion at
the plant and soil surfaces through thermal decomposition (Cape et al., 2009), aqueous
reactions in the liquid water accumulated at the surface (Altimir et al., 2004, 2006), lightstimulated reactions (Coe et al., 1995) and the gas-phase reactions of O3 with reactive
Biogenic Volatile Organic Compounds (BVOC) and Nitrous Oxide (NO) (Wolfe and
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Thornton, 2011; Wolfe et al., 2011a,b). The extent of uptake depends on the timeintegrated absorbed O3 flux (i.e. the dose), which is a function of non-stomatal
conductance and ambient O3 concentration (Wohlfahrt et al., 2009). Concentration of
ambient O3 in the troposphere (within the canopy, sub-canopy, canopy air space, ground
surface) thus has some control on the rates of environmental O3 flux and plant deposition,
explaining the influence of the [O3] in the Air parameter on the O3canopy , O3 flux
and
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O3 fluxPLANT model outputs. This would further explain the number of first order interactions
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which incorporated vegetative parameters with the [O3] in the Air input. However it
should be noted that the relationship between ambient O3 concentration and uptake is
non-linear, where highest rates of uptake are found during periods where stomatal
conductance is highest and stomata are relatively unconstrained by stress factors, not
when ambient O3 concentrations are at their maximum (Bytnerowicz et al, 2003).
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In forest trees, the uptake of O3 also depends upon the daily diurnal rhythms that control
the opening and closing of stomata. Diurnal fluctuations in the stem radius of large trees
have been observed in a number of species and control the supply of water to the
meristematic tissues (Zweifel et al., 2005; McLaughlin et al., 2007). Exposure of forest
trees to increased levels of O3 was found to amplify these diurnal patterns indicating that
the trees were experiencing reduced hydration. The annual reduction in growth rate
ranged from -14 to -63% in a year in which O3 exposure was particularly high but was
also dependent upon species, with a drought tolerant species (Q. prinus, chestnut oak)
showing greatest resistance (McLaughlin et al., 2007). In a second tree species, Pinus
ponderosa, growing under seasonal drought conditions in California, the uptake of O3 was
highest in early summer when water availability was higher (Panek, 2004). However, as
the summer progressed and water became limiting, O3 uptake was highest in the morning
even though the concentration of was higher later in the day (Panek, 2004). The
conclusion of both of these aforementioned studies was that the uptake of O3 does not
depend upon concentration but the availability of water that drives the opening of the
stomata and allows O3 to penetrate the leaf (Panek, 2004; McLaughlin et al., 2007). In the
instance of external plant parts, deposition on the cuticles can be limited under dry
conditions (Cape et al., 2009), but on wet canopies this process may represent a major
sink for O3 (Altimir et al., 2006), particularly when O3 concentrations are low, explaining
the significant influence of the CR parameter on these model outputs.
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The general contention reported in the literature is that sensitivity analyses of models
tend to be perfunctory. However, Shin et al. (2013) have identified a number of questions
which need to be considered when performing SA of any model, highlighting two key
issues related to uncertainty and identifiability. Questions of parameter range selection,
data sampling size and SA method all need to be addressed to minimise uncertainty in SA.
For example, reducing or expanding the variations in input parameter ranges can affect
the sensitivity index, thus it is important that the ranges used yield parameter sets that
are considered plausible, such that results are not biased by implausible model
realisations. We tried to address this issue through refining a-priori values from real
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observations to allow for the determination of more plausible input parameter sets and to
yield the posterior distribution of each model output considered. Questions related to the
identifiability of models in SA are concerned with changing objective functions,
parameter fixing, changing model structures or changing data periods amongst others.
For example, as was the case in our study, there can be a change in the number of
insensitive model parameters if different data periods are used, although some model
parameters are insensitive for all data periods. While a modeller can easily use SA to help
assess and improve their model in a particular case study, consideration of such issues
must be taken when interpreting any results to avoid drawing generalisations or trying to
apply generalisations to new situations.
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Results obtained herein can be used practically to assist in future model parameterisation
and implementation in diverse ecosystem conditions. Such findings provide further
confidence to current ongoing efforts which focus on the development of operationally
distributed products based on the synergy of the SimSphere model with EO data. The
results of this study are not directly related to the development and future exploitation of
such operational products but have significant implications for the development of the
model as a useful and practical educational tool. Our results extend our understanding of
the model structure and further establish its coherence to that of a natural system’s
behaviour. This development represents a significant step towards the all-inclusive
validation of the SimSphere model which is of high interest to the global user community.
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7. CONCLUSIONS
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The SA study performed herein has attempted to analyse the performance of
SimSphere for a number of yet unexplored parameters that are important contributors to
a number of atmosphere-land surface interactions and feedbacks between the different
components of the land surface. Results confirmed that model outputs are only
significantly sensitive to a small group of model inputs based primarily on vegetative
factors, CO2 and O3 fluxes (Table 4). Fr, LAI, CR and VH were the most important
vegetative parameters which had most influence on all but one output. The influence of
[Ca] and [O3] in the air were also significant parameters, especially in the case of the CO2
Canopy output. To our knowledge there have been few studies so far exploring the
validation and verification of the SimSphere model. To this end, this study represents a
significant step forward in contributing to current global efforts in that direction. All in
all, our findings provided further evidence supporting the model coherence and
correspondence to the behaviour of real world processes, natural feedbacks and
interactions. Future research should aim to further explore our understanding of the
SimSphere structure through performing direct comparisons of model outputs against
reference data from actual in-situ observations and at different ecosystems worldwide.
This would allow further confirming its potential role as an operational tool for climate
research, land cover and land use change monitoring, environmental management, water
resources and agricultural sustainability.
Page | 29
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Acknowledgments
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Dr. Petropoulos gratefully acknowledges the financial support provided by the Marie
Curie Career Re-Integration Grant “TRANSFORM-EO” project supporting the
implementation of this research work. Authors are also grateful to the anonymous
reviewers for their constructive comments which results in improving the manuscript.
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