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The application of detailed process-oriented simulation models for gross primary production (GPP) estimation is constrained by the scarcity of the data needed for their parametrization. In this manuscript, we present the development and test of the assimilation of Moderate Resolution Imaging Spectroradiometer (MODIS) satellite Normalized Difference Vegetation Index (NDVI) observations into a simple process-based model driven by basic meteorological variables (i.e., global radiation, temperature, precipitation and reference evapotranspiration, all from global circulation models of the European Centre for Medium-Range Weather Forecasts). The model is run at daily time-step using meteorological forcing and provides estimates of GPP and LAI, the latter used to simulate MODIS NDVI though the coupling with the radiative transfer model PROSAIL5B. Modelled GPP is compared with the remote sensing-driven MODIS GPP product (MOD17) and the quality of both estimates are assessed against GPP from European eddy covariance flux sites over crops and grasslands. Model performances in GPP estimation (R ² = 0.67, RMSE = 2.45 gC m ⁻² d ⁻¹ , MBE = -0.16 gC m ⁻² d ⁻¹ ) were shown to outperform those of MOD17 for the investigated sites (R 2 = 0.53, RMSE = 3.15 gC m ⁻² d ⁻¹ , MBE = -1.08 gC m ⁻² d ⁻¹ ).
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remote sensing
Article
Assimilation of Earth Observation Data Over
Cropland and Grassland Sites into a Simple
GPP Model
Michele Meroni 1, * , Dominique Fasbender 1, Raul Lopez-Lozano 1and Mirco Migliavacca 2
1Joint Research Centre (JRC), European Commission, Via E. Fermi 2749, I-21027 Ispra, Italy;
Dominique.Fasbender@ec.europa.eu (D.F.); Raul.Lopez-Lozano@inra.fr (R.L.-L.)
2Max Planck Institute for Biogeochemistry, Hanks Knöll Straße 10, D-07745 Jena, Germany;
mmiglia@bgc-jena.mpg.de
*Correspondence: michele.meroni@ec.europa.eu
Received: 11 February 2019; Accepted: 22 March 2019; Published: 27 March 2019


Abstract:
The application of detailed process-oriented simulation models for gross primary
production (GPP) estimation is constrained by the scarcity of the data needed for their parametrization.
In this manuscript, we present the development and test of the assimilation of Moderate
Resolution Imaging Spectroradiometer (MODIS) satellite Normalized Difference Vegetation Index
(NDVI) observations into a simple process-based model driven by basic meteorological variables
(i.e., global radiation, temperature, precipitation and reference evapotranspiration, all from global
circulation models of the European Centre for Medium-Range Weather Forecasts). The model is run
at daily time-step using meteorological forcing and provides estimates of GPP and LAI, the latter
used to simulate MODIS NDVI though the coupling with the radiative transfer model PROSAIL5B.
Modelled GPP is compared with the remote sensing-driven MODIS GPP product (MOD17) and the
quality of both estimates are assessed against GPP from European eddy covariance flux sites over
crops and grasslands. Model performances in GPP estimation (R
2
= 0.67, RMSE = 2.45 gC m
2
d
1
,
MBE =
0.16 gC m
2
d
1
) were shown to outperform those of MOD17 for the investigated sites
(R2= 0.53, RMSE = 3.15 gC m2d1, MBE = 1.08 gC m2d1).
Keywords: gross primary production; crop; grassland; MODIS; data assimilation
1. Introduction
Gross primary production (GPP) of crops and rangelands is important for understanding CO
2
uptake of these ecosystems and ultimately for monitoring the provision of services (food, feed,
and fibers) [
1
]. Detailed crop growth models (CGMs) (e.g., WOFOST, [
2
]; CROPSYST, [
3
]), describe
plant eco-physiological processes such as light interception and absorption, carbon assimilation,
as determined by environmental conditions (weather, soil properties, agro-management, etc.) and
vegetation characteristics. Nevertheless, the operational use of such detailed models presents
important limitations related to the amount and availability of experimental data needed to properly
parameterize, calibrate, and evaluate them, especially over large areas. In fact, complex CGMs
require a large number of input parameters whose value is often not available and/or highly
uncertain. Moreover, the unrealistic spatial and temporal representation of key parameters representing
vegetation characteristics and plant functional traits controlling CO
2
uptake was shown to hamper the
simulation of GPP at various scales [
4
,
5
]. Uncertainties in model inputs are then transferred into large
errors in model estimates [6].
Earth observation (EO) data can provide spatially distributed information to increase the reliability
and usefulness of crop models [
7
]. Various methods have been developed to ingest EO data into these
Remote Sens. 2019,11, 749; doi:10.3390/rs11070749 www.mdpi.com/journal/remotesensing
Remote Sens. 2019,11, 749 2 of 20
models, ranging from the “forcing strategy” (i.e., the direct use of EO as driving variable) to various
assimilation techniques. With assimilation, the model does not require EO data as input but the model
outputs include some EO variables. For a review of the assimilation techniques see Dorigo et al. [
8
]
and Moulin et al. [
9
]. Examples of assimilation of EO data into complex ecosystem models for carbon
flux estimation are available for forest ecosystems. Quaife et al. [
10
] assimilated surface reflectance to
improve GPP estimation of a pine forest. Bacour et al. [
11
] assimilated the fraction of photosynthetically
active radiation to estimate the net ecosystem exchange at two forest sites. Migliavacca et al. [
12
]
assimilated the normalized difference vegetation index to estimate GPP of a poplar plantation.
The present study aims at estimating crop and grassland GPP with an approach based on the
assimilation of EO observations into a simple process-based model of vegetation growth. In view
of the spatial application of the model (and the inherent restriction of data availability to calibrate
the model), the crop model is kept as simple as possible (i.e., reduced parameterization). In addition,
only publicly and freely available EO data and gridded meteorological variables estimated from global
circulation model are employed.
The core of the proposed model is composed of a set of equations building on those of the GRAMI
model [
13
15
]. Specific differences are detailed in Section 3.1. The growth model is coupled with
the canopy radiative transfer (RT) model PROSAIL5B [
16
] to translate model estimates of leaf area
index (LAI) into Normalized Difference Vegetation Index (NDVI) of the Moderate Resolution Imaging
Spectroradiometer (MODIS) at the time of actual satellite overpass (i.e., for actual observation and sun
geometry), similarly to [
12
]. Besides this coupling, the canopy RT model was used in the growth model to
compute the absorbed photosynthetically active radiation (APAR), thus ensuring internal consistency in
the definition of the simplified canopy radiative regime. Finally, the coupled model is “constrained” by a
satellite phenology retrieval model [
17
] that is used to provide a first identification of the likely growth
period. For simplicity, we will hereafter refer to such a model scheme as to “Sim model”.
EO data are not used as input (i.e., forcing) but are assimilated into the model to adjust the model
parameters and initial conditions. In principle this means that the model benefit from EO data but
does not depend on it. Assimilating EO data (i.e., NDVI) into a simple process-based present two main
advantages against classical data-driven GPP algorithms: (i) the process of growth is modelled also in
absence of EO data (thus increased robustness against missing or noisy EO data); (ii) weather forecasts
can be used to run the model to make short-term GPP prediction (given the current model state) that
are progressively adjusted when more observations become available. This latter point is of particular
interest in view of operational monitoring and forecasting applications.
In this study, GPP estimates by the Sim model are validated using GPP derived at eddy
covariance flux sites in Europe and compared to the standard MODIS GPP product (MOD17) used as
benchmark [
18
]. The research questions addressed in this study are: (1) can a simple growth model use
modelled meteorological variables and assimilate EO data to adequately simulate crop and grassland
GPP? and, (2) what is the estimation accuracy and how does it compare with that of the standard
MODIS GPP product?
2. Data
Table 1provides an overview the data used by the study and their specific use. Detailed
description of the datasets is given in Sections 2.12.3.
Remote Sens. 2019,11, 749 3 of 20
Table 1.
Data used in the analysis. ECMWF stands for European Centre for Medium-Range Weather
Forecasts; MODIS: Moderate Resolution Imaging Spectroradiometer; NVDI: Normalized Difference
Vegetation Index; GPP: gross primary production.
Variable Source Main Specifications Purpose
Global radiation, air temperature,
precipitation, reference potential
evapotranspiration
Downscaled ECMWF
ERA-Interim, available
from MARSOP
repository 1
Daily data, 25 km spatial
resolution Model input
NDVI MODIS2MOD- and MYD-13Q1,
16 day composites, 250 m
spatial resolution
Model re-calibration
Surface reflectance MODIS 2MOD- and MYD-09A, 8
day composites, 500 m
spatial resolution
Estimation of canopy
background reflectance
GPP Eddy flux tower 3Daily data GPP validation
GPP MODIS 2MOD17A2H, 8 day
composites, 500 m
spatial resolution
GPP estimates
intercomparison
1
https://marswiki.jrc.ec.europa.eu/agri4castwiki/index.php/Welcome_to_WikiMCYFS.
2
Data retrieved through
the Google Earth Engine. 3From European Flux Database Cluster and FLUXNET2015.
2.1. Meteorological Data
Meteorological data gathered from the European Centre for Medium-Range Weather Forecasts
(ECMWF) forecasting system includes: global radiation, air temperature, precipitation, and potential
reference evapotranspiration. Data are from ERA-Interim reanalysis model and are produced at
3-hourly time-step at a spatial resolution of approximately 80 km. Variables are then temporally
aggregated to daily mean air temperature and cumulative precipitation and evapotranspiration
values. Weather data are taken from the JRC MARSOP project repository [
19
], where ERA-Interim is
down-scaled onto a 25 km reference grid, including bias correction for all elements except precipitation.
It is possible that the modelled and downscaled meteorological data may not perfectly represent
local meteorology [
20
] and thus contribute to the mismatch between modelled and measured GPP.
However, this topic is not specifically addressed here also because the main aim of the study is to
develop and test a methodology for GPP calculation at continental and regional scale and therefore
should rely on meteorology from reanalysis, which is therefore here consider as one of the source
of uncertainty.
2.2. MODIS NDVI, Reflectances and GPP
As source of EO data we selected MODIS data as it provides a relatively long archive of
observations (i.e., from year 2000) and a good compromise between spatial resolution (i.e., 250 m) and
temporal resolution of acquisition (i.e., daily revisit). We retrieved NDVI from the MODIS MOD13Q1
and MYD13Q1 version 6 products using the Google Earth Engine. These are 250 m spatial resolution
16-day NDVI composite from Terra and Aqua satellites produced with an 8-day phase shift. Besides
NDVI, the following information was retrieved for each observation: reflectances in the blue, red,
NIR, and MIR bands, day of acquisition, sun-sensor-target geometry (SZA, Solar Zenith Angle; VZA,
View Zenith Angle, RAA, Relative Azimuth Angle), and Vegetation Index (VI) quality and usefulness.
Only reliable observations were retained from further processing, i.e., observations with VI reliability
greater than two and VI usefulness greater than seven where excluded. MOD09A1 and MYD09A1
(surface reflectance 8-day composite at 500 m) were also acquired to determine the background
contribution to canopy NDVI as explained in Section 3.2. In addition, we retrieved the MODIS GPP
8-day version 6 product (MOD17A2H) at 500 m spatial resolution. MODIS GPP 8-day was scaled to
mean daily value (gC m
2
d
1
) over the 8-day period. We used the flux tower locations to extract the
time series of MODIS data by selecting the pixel where the flux tower coordinates falls within.
Remote Sens. 2019,11, 749 4 of 20
2.3. Eddy Covariance Flux Tower GPP
Eddy covariance (EC) is an established technique to quantify turbulent exchanges of CO
2
between the surface and the atmosphere (for a descrption see Baldocchi et al. [
21
]; Franz et al. [
22
]).
European flux data have been collected from the European Flux Database Cluster (EFDC, a repository
of flux observations for various European projects), and the FLUXNET2015 database (a coordinated
effort to harmonize flux observations for as many sites as possible globally [
23
]). For the purposes of
this study, only flux measurements over cropland and grassland were acquired for a total of 58 sites.
Among the different GPP products available in the two datasets we selected half-hourly GPP
estimated from net ecosystem exchange (NEE) measurements quality-checked, filtered for low friction
velocity conditions, gap-filled and partitioned as consolidated in the FLUXNET methodology [
24
].
Specifically, we used the GPP product computed using an annual friction velocity threshold to filter
NEE, NEE gap-filling based on Marginal Distribution Sampling [
25
], and finally estimates GPP using
night-time flux partitioning [
25
]. Daily GPP values were computed by aggregating half-hourly GPP
estimates, and eventually aggregated to 8-day mean daily value for the validation against modelled
GPP. Surface homogeneity of all EC sites was visually inspected using Google Earth to eliminate sites
with obvious heterogeneity of land cover within the MODIS pixel (e.g., [
26
,
27
]). As a result, only the EC
site FR-Avi (Avignon, France) was excluded for further analysis. The location of the retained sites and
period covered by flux measurements is shown in Figure 1(30 cropland sites and 27 grassland sites).
Remote Sens. 2019, 11, 749 4 of 21
effort to harmonize flux observations for as many sites as possible globally [23]). For the purposes of
this study, only flux measurements over cropland and grassland were acquired for a total of 58 sites.
Among the different GPP products available in the two datasets we selected half-hourly GPP
estimated from net ecosystem exchange (NEE) measurements quality-checked, filtered for low
friction velocity conditions, gap-filled and partitioned as consolidated in the FLUXNET methodology
[24]. Specifically, we used the GPP product computed using an annual friction velocity threshold to
filter NEE, NEE gap-filling based on Marginal Distribution Sampling [25], and finally estimates GPP
using night-time flux partitioning [25],. Daily GPP values were computed by aggregating half-hourly
GPP estimates, and eventually aggregated to 8-day mean daily value for the validation against
modelled GPP. Surface homogeneity of all EC sites was visually inspected using Google Earth to
eliminate sites with obvious heterogeneity of land cover within the MODIS pixel (e.g., [26,27]). As a
result, only the EC site FR-Avi (Avignon, France) was excluded for further analysis. The location of
the retained sites and period covered by flux measurements is shown in Figure 1 (30 cropland sites
and 27 grassland sites).
Figure 1. Location of eddy covariance (EC) sites and period covered by flux measurements. Green
cross are for grassland sites whereas orange dots are for cropland sites.
3. Methods
3.1. GPP Model
The vegetation growth model used in this study is composed by a set of equations similar to that
of GRAMI model [13-15]. The model runs at daily time step and is built around the core equation
describing the conversion of absorbed light into gross primary production, GPP [28]:
𝐺𝑃𝑃(i)=𝜀
𝜀(i) 𝐹𝐴𝑃𝐴𝑅(i) 𝑃𝐴𝑅(i) (1)
where i is the day of the year, GPP is the daily gross primary production, εm is the maximum light
conversion factor (i.e., the light use efficiency coefficient), εws is the water stress reduction factor to
the light use efficiency, PAR is the photosynthetically active radiation and FAPAR is the fraction of
the absorbed PAR. The value of εm for crop and grassland targets is set to 1.7 and 1.1 gC m2 d1 MJ1,
respectively. These values were derived from a preliminary optimization procedure against EC data
of four sites as described in Section 3.4. FAPAR is computed as a function of LAI by the same RT
model used to simulate NDVI to ensure internal consistency (see Section 3.2). PAR is estimated as
0.48 * Global Radiation from ECMWF (in MJ m2) according to Tsubo and Walker [29]. Despite we do
not account for direct effect of temperature on εm with an additional stress reduction factor,
Figure 1.
Location of eddy covariance (EC) sites and period covered by flux measurements. Green
cross are for grassland sites whereas orange dots are for cropland sites.
3. Methods
3.1. GPP Model
The vegetation growth model used in this study is composed by a set of equations similar to that
of GRAMI model [
13
15
]. The model runs at daily time step and is built around the core equation
describing the conversion of absorbed light into gross primary production, GPP [28]:
GPP(i)=εmεws (i)FAPAR(i)PAR(i)(1)
where i is the day of the year, GPP is the daily gross primary production,
εm
is the maximum light
conversion factor (i.e., the light use efficiency coefficient),
εws
is the water stress reduction factor to the
light use efficiency, PAR is the photosynthetically active radiation and FAPAR is the fraction of the
absorbed PAR. The value of
εm
for crop and grassland targets is set to 1.7 and
1.1 gC m2d1MJ1
,
Remote Sens. 2019,11, 749 5 of 20
respectively. These values were derived from a preliminary optimization procedure against EC data
of four sites as described in Section 3.4. FAPAR is computed as a function of LAI by the same RT
model used to simulate NDVI to ensure internal consistency (see Section 3.2). PAR is estimated as
0.48 * Global
Radiation from ECMWF (in MJ m
2
) according to Tsubo and Walker [
29
]. Despite we do
not account for direct effect of temperature on
εm
with an additional stress reduction factor, temperature
plays a role in determining
εws
and leaf senescence (introduced below). In addition, we assume that no
photosynthesis occurs when the mean daily temperature is below the base temperature used for the
computation of growing degree days (Equation (4)).
A fraction of GPP is used by the plants for respiration, while the remaining net primary production
(NPP) is used for the growth. In this simplified modelling we neglect temperature, nitrogen and
biomass dependency of maintenance respiration and, based on the findings of Suleau et al. [
30
],
and we consider respiration proportional to GPP. The ratio
γ
between respiration and GPP was set to
0.25 as in Cui et al. [31].
NPP(i)=(1γ)GPP(i)(2)
A fraction of the daily NPP is allocated to leaf tissues according to the following equation:
LAI(i)=NPP(i)Pl(i)CF SLA LAIsen(i)(3)
where
LAI is the daily variation of leaf area index (LAI), Pl is the dynamic coefficient of partitioning
into leaves, CF is the constant conversion factor from carbon (gC) to dry matter content, SLA is the
constant specific leaf area (leaf area per unit weight) and LAI
sen
is leaf area that is lost through leaf
senescence. CF is set to 1/0.45 as in Lobell et al. [
32
]. SLA (m
2
g
1
) is subject to optimization (described
in Section 3.5) as it is crop- and grassland-type specific and plays a major role in controlling leaf
area expansion.
Senescence (LAI
sen
) and partitioning into leaves (Pl) are modelled using growing degree days
(GDD), defined as the sum of the following daily quantity from emergence:
GDD(i) = Max [T(i) Tb, 0] (4)
where Tis the mean daily air temperature and Tb is the base temperature. Tb is set to the standard
value of 0 C for crops and to 5C for grassland according to Fu et al. [33].
Leaf senescence is empirically modelled as proposed by Maas [
14
] for the GRAMI model. The LAI
emerged at time i with GDD(i) is removed after J(i) growing degree days. The leaf lifespan J(i) of LAI
produced on day i is computed as a function of GDD(i) using the following linear equation:
J(i) = c+d GDD(i) (5)
where the parameters cand dcontrol the magnitude of the lifespan as a function of the GDD at
emergence. A positive slope (d> 0) increase the lifespan of the leaves emitted later in the season.
It is noted that senescence is modulated only as a function of accumulated temperature while other
possible stress factors (i.e., water deficiency) are neglected.
In order to select a parametric function to model the temporal evolution of partitioning into leaves
we inspected the partitioning look-up tables of the crop growth model WOFOST [
34
]. Such look-up
tables are crop specific, derived from experimental data, and express partitioning into leaves as a
function of crop development stage, in turn function of GDD. A preliminary analysis of such data
showed that partition into leaves could be well fitted by a three parameters logistic decay function
of GDD (data not shown). Although the functional form was selected to mimic partitioning in crops,
it appears generic enough to be used for grassland as well.
Pl(GDD)=Plmax 1
1+ek(GDDGDD0)(6)
Remote Sens. 2019,11, 749 6 of 20
where Pl
max
is the curve’s asymptotic maximum value, kis the steepness of the curve, and GDD
0
is the
x-value of the logistic midpoint.
For the intended application it was convenient to express kand GDD
0
as a function of the GDD
values GDD
min
and GDD
max
at which the function takes the actual values of (1
co) * Pl
max
and co
*Pl
max
, where co is cutoff value used to numerically deal with the asymptotic function. The cutoff
value co is set to 0.05 to yield function values close to its asymptotic maximum (Pl
max
) and minimum
(0). GDD
max
is the GDD at which there is (nearly) no more partitioning to leaves. GDD
min
is the GDD
at which partitioning to leaves is at its maximum, here assumed to be at emergence, where GDD is
equal 0. By fixing this latter we reduce the parameters of the logistic curve to two. Using the following
intermediary variables:
Cmin =ln1
1co 1,Cmax =ln1
co 1(7)
We can rewrite kand GDD0of Equation (6) as:
k=Cmax Cmin
GDDmax ,GDD0=1
kCmax (8)
The stress factor
εws
is computed to account for possible water limitations. The formulation is
similar to that of the CASA model [
35
] where photosynthesis is limited by water availability up to a
maximum of 50%:
εws = min (1, 0.5 + 0.5 AET/PET) (9)
where AET and PET are the actual and potential evapotranspiration. We assume that all the precipitation
can be used for evapotranspiration (i.e., AET equals precipitation). Differently from the CASA model
and similar applications (e.g., [
36
,
37
]) that compute AET and PET over a period of one to two months
(extending backwards in time) we extend back in thermal time, i.e., GDD. In this way, by fixing a GDD
period over which precipitation and potential evapotranspiration are considered, we extend back in
time over a shorter (longer) period if the temperature was warmer (colder). In addition, considering
that more recent weather conditions have a greater effect on the physiological status of the plant we
average PET and precipitation with exponentially declining weights when going back into the past (in the
GDD dimension). For instance, for the precipitation we compute the following exponentially weighted
precipitation (EWP, used in Equation (9) in place of AET):
EWP(i)=Rx=0
x=min[P(GDD(i)+x),C AP]ex/hl dx
R0
ex/hl dx (10)
where xis the thermal time extending back from GDD at time i, CAP is the maximum value of daily
precipitation (set to 200 mm, above this threshold water is assumed to exceed storage capacity),
and hl is the exponential decay half-life that controls the steepness of the weights decay. It is thus
the GDD span in which the weights fall to one half. The hl parameter is set to 180 GDD (that for
instance is equivalent to 10 days with mean temperature of 18
C and 20 days with mean temperature
of 9
C). This formulation depicts an exponentially declining memory of plants to water stress.
The exponentially weighted PET (EWPET) is computed in a similar way (but omitting CAP) and used
in Equation (9) in place of PET.
3.2. Radiative Transfer Model
The assimilation of EO data into the model is achieved by linking the canopy reflectance RT
model PROSAIL5B [
16
] to the GPP model described in Section 3.1. While the GPP model simulates the
temporal trajectory of the leaf area index (LAI), the link with the canopy RT model allows simulating
the NDVI that the MODIS sensor would observe for the satellite overpass time. The RT simulation
Remote Sens. 2019,11, 749 7 of 20
is performed using the actual sun-target-sensor geometry as specified by the MODIS observations.
In order to minimize the number of free parameters, all RT parameters are fixed to nominal values
except LAI, SLA, and background reflectance. Although the leaf chlorophyll content can exhibit a
seasonal cycle affecting GPP, we opted to keep the model simple and we assumed that actual variation
in chlorophyll can be represented in the model by LAI variation alone, having the effect of modulating
the total canopy chlorophyll content (LAI x leaf chlorophyll content [
38
]) when the leaf chlorophyll
content is fixed. The values used for the fixed parameters are presented in Table 2. Values refer to
literature data for green vegetation (e.g., [
39
,
40
]). The fraction of diffuse incoming solar radiation is
fixed and was determined by MODTRAN5 [
41
] simulations for mid-latitude clear sky conditions in
summer time.
Table 2. PROSAIL5B fixed parameters values.
Variable Value
Cab, Leaf chlorophyll content 30 µg cm2
Cw, leaf equivalent water thickness 0.015 g cm2
Ns, leaf structure coefficient 1.6 (-)
Lidf_a and Lidf_b describing leaf angle distribution 035, 01.15 (spherical distribution)
Hot spot size parameter 0.5
The reflectance spectrum of the canopy background needed by the RT model to simulate the top
of canopy reflectance is determined as follows. For a given pixel, we first select all original NDVI
observations with a value smaller than the 5th percentile of the entire NDVI historical distributions
(i.e., year 2000—time of simulation). Under the assumption that the time series contains NDVI
observations acquired when the green grassland or crop cover is minimal or absent, such observations
are considered representative of the background reflectance. As this subset of low-NDVI observations
may contain unrealistic outliers (low NDVI values due to undetected cloud cover), we subsample it by
selecting the five observations showing the minimum difference between the original NDVI and the
NDVI temporally smoothed with the Savitzky-Golay filter [
42
]. In this way, we discard low-NDVI
observations that are far from the smoothed temporal profile (i.e., negative spikes) and may be thus due
to undetected clouds rather than absence of vegetation. Background reflectance in the seven MODIS
bands coming with MxD09A1 products (see Section 2.2) is computed averaging the reflectances of the
selected five observations. Finally, as a full spectrum at 1-nm sampling step is needed by the RT model,
the MODIS reflectances are fitted using the Price functions for the soil reflectance [43].
Once the full top of canopy reflectance spectrum (i.e., 400–2500 nm) is simulated with the 1-nm
sampling interval used by the RT model, the MODIS relative spectral response functions (http://
mcst.gsfc.nasa.gov/calibration/parameters) are used to convolve the spectrum into the MODIS bands.
The NDVI is then computed from the MODIS-like red and near infrared bands.
FAPAR used in Equation (1) of the Sim model is computed by PROSAIL5B as the actual
instantaneous spectral canopy absorption in the PAR region at 10:00 local solar time. The absorption at
this local time is close to the daily integrated value under clear sky condition [
44
]. The FAPAR value is
computed as the weighted average of the spectral canopy absorption in the PAR region (400 to 700 nm).
Spectral observations are weighted by their contribution to total incident irradiance at ground level
using MODTRAN5 simulations for mid-latitude clear sky conditions in summer time.
3.3. Land Surface Phenology Model
The initial identification of the timing of the onset of growing season is estimated by computing
the multi-annual mean of the satellite-based phenological timings retrieved for the pixel temporal
profile (2000–2016). Among other phenological timings retrieved fitting a double hyperbolic tangent
model to upper envelop of the NDVI time series as described in Meroni et al. [
17
], we use the number
of growing cycles per solar year (either one or two), the start of growing season (SOS) and the time of
Remote Sens. 2019,11, 749 8 of 20
maximum development (TOM). Besides setting the first guess of the simulation start day, this land
surface phenology timings are used to set the first guesses of cof Equation (5) and GDD
max
of Equation
(8) as the multi-annual average GDD accumulated between SOS and TOM.
3.4. Definition of εmax
Values in the range from 0.86 to 2.5 (gC m
2
d
1
MJ
1
) have been reported for grassland and
crop
εmax
in the literature [
45
47
]). Various definitions also exists for it in different communities and in
different modelling setups (e.g., depending on weather non-photosynthetic tissues are included in the
definition of FAPAR) [
48
]. Here we used an empirical parametrization that was derived using EC GPP
data of two crop and two grass sites randomly extracted from the EC database (BE-Lon and FR-Aur for
a total of 17 site-year crop samples; CZ-BK2 and IT-MBo for a total of 17 site-year grassland samples).
A nested inversion of the Sim model was run on the two calibration sites. The inversion set-up was
configured in standard mode (Section 3.5) and run iteratively for the calibration sites changing the
value of
εmax
in steps of 0.1 between 0.8 and 2.5 gC m
2
d
1
MJ
1
. The value minimizing the RMSE
between the modelled and observed GPP was then selected. As a result, crop and grass
εmax
was set
to 1.7 and 1.1 gC m
2
d
1
MJ
1
, respectively. It is noted that
εmax
of crops was estimated using sites
where C3 crops were numerically more represented (only one year of maize, a C4 crop, is present
for the site BE-Lon) and may thus underestimate the
εmax
of C4 crops (maize in our data sample)
(Xin et al., 2015). However, the vast majority of the crop samples is indeed represented by C3 crops.
3.5. Inversion Set-Up
Selected model parameters are derived through model inversion [
49
]. Here we use
model-recalibration as assimilation strategy [
8
,
9
] to retrieve the set of model parameters described in
Table 3. Recalibration is performed by searching those parameter values that maximize the agreement
between the observed MODIS NDVI temporal profile and the simulated one. This is computationally
achieved minimizing a cost function defined by the sum of square differences of the two temporal
profiles of NDVI. Numerical optimization is performed using Levenberg-Marquardt least-squares
constrained minimization (IDL routine MPFIT [
50
]). Since NDVI may be biased towards low values
owing to the presence of undetected clouds, the optimization is adapted to the upper envelope of
the observations using an iterative weighting scheme similar to that proposed by Chen et al. [
51
].
When two growing cycles per solar year are present, they are treated separately.
Table 3.
Model parameters subject to optimization. LSP stands for Land Surface Phenology,
the satellite-based phenological timings described in Section 3.3. FG stands for first guess.
Variable Units Description First Guess Range Reference
DOY0 Day of year
Day at which the simulation
starts and LAI is set to LAI0, i.e.,
the “emergence” date.
LSP ±60 days -
LAI0 m2m2Leaf area index at DOY0 0.02 0.01–0.08 -
SLA m2g1Specific Leaf Area 0.012 0.002–0.025 [5255]
c GDD Leaf lifespan offset Equation (5)
Multi-annual
average of
GDD from SOS
to TOM
250-FG * 1.5 -
d - Leaf lifespan gain Equation (5) 0.0 0–3 [14]
Plmax -
Maximum leaf partitioning ratio
Equation (6) 0.3 0.1–0.8 [56]
GDDmax GDD
GDD from emergence after
which no partitioning to leaves
occur Equation (8)
Same as parameter c -
Remote Sens. 2019,11, 749 9 of 20
The iterative minimization requires setting initial values and boundaries for the model parameters
(first guess in Table 3).
The water stress factor of Equation (9) is defined on precipitation and evapotranspiration and does
not obviously take into account that irrigation water might be administrated to both crops and grasses.
As irrigation practices cannot be known a priori, we adopted the following strategy. Optimization is
performed twice, without and with water limitation according to Equation (9). The run proving the
best fit to observed NDVI is retained. The forward model and the inversion procedure are implemented
in IDL (Harris Geospatial Solution).
3.6. Validation
Simulated and observed daily GPP are temporally aggregated to 8-day MODIS temporal
resolution. GPP data from 28 crop and 25 grassland EC sites are used in the validation. Simulation
performances are assessed analyzing the simulated vs. observed GPP scatter plots in terms of:
coefficient of determination (R
2
), root mean square error (RMSE), and mean bias error (MBE), slope and
offset the ordinary-least-squared (OLS) regression model. All these metrics inform about the predictive
power of the model as the GPP data were not used for model calibration. Finally, results were
compared to those obtained with MODIS GPP product MOD17 that was used as benchmark model.
Model performances in space (across sites) and time were further assessed by analyzing (1) the
correlation between site averages of annual cumulative GPP observed and modeled, and (2) the ability
of the models to track site-level inter-annual variability of GPP. The annual cumulative GPP value is
computed summing GPP data over the calendar year (i.e., from 1st of January to 31st December).
4. Results
4.1. Site Examples
The ability of the Sim model to simulate the actual dynamics of GPP is first illustrated on several
crops and grassland sites where the model has shown different degrees of realism. Examples of
simulated GPP and NDVI compared to the observed time series are reported in Figures 2and 3for
crop sites and Figures 46for grassland sites. For both crops and grassland sites we selected example
sites with contrasting performances of the model (i.e., nice vs. poor fit).
Remote Sens. 2019, 11, 749 10 of 21
d1). Although some under- and over-estimation occurs in some years (e.g., 2009 and 2012,
respectively) the Sim model GPP estimates are not affected by systematic underestimation as in the
case of the MOD17 product.
Figure 2. Observed and modelled GPP and NDVI for the crop site DE-Kli. Left panels: (top) time
series of GPP from eddy covariance measurements (EC), Sim model (Sim), and MODIS GPP (MOD17);
(bottom) observed (MODIS) and simulated NDVI (Sim). Right panels: scatter plots of EC GPP versus
GPP simulated by the Sim model (top panel) and MOD17 GPP (bottom panel). For the right panels:
dashed black line is the 1:1 line, blue continues line is the linear regression; root mean square error
(RMSE) between modelled and observed GPP and the coefficient of determination (R2) of the linear
regression are reported.
In the cropland site IT-BCi (Italy, 40.52375°N, 14.95744°E; [58]) shown in Figure 3 both the Sim
model and MOD17 exhibit significant GPP underestimation at high EC GPP levels. Although the Sim
model is able to differentiate the two seasons (maize in summer and fennel or rye-grass in winter)
depicted by the observed NDVI, it largely underestimates the GPP of the summer crop (i.e., maize).
Underestimation of the summer crop occur even though the Sim model does not select water
limitation in most of the years (i.e., because the observed NDVI is better matched by model runs
without water limitation), which is in agreement with reported irrigation practices. The scatter plots
of Figure 3 show that underestimation of the Sim model is nonetheless less severe than the MODIS
one. A plausible explanation for this difference may be related to an underestimate of the maximum
light use efficiency (εm) that is not able to reproduce the photosynthesis level attained by the C4 crop
under a Mediterranean climate and served by irrigation. In fact, both the Sim model and MOD17 use
a constant εm of all crops that is likely not representative for this site because the εm of C4 crops is
typically larger than that of C3 crops [47]. However, it is noted that in different climatic conditions
the model does not underestimate C4 GPP, as for example in the cropland site DE-Kli of Figure 2
where maize was grown in year 2007 and 2012. In general, we do not observe a systematic
underestimation of maize GPP (see Sections 4.2 and 5 for a discussion).
Figure 2.
Observed and modelled GPP and NDVI for the crop site DE-Kli.
Left
panels: (top) time series of
GPP from eddy covariance measurements (EC), Sim model (Sim), and MODIS GPP (MOD17); (bottom)
observed (MODIS) and simulated NDVI (Sim).
Right
panels: scatter plots of EC GPP versus GPP simulated
by the Sim model (top panel) and MOD17 GPP (bottom panel). For the
right
panels: dashed black lineis
the 1:1 line, blue continues line is the linear regression; root mean square error (RMSE) between modelled
and observed GPP and the coefficient of determination (R2) of the linear regression are reported.
Remote Sens. 2019,11, 749 10 of 20
Remote Sens. 2019, 11, 749 11 of 21
Figure 3. Observed and modelled GPP and NDVI for the cropland site IT-BCi. Description of plots as
Figure 2.
Figures 4–6 show the observed NDVI and GPP along with the same variables modelled by the
Sim model for three EC grassland sites.
Figure 4 shows the grassland site HU-Bug (Hungary, 47.84690°N, 19.72600°E; [59]), a semi-arid
sandy grassland extensively grazed. The Sim model detects two growing cycles per year that are
originated from a biomass reduction during the summer due to grazing and/or sever water
limitations [60]. In years when no double cycles is visible in the measured GPP, NDVI shows only a
moderate reduction during the summer and coherently, the two season modelled by Sim are nearly
merged together (e.g., years 2005 and 2006). GPP estimation accuracy is high for both the Sim model
and MOD17 for this site (see scatter plots of Figure 4)
Figure 4. Observed and modelled GPP and NDVI for the grassland site HU-Bug. Description of plots
as Figure 2.
Figure 5 shows an example of a grassland site where the GPP estimated by Sim outperforms that
of MOD17. It refers to the grassland site of AT-Neu (Austria, 47.11667°N, 11.31750°E; [61]). The Sim
model correctly diagnoses one growing cycle per year. Growing cycles are neatly separated by snow
cover extending from mid-November to mid-March where measured GPP is close to zero and
observed NDVI is very low or missing. While NDVI is nicely fitted by the model, GPP tends to be
underestimated by both MOD17 and (to a much lesser extent) by the Sim model. The effect of the fit
Figure 3.
Observed and modelled GPP and NDVI for the cropland site IT-BCi. Description of plots as
Figure 2.
Remote Sens. 2019, 11, 749 11 of 21
Figure 3. Observed and modelled GPP and NDVI for the cropland site IT-BCi. Description of plots as
Figure 2.
Figures 4–6 show the observed NDVI and GPP along with the same variables modelled by the
Sim model for three EC grassland sites.
Figure 4 shows the grassland site HU-Bug (Hungary, 47.84690°N, 19.72600°E; [59]), a semi-arid
sandy grassland extensively grazed. The Sim model detects two growing cycles per year that are
originated from a biomass reduction during the summer due to grazing and/or sever water
limitations [60]. In years when no double cycles is visible in the measured GPP, NDVI shows only a
moderate reduction during the summer and coherently, the two season modelled by Sim are nearly
merged together (e.g., years 2005 and 2006). GPP estimation accuracy is high for both the Sim model
and MOD17 for this site (see scatter plots of Figure 4)
Figure 4. Observed and modelled GPP and NDVI for the grassland site HU-Bug. Description of plots
as Figure 2.
Figure 5 shows an example of a grassland site where the GPP estimated by Sim outperforms that
of MOD17. It refers to the grassland site of AT-Neu (Austria, 47.11667°N, 11.31750°E; [61]). The Sim
model correctly diagnoses one growing cycle per year. Growing cycles are neatly separated by snow
cover extending from mid-November to mid-March where measured GPP is close to zero and
observed NDVI is very low or missing. While NDVI is nicely fitted by the model, GPP tends to be
underestimated by both MOD17 and (to a much lesser extent) by the Sim model. The effect of the fit
Figure 4.
Observed and modelled GPP and NDVI for the grassland site HU-Bug. Description of plots
as Figure 2.
Remote Sens. 2019, 11, 749 12 of 21
operated on the upper envelope of the observed NDVI is clearly visible in several years (e.g., 2006,
2007).
Figure 5. Observed and modelled GPP and NDVI for the grassland site At-Neu. Description of plots
as Figure 2.
Figure 6 shows the results for a grassland site where estimation errors are among the largest in
the dataset (IT-Amp, Italy, 41.90410°N, 13.60516°E; [62]). The site is characterized by a distinct
summer drought with senescence occurring in June, followed by a cut and subsequent animal grazing
and moderate vegetation regrowth. Although the Sim model is able to reproduce this temporal
pattern in both NDVI and GPP, it fails to match the GPP magnitude in the main growing period of
some years (i.e., 2004, 2006, 2008). It is noted that, in contrast to MOD17 that does not reproduce the
GPP reduction between the two growing cycles, the model simulations do detect the break between
the cycles and correctly represent the difference in GPP magnitude of the main (spring) and
secondary cycle (late summer to autumn).
Figure 6. Observed and modelled GPP and NDVI for the grassland site IT-Amp. Description of plots
as Figure 2.
4.2. Overall Agreement between Modelled and Observed GPP
Figure 5.
Observed and modelled GPP and NDVI for the grassland site At-Neu. Description of plots
as Figure 2.
Remote Sens. 2019,11, 749 11 of 20
Remote Sens. 2019, 11, 749 12 of 21
operated on the upper envelope of the observed NDVI is clearly visible in several years (e.g., 2006,
2007).
Figure 5. Observed and modelled GPP and NDVI for the grassland site At-Neu. Description of plots
as Figure 2.
Figure 6 shows the results for a grassland site where estimation errors are among the largest in
the dataset (IT-Amp, Italy, 41.90410°N, 13.60516°E; [62]). The site is characterized by a distinct
summer drought with senescence occurring in June, followed by a cut and subsequent animal grazing
and moderate vegetation regrowth. Although the Sim model is able to reproduce this temporal
pattern in both NDVI and GPP, it fails to match the GPP magnitude in the main growing period of
some years (i.e., 2004, 2006, 2008). It is noted that, in contrast to MOD17 that does not reproduce the
GPP reduction between the two growing cycles, the model simulations do detect the break between
the cycles and correctly represent the difference in GPP magnitude of the main (spring) and
secondary cycle (late summer to autumn).
Figure 6. Observed and modelled GPP and NDVI for the grassland site IT-Amp. Description of plots
as Figure 2.
4.2. Overall Agreement between Modelled and Observed GPP
Figure 6.
Observed and modelled GPP and NDVI for the grassland site IT-Amp. Description of plots
as Figure 2.
Figures 2and 3show the observed NDVI and GPP along with the same variables modelled by
the Sim model for two EC crop sites. For comparison, the MODIS GPP estimates are also reported.
In the cropland site DE-Kli (Germany, 50.89288
N, 13.52251
E; [
57
]), rapeseed, winter wheat,
maize, and spring barley were cultivated in rotation (Figure 2). The NDVI signal captures the crop
growth between sowing and harvest as well as the unmanaged vegetation growth occurring in the
fallow land between crop cycles. This is possible thanks to the preliminary application of phenology
algorithm that detects two growing seasons per year. The Sim model fits well the observed NDVI and
is also able to track GPP temporal evolution with good accuracy (R
2
= 0.85, RMSE = 1.66 gC m
2
d
1
).
Although some under- and over-estimation occurs in some years (e.g., 2009 and 2012, respectively)
the Sim model GPP estimates are not affected by systematic underestimation as in the case of the
MOD17 product.
In the cropland site IT-BCi (Italy, 40.52375
N, 14.95744
E; [
58
]) shown in Figure 3both the
Sim model and MOD17 exhibit significant GPP underestimation at high EC GPP levels. Although
the Sim model is able to differentiate the two seasons (maize in summer and fennel or rye-grass
in winter) depicted by the observed NDVI, it largely underestimates the GPP of the summer crop
(i.e., maize). Underestimation of the summer crop occur even though the Sim model does not select
water limitation in most of the years (i.e., because the observed NDVI is better matched by model runs
without water limitation), which is in agreement with reported irrigation practices. The scatter plots
of Figure 3show that underestimation of the Sim model is nonetheless less severe than the MODIS
one. A plausible explanation for this difference may be related to an underestimate of the maximum
light use efficiency (
εm
) that is not able to reproduce the photosynthesis level attained by the C4 crop
under a Mediterranean climate and served by irrigation. In fact, both the Sim model and MOD17 use
a constant
εm
of all crops that is likely not representative for this site because the
εm
of C4 crops is
typically larger than that of C3 crops [
47
]. However, it is noted that in different climatic conditions the
model does not underestimate C4 GPP, as for example in the cropland site DE-Kli of Figure 2where
maize was grown in year 2007 and 2012. In general, we do not observe a systematic underestimation
of maize GPP (see Sections 4.2 and 5for a discussion).
Figures 46show the observed NDVI and GPP along with the same variables modelled by the
Sim model for three EC grassland sites.
Figure 4shows the grassland site HU-Bug (Hungary, 47.84690
N, 19.72600
E; [
59
]), a semi-arid
sandy grassland extensively grazed. The Sim model detects two growing cycles per year that
are originated from a biomass reduction during the summer due to grazing and/or sever water
Remote Sens. 2019,11, 749 12 of 20
limitations [
60
]. In years when no double cycles is visible in the measured GPP, NDVI shows only a
moderate reduction during the summer and coherently, the two season modelled by Sim are nearly
merged together (e.g., years 2005 and 2006). GPP estimation accuracy is high for both the Sim model
and MOD17 for this site (see scatter plots of Figure 4)
Figure 5shows an example of a grassland site where the GPP estimated by Sim outperforms
that of MOD17. It refers to the grassland site of AT-Neu (Austria, 47.11667
N, 11.31750
E; [
61
]).
The Sim model correctly diagnoses one growing cycle per year. Growing cycles are neatly separated
by snow cover extending from mid-November to mid-March where measured GPP is close to zero
and observed NDVI is very low or missing. While NDVI is nicely fitted by the model, GPP tends
to be underestimated by both MOD17 and (to a much lesser extent) by the Sim model. The effect
of the fit operated on the upper envelope of the observed NDVI is clearly visible in several years
(e.g., 2006, 2007).
Figure 6shows the results for a grassland site where estimation errors are among the largest in
the dataset (IT-Amp, Italy, 41.90410
N, 13.60516
E; [
62
]). The site is characterized by a distinct summer
drought with senescence occurring in June, followed by a cut and subsequent animal grazing and
moderate vegetation regrowth. Although the Sim model is able to reproduce this temporal pattern in
both NDVI and GPP, it fails to match the GPP magnitude in the main growing period of some years
(i.e., 2004, 2006, 2008). It is noted that, in contrast to MOD17 that does not reproduce the GPP reduction
between the two growing cycles, the model simulations do detect the break between the cycles and
correctly represent the difference in GPP magnitude of the main (spring) and secondary cycle (late
summer to autumn).
4.2. Overall Agreement between Modelled and Observed GPP
Density scatter plots of EC measured GPP vs. the GPP estimated by the Sim model and MOD17
are shown Figures 7and 8while main statistics are compared Table 4.
Remote Sens. 2019, 11, 749 13 of 21
Density scatter plots of EC measured GPP vs. the GPP estimated by the Sim model and MOD17
are shown Figures 7 and 8 while main statistics are compared Table 4.
GPP estimated by the Sim model (Figure 7) tracks well the EC GPP with a RMSE of 2.45 gC m2
d1 and a small bias (MBE) of 0.16 when all sites are considered together. When considering the two
ecosystem types separately, we observed that the RMSE error is slightly larger for crops (2.7 gC m2
d1) than for grasslands (2.20 gC m2 d1). The MBE is small, positive for crops (0.26 gC m2 d1) and
negative grasslands (0.53 gC m2 d1). The regression line is in all cases below the 1:1 line indicating
a reduction of the variability of estimated GPP as compared to the measured one. Such an effect is
larger for MOD17 estimates (Figure 8). Overall, Sim model estimates appears to overestimate EC GPP
al low GPP levels and underestimate it at high GPP levels. It is noted that EC GPP can be negative,
representing an obvious artifact of the partitioning algorithm (i.e., processing to determine total
respiration). Nevertheless, we opted for keeping the EC measurements untouched.
The agreement with EC measurements of GPP is larger for the Sim model with respect to
MOD17. Sample scatter and deviation from the 1:1 line is in all cases smaller for the Sim model.
Agreement statistics of the Sim Model and MOD 17 are reported in Table 4.
(A) (B) (C)
Figure 7. Scatter plots of EC GPP versus GPP estimated by the Sim model for all sites (A), crop sites
(B), and grassland sites (C). The dashed line is the 1:1 line while the continuous line is the ordinary
least square linear regression. The following statistics are reported: coefficient of determination (R2),
Perason’s correlation coefficient (r), p-value of the linear regression, gain and offset of the linear
regression line, Root Mean Square Error (RMSE), Mean Bias Error (MBE), and total number of data
points (n).
(A) (B) (C)
Figure 7.
Scatter plots of EC GPP versus GPP estimated by the Sim model for all sites (
A
), crop sites
(
B
), and grassland sites (
C
). The dashed line is the 1:1 line while the continuous line is the ordinary
least square linear regression. The following statistics are reported: coefficient of determination (R
2
),
Perason’s correlation coefficient (r), p-value of the linear regression, gain and offset of the linear
regression line, Root Mean Square Error (RMSE), Mean Bias Error (MBE), and total number of data
points (n).
Remote Sens. 2019,11, 749 13 of 20
Remote Sens. 2019, 11, 749 13 of 21
Density scatter plots of EC measured GPP vs. the GPP estimated by the Sim model and MOD17
are shown Figures 7 and 8 while main statistics are compared Table 4.
GPP estimated by the Sim model (Figure 7) tracks well the EC GPP with a RMSE of 2.45 gC m2
d1 and a small bias (MBE) of 0.16 when all sites are considered together. When considering the two
ecosystem types separately, we observed that the RMSE error is slightly larger for crops (2.7 gC m2
d1) than for grasslands (2.20 gC m2 d1). The MBE is small, positive for crops (0.26 gC m2 d1) and
negative grasslands (0.53 gC m2 d1). The regression line is in all cases below the 1:1 line indicating
a reduction of the variability of estimated GPP as compared to the measured one. Such an effect is
larger for MOD17 estimates (Figure 8). Overall, Sim model estimates appears to overestimate EC GPP
al low GPP levels and underestimate it at high GPP levels. It is noted that EC GPP can be negative,
representing an obvious artifact of the partitioning algorithm (i.e., processing to determine total
respiration). Nevertheless, we opted for keeping the EC measurements untouched.
The agreement with EC measurements of GPP is larger for the Sim model with respect to
MOD17. Sample scatter and deviation from the 1:1 line is in all cases smaller for the Sim model.
Agreement statistics of the Sim Model and MOD 17 are reported in Table 4.
(A) (B) (C)
Figure 7. Scatter plots of EC GPP versus GPP estimated by the Sim model for all sites (A), crop sites
(B), and grassland sites (C). The dashed line is the 1:1 line while the continuous line is the ordinary
least square linear regression. The following statistics are reported: coefficient of determination (R2),
Perason’s correlation coefficient (r), p-value of the linear regression, gain and offset of the linear
regression line, Root Mean Square Error (RMSE), Mean Bias Error (MBE), and total number of data
points (n).
(A) (B) (C)
Figure 8.
Scatter plots of EC GPP vs. GPP estimated by MOD17 for all sites (
A
), crop sites (
B
),
and grassland sites (C). Description of plots as Figure 7.
Table 4.
Summary statistics of GPP estimation performances. R
2
, RMSE, and MBE are derived from
the scatter plots of Figures 7and 8and represent the coefficient of determination of the ordinary least
square linear regression, the Root Mean Square Error and the Mean Bias Error, respectively. The percent
variation refers to the statistic of the Sim model as compared to that of MOD17. * The percent variation
on MBE is computed on absolute values.
Modelled vs. Observed
All sites Crops Grasslands
Model R2RMSE MBE R2RMSE MBE R2RMSE MBE
MOD17 0.53 3.15 1.08 0.53 3.52 0.97 0.55 2.79 1.17
Sim model 0.67 2.45 0.16 0.68 2.70 0.26 0.68 2.20 0.53
%variation
+26.42
22.2 85.19 * +28.3 23.3 73.2 * +23.64 21.2 54.7 *
GPP estimated by the Sim model (Figure 7) tracks well the EC GPP with a RMSE of
2.45 gC m2d1
and a small bias (MBE) of
0.16 when all sites are considered together.
When considering the two ecosystem types separately, we observed that the RMSE error is slightly
larger for crops (2.7 gC m
2
d
1
) than for grasslands (2.20 gC m
2
d
1
). The MBE is small, positive
for crops (0.26 gC m
2
d
1
) and negative grasslands (
0.53 gC m
2
d
1
). The regression line is in
all cases below the 1:1 line indicating a reduction of the variability of estimated GPP as compared
to the measured one. Such an effect is larger for MOD17 estimates (Figure 8). Overall, Sim model
estimates appears to overestimate EC GPP al low GPP levels and underestimate it at high GPP
levels. It is noted that EC GPP can be negative, representing an obvious artifact of the partitioning
algorithm (i.e., processing to determine total respiration). Nevertheless, we opted for keeping the EC
measurements untouched.
The agreement with EC measurements of GPP is larger for the Sim model with respect to MOD17.
Sample scatter and deviation from the 1:1 line is in all cases smaller for the Sim model. Agreement
statistics of the Sim Model and MOD 17 are reported in Table 4.
Figure 9shows the model reliability to predict the total annual GPP and confirms that the Sim
model outperforms MOD17.
Maize sites-years are highlighted in green to evaluate whether a negative bias exists for C4 crops
(maize in our sample) as consequence of using a fixed value of εmfor all crops.
Remote Sens. 2019,11, 749 14 of 20
Remote Sens. 2019, 11, 749 14 of 21
Figure 8. Scatter plots of EC GPP vs. GPP estimated by MOD17 for all sites (A), crop sites (B), and
grassland sites (C). Description of plots as Figure 7.
Table 4. Summary statistics of GPP estimation performances. R2, RMSE, and MBE are derived from
the scatter plots of Figures 7 and 8 and represent the coefficient of determination of the ordinary least
square linear regression, the Root Mean Square Error and the Mean Bias Error, respectively. The
percent variation refers to the statistic of the Sim model as compared to that of MOD17. * The percent
variation on MBE is computed on absolute values.
Modelled vs. Observed
All sites Crops Grasslands
Model R² RMSE MBE RMSE MBE RMSE MBE
MOD17 0.53 3.15 -1.08 0.53 3.52 -0.97 0.55 2.79 -1.17
Sim model 0.67 2.45 -0.16 0.68 2.70 0.26 0.68 2.20 -0.53
%variation +26.42 -22.2 -85.19* +28.3 -23.3 -73.2* +23.64 -21.2 -54.7*
Figure 9 shows the model reliability to predict the total annual GPP and confirms that the Sim model
outperforms MOD17.
Maize sites-years are highlighted in green to evaluate whether a negative bias exists for C4 crops
(maize in our sample) as consequence of using a fixed value of εm for all crops.
Figure 9. Scatter plots of annual GPP: EC GPP versus GPP estimated by the Sim model (left) and
MOD17 (right). Circle and triangle symbols denote crop and grassland sites, respectively. Symbol
color ranges from red to blue and indicated the site latitude. Crop symbols with green circle outline
highlight site-year data points referring to maize. The dashed line is the 1:1 line while the continuous
line is the ordinary least square linear regression. The coefficient of determination (R2), the Root Mean
Square Error (RMSE), Mean Bias Error (MBE), and the number of data points (n) are reported for all
sites together, only crop sites and only grassland sites. Incomplete years (with partial EC
measurements temporal cover) were excluded from this analysis.
In order to further disentangle the ability of the model in the spatial and temporal dimensions,
we compared the mean annual GPP per site (spatial dimension Figure 10) and the site-level statistics
of correlation between annual GPP time series (temporal dimension, Figure 11).
Figure 9.
Scatter plots of annual GPP: EC GPP versus GPP estimated by the Sim model (
left
) and
MOD17 (
right
). Circle and triangle symbols denote crop and grassland sites, respectively. Symbol
color ranges from red to blue and indicated the site latitude. Crop symbols with green circle outline
highlight site-year data points referring to maize. The dashed line is the 1:1 line while the continuous
line is the ordinary least square linear regression. The coefficient of determination (R
2
), the Root Mean
Square Error (RMSE), Mean Bias Error (MBE), and the number of data points (n) are reported for all
sites together, only crop sites and only grassland sites. Incomplete years (with partial EC measurements
temporal cover) were excluded from this analysis.
In order to further disentangle the ability of the model in the spatial and temporal dimensions,
we compared the mean annual GPP per site (spatial dimension Figure 10) and the site-level statistics
of correlation between annual GPP time series (temporal dimension, Figure 11).
Remote Sens. 2019, 11, 749 15 of 21
Figure 10. Scatter plots of mean annual GPP per site: EC GPP versus GPP estimated by the Sim model
(left) and MOD17 (right). Description of plots as Figure 9. Incomplete years (with partial EC
measurements temporal cover) were excluded from this analysis. As a result, a subsample of 45 sites
having at least one complete year was available.
The Sim model explains 39% of the spatial variability of GPP with a RMSE 0.34 kgC m
2
y
1
(Figure 10). MOD17 performances are lower (explain variability = 23%, RMSE = 0.52 kgC m
2
y
1
) and
show consistent underestimate at mid to high annual GPP values. Inter-annual GPP variability is
equally and relatively well tracked by both the Sim model and MOD17 (Figure 11). Despite this,
examples of sites showing negative correlation are present both when comparing Sim model and
MOD17 with EC over time. One example of such sites is the grassland site of IT-Amp reported in
Figure 6 where, despite both the Sim model and MOD17 are able to track the intra-annual variation
of the GPP, they both fail in modulating the inter-annual variation (r = 0.47 and 0.46 for Sim model
and MOD17 respectively).
Figure 11. Histograms of the site-level Pearson correlation coefficient (r) between EC and modelled
annual GPP for the Sim model (top row) and MOD17 (bottom row). Distribution of r for all sites (left
column), crop sites (central column), and grassland sites (right column). Incomplete years (with
partial EC measurements temporal cover) were excluded from this analysis. The site-level correlation
was computed only when at least four years were available (average, minimum, and maximum years
per site is 6, 4 and 11).
Figure 10.
Scatter plots of mean annual GPP per site: EC GPP versus GPP estimated by the Sim
model (
left
) and MOD17 (
right
). Description of plots as Figure 9. Incomplete years (with partial EC
measurements temporal cover) were excluded from this analysis. As a result, a subsample of 45 sites
having at least one complete year was available.
Remote Sens. 2019,11, 749 15 of 20
Remote Sens. 2019, 11, 749 15 of 21
Figure 10. Scatter plots of mean annual GPP per site: EC GPP versus GPP estimated by the Sim model
(left) and MOD17 (right). Description of plots as Figure 9. Incomplete years (with partial EC
measurements temporal cover) were excluded from this analysis. As a result, a subsample of 45 sites
having at least one complete year was available.
The Sim model explains 39% of the spatial variability of GPP with a RMSE 0.34 kgC m
2
y
1
(Figure 10). MOD17 performances are lower (explain variability = 23%, RMSE = 0.52 kgC m
2
y
1
) and
show consistent underestimate at mid to high annual GPP values. Inter-annual GPP variability is
equally and relatively well tracked by both the Sim model and MOD17 (Figure 11). Despite this,
examples of sites showing negative correlation are present both when comparing Sim model and
MOD17 with EC over time. One example of such sites is the grassland site of IT-Amp reported in
Figure 6 where, despite both the Sim model and MOD17 are able to track the intra-annual variation
of the GPP, they both fail in modulating the inter-annual variation (r = 0.47 and 0.46 for Sim model
and MOD17 respectively).
Figure 11. Histograms of the site-level Pearson correlation coefficient (r) between EC and modelled
annual GPP for the Sim model (top row) and MOD17 (bottom row). Distribution of r for all sites (left
column), crop sites (central column), and grassland sites (right column). Incomplete years (with
partial EC measurements temporal cover) were excluded from this analysis. The site-level correlation
was computed only when at least four years were available (average, minimum, and maximum years
per site is 6, 4 and 11).
Figure 11.
Histograms of the site-level Pearson correlation coefficient (r) between EC and modelled
annual GPP for the Sim model (
top
row) and MOD17 (
bottom
row). Distribution of r for all
sites (
left
column), crop sites (
central
column), and grassland sites (
right
column). Incomplete
years (with partial EC measurements temporal cover) were excluded from this analysis. The
site-level correlation was computed only when at least four years were available (average, minimum,
and maximum years per site is 6, 4 and 11).
The Sim model explains 39% of the spatial variability of GPP with a RMSE 0.34 kgC m
2
y
1
(Figure 10). MOD17 performances are lower (explain variability = 23%, RMSE = 0.52 kgC m
2
y
1
)
and show consistent underestimate at mid to high annual GPP values. Inter-annual GPP variability
is equally and relatively well tracked by both the Sim model and MOD17 (Figure 11). Despite this,
examples of sites showing negative correlation are present both when comparing Sim model and
MOD17 with EC over time. One example of such sites is the grassland site of IT-Amp reported in
Figure 6where, despite both the Sim model and MOD17 are able to track the intra-annual variation of
the GPP, they both fail in modulating the inter-annual variation (r =
0.47 and
0.46 for Sim model
and MOD17 respectively).
5. Discussion
Crop and grassland GPP was estimated inverting the Sim model against MODIS 250 m NDVI and
validated with EC data. The Sim model showed better performances in GPP estimation as compared
to MOD17 that was found to be affected by GPP underestimation, in agreement with Zhu et al. [
63
].
Table 4shows that the improvement of the agreement statistics is large when comparing the Sim model
with MOD17, e.g., the variance of measured GPP explained by the estimates (i.e., R
2
) is increased of a
26.4% and RMSE is reduced by a 22.2% when considering all EC sites.
In addition to the obvious differences between the Sim model and MOD17 modelling approaches,
we note that the different spatial resolution of the two GPP estimates may contribute to explain the
poorer performances of MOD17. In fact, while the Sim model uses NDVI at 250 m, MOD17 is driven by
FAPAR at 500 m. Therefore, MOD17 may be more affected by site heterogeneity and less representative
of the flux tower footprint [26,27].
It is noted that the removal of the intra-annual variability of GPP operated by the computation
of the annual GPP reduces the R
2
of both modelling approaches (compare Figures 8and 9). The Sim
model captures better the seasonal dynamics of GPP than the variability among sites (Figure 10) and
years (Figure 11) in agreement with the findings of Verma et al. [
64
] that, comparing a suite of remote
Remote Sens. 2019,11, 749 16 of 20
sensing based GPP model, found reduced skills in tracking inter-annual as compared to intra-annual
GPP variability
Regarding the potential underestimation of C4 crops, we showed that although some maize
sites are underestimated by the Sim model, a systematic negative bias of the Sim model is
not verified, as maize samples are well distributed above and below the 1:1 line of Figure 9.
Moreover, the discrepancies between the Sim model and observed annual GPP seems not
influenced by latitude (used to color-code the data points in Figures 9and 10), and thus climatic
differences—essentially temperature—among sites are not introducing an additional bias. This is
relevant, as temperature was not considered directly as a reduction factor of εm.
Performances of the Sim model GPP estimation are in line with those of other remote sensing based
models calibrated with EC flux data. For instance, similar RMSEs are achieved by Verma et al. [
64
] over
croplands and grasslands using leave-one-out cross-calibration (i.e., n
1 sites are used to calibrate
the model used to predict GPP at the left-out nth site). Larger R
2
for GPP estimation (0.78) were
achieved by Tramontana et al. [
65
] using MODIS and meteorological data to train machine learning
methods on EC observations. In this study, accuracy was evaluated using 10-fold cross-validation.
Despite comparable accuracy, it is noted that the validation protocol is much more conservative in this
study: we used four sites for the determining and fixing the value of
εmax
and the remaining 53 sites
for validation.
This study demonstrated that the assimilation of NDVI observations into simple growth model is
effective for estimating crop and grassland GPP. In contrast to MOD17 and other approaches using of
EO data as input, the proposed model is driven solely by weather variables and remote sensing is used
to re-calibrate the model parameters. This opens the possibility of using the model to forecast seasonal
GPP within the season, running the inversion using observed NDVI and weather estimates available
at a given time in the growing period, and using weather forecast for the remaining of the season.
Currently, the estimation of model parameters during the assimilation of NDVI is time-demanding.
This is a disadvantage against data-driven GPP models, where parameter values are known a priori.
Processing time currently amounts to about 20 s to optimize the model parameters over a single season
on a standard desktop computer. Therefore, an operational wall-to-wall application of the model will
require to optimize the code in order to run on parallel computing infrastructures.
Further analysis will focus on evaluating the potential improvements of considering different
maximum light use efficiency for C3 and C4 crops and a direct impact of temperature on GPP through
a stress factor in addition to that of water stress.
6. Conclusions
A simple crop growth model composed by few equations building on the framework of the
GRAMI model was coupled with the canopy radiative transfer model PROSAIL5B and reparametrized
against MODIS NDVI observations to estimate GPP of crop and grass ecosystems over Europe.
The model requires four meteorological variables as input (incident radiation, air temperature,
precipitation and reference potential evapotranspiration) and a preliminary identification of the
growing period. In this study, we used meteorological variable estimates from a global circulation
model (ECMWF ERA-INTERIM) and the results of a satellite-based land surface phenology retrieval
for the initial definition of growing period. GPP estimates from eddy covariance flux sites were used
to (1) set the maximum light use efficiency value (2 crop and 2 grassland sites), and (2), validate GPP
estimates (28 crop and 25 grassland sites). The approach resulted in acceptable accuracy of GPP 8-day
estimates (RMSE = 2.45 gC m
2
d
1
, R
2
= 0.67, n = 11209). Performances were shown to be improved
of about 20% compared to those of standard MODIS MOD17 GPP product, used as benchmark.
Author Contributions:
M.M. (Michele Meroni) developed and coded the coupled Sim Model and wrote the
majority of the manuscript. D.F. provided essential contributions in preliminary mathematical development of the
algorithm. R.L.-L. and M.M. (Mirco Migliavacca) contributed to the conceptual development of the GPP model
Remote Sens. 2019,11, 749 17 of 20
and provided substantial inputs for the set-up of the validation part. All authors contributed to the writing of
the manuscript.
Funding: This research received no external funding.
Acknowledgments:
This work used eddy covariance data acquired and shared by the FLUXNET community,
including these networks: AmeriFlux, AfriFlux, AsiaFlux, CarboAfrica, CarboEuropeIP, CarboItaly, CarboMont,
ChinaFlux, Fluxnet-Canada, GreenGrass, ICOS, KoFlux, LBA, NECC, OzFlux-TERN, TCOS-Siberia, and USCCC.
The ERA-Interim reanalysis data are provided by ECMWF and processed by LSCE. The FLUXNET eddy
covariance data processing and harmonization was carried out by the European Fluxes Database Cluster,
AmeriFlux Management Project, and Fluxdata project of FLUXNET, with the support of CDIAC and ICOS
Ecosystem Thematic Center, and the OzFlux, ChinaFlux, and AsiaFlux offices. We thank the following projects
for supporting EC measurements and their harmonization: European Fluxes Database Cluster, NitroEurope
IP and ECLAIRE. The authors would like to thank all the PIs of eddy covariance sites, including those that
shared restricted access data with us. We thank the following PIs for sharing their data and their comments on
the present paper: Mark Sutton and Eiko Nemitz (NERC, Edinburgh), Sergiy Medinets (Mechnikov University,
Odessa), and Aurore Brut (CESBIO, Toulouse). We thank Josh Hooker, Gregory Duveiller, and Alessandro
Cescatti (European Commission, Joint Research Centre) for collecting and harmonizing EC data and for their
valuable suggestions. Finally, this research was supported by the Exploratory Research initiative of the European
Commission—Joint Research Centre.
Conflicts of Interest: The authors declare no conflict of interest.
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... In addition, Dieguez et al. [92] applied a harmonic oscillation function based on the obtained maximum and minimum NPP data from satellite products to fit the NPP dynamic curve for Uruguayan grasslands considering the effects of climate and grazing. Meroni et al. [93] estimated GPP by the assimilation of MODIS NDVI into a crop growth model that was driven by meteorological variables. The results showed that the assimilation method outperformed MODIS products with a 0.14 improvement in R 2 . ...
... Therefore, adding some appropriate variables to the estimation process, depending on the characteristics of the grassland under study, can help improve the accuracy of the results. [40] linear regression typical red-edge chlorophyll index satellite 0.77 Sakowska et al. [87] linear regression alpine NIDI satellite 0.90 Li et al. [88] exponential regression typical, desert MSAVI satellite 0.72 Zheng et al. [48] power function regression typical, desert NDVI satellite 0.74 Dieguez et al. [92] harmonic oscillation function typical NPP product satellite 0.78 Matthew et al. [91] piecewise regression mixed maximum NDVI satellite 0.79 Cerasoli et al. [28] MLR typical spectral bands, vegetation indices ground, satellite 0.80 Xu et al. [90] MLR typical EVI, land surface temperature satellite 0.89 Gómez et al. [94] MLR alpine GPP product satellite 0.80 Meroni et al. [93] assimilation typical NDVI satellite 0.67 ...
... In particular, although the NDVI has many limitations as we mentioned above, it does not mean that the utilization of the NDVI should be abandoned. Some studies [63,93] have proved that the combined use of the NDVI can sometimes yield significant enhancements to their results. Thus, to obtain robust results, it is essential to select a right combination of variables according to the environmental and spectral characteristics of the grassland under study or to create more suitable vegetation indices [44]. ...
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The application of remote sensing technology in grassland monitoring and management has been ongoing for decades. Compared with traditional ground measurements, remote sensing technology has the overall advantage of convenience, efficiency, and cost effectiveness, especially over large areas. This paper provides a comprehensive review of the latest remote sensing estimation methods for some critical grassland parameters, including above-ground biomass, primary productivity, fractional vegetation cover, and leaf area index. Then, the applications of remote sensing monitoring are also reviewed from the perspective of their use of these parameters and other remote sensing data. In detail, grassland degradation and grassland use monitoring are evaluated. In addition, disaster monitoring and carbon cycle monitoring are also included. Overall, most studies have used empirical models and statistical regression models, while the number of machine learning approaches has an increasing trend. In addition, some specialized methods, such as the light use efficiency approaches for primary productivity and the mixed pixel decomposition methods for vegetation coverage, have been widely used and improved. However, all the above methods have certain limitations. For future work, it is recommended that most applications should adopt the advanced estimation methods rather than simple statistical regression models. In particular, the potential of deep learning in processing high-dimensional data and fitting non-linear relationships should be further explored. Meanwhile, it is also important to explore the potential of some new vegetation indices based on the spectral characteristics of the specific grassland under study. Finally, the fusion of multi-source images should also be considered to address the deficiencies in information and resolution of remote sensing images acquired by a single sensor or satellite.
... These two site-based datasets were specifically used to validate the performances of models and methods used to estimate the ecohydrological factors. However, the stated site-based gridded datasets were then uniformly resampled to 0.05 0 x 0.05 0 spatial resolution to match the resolutions of all datasets mentioned in Section 2.2 (Meroni et al., 2019;. ...
... We coupled the Carnegie-Ames-Stanford Approaches (CASA) model and the Gramineous crop growth (GRAMI) model through a consistant set of similar equation model to enhance the forest vegetation growth (Meroni et al., 2019;Ko et al., 2006;Maas, 1993). This coupled model was used to simulate GPP at yearly time step during 1992-2016 as baseline and the future periods of 2030's, 2050's and 2080's. ...
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... processes-and it strongly improved the estimation with an R 2 of 0.regrowths were not considered. Similarly, the observed RMSE are within the values reported by other models over this cropland (e.g.,Meroni et al., 2019;Pique et al., 2020). Furthermore, with the inclusion of regrowths and weeds, RMSE dropped by 24% in and by 13% in . ...
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Croplands represent an important unit within the global climate, and in response to population, they are expanding. Hence, understanding and quantifying the land-atmosphere interactions via water, energy and carbon exchanges is crucial. In this context, the first objective of this thesis studied the variability of the energy balance over different crops, phenologies, and farm practices at Lamasquère and Auradé. Secondly, in response to water scarcity and increasing drought in southwestern France, two land surface models (ISBA and ISBA-MEB) of different configurations were evaluated over some wheat and maize years to test their ability to estimate energy and water fluxes using measurements from an eddy covariance system as reference. Finally, in response to the contribution of croplands to increasing atmospheric carbon dioxide, the capability of the ISBA-MEB model to correctly simulate the major carbon components was tested over 11 seasons of maize and wheat.
... These well processed GPP EC data from 2001 to 2014 were freely obtained from the Max Planck Institute for Biogeochemistry's website at 0.08°× 0.08°spatial resolution (Biogeochemistry, 2019). They were then resampled to 0.5°× 0.5°spatial resolution to match with the other data sets used in this study and were used to validate the accuracy of simulated GPP results (Meroni et al., 2019;L. Wang, Zhu, et al., 2017). ...
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... Eddy covariance towers are typically installed at low heights above the canopy in order to provide meaningful and easily interpretable data quantifying the carbon balance components about the surrounding vegetation. These datasets are widely used to construct, validate and optimize biogeochemical and other models (like data oriented upscaled products, crop models, hydrological models and phenology models) that are used in different spatial scales (Heinsch et al., 2006;Friend et al., 2007;Stöckli et al., 2008;Mahecha et al., 2010;Schwalm et al., 2010;Chen et al., 2011;Jung et al., 2011;Verma et al., 2014;Xiao et al., 2014;Wu et al., 2016;Meroni et al., 2019). In this sense spatial heterogeneity of the surrounding vegetation causes problems as patches of different land use types might be present in the source area that represent noise (if the signal is defined as the measured NEE that is representative to the target vegetation type). ...
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Accurate representation of photosynthesis in terrestrial biosphere models (TBMs) is essential for robust projections of global change. However, current representations vary markedly between TBMs, contributing uncertainty to projections of global carbon fluxes. Here we compared the representation of photosynthesis in seven TBMs by examining leaf and canopy level responses of photosynthetic CO2 assimilation (A) to key environmental variables: light, temperature, CO2 concentration, vapor pressure deficit and soil water content. We identified research areas where limited process knowledge prevents inclusion of physiological phenomena in current TBMs and research areas where data are urgently needed for model parameterization or evaluation. We provide a roadmap for new science needed to improve the representation of photosynthesis in the next generation of terrestrial biosphere and Earth system models.