M. Gu´erif, C.L. Duke Agriculture, Ecosystems and Environment 81 2000 57–69 61
Table 2 Characteristics of sugar beet vegetation parameters for young and
mature crops LAI2.0
LAI2.0 Mean
S.D. Mean
S.D. ρ
f
Green 0.14
0.015 0.15
0.014 Red
0.06 0.007
0.07 0.008
NIR 0.46
0.001 0.46
0.001 τ
f
Green 0.14
0.016 0.15
0.015 Red
0.05 0.011
0.06 0.071
NIR 0.49
0.001 0.49
0.001 θ
L
60.0 6.0
45.0 4.5
humidity was considered as dry 5, intermediate 10, or humid 25. Therefore, the parameterisa-
tions of soil reflectance–humidity relationships shown in Table 1 allowed the calculation of soil spectral re-
flectance. Plant optical properties and geometry were derived from the mean values in Table 3, according to
the estimate of LAI given by the model.
The errors in estimating canopy reflectance using both options were quantified by a Monte Carlo tech-
nique Duke and Guérif, 1998. Synthetic reflectance values which represent an ‘image’ of the regional
variations in crops reflectance and will be referred to hereafter as ‘real’ reflectance were created with the
SAIL model. The distributions given in Table 2 were used for the plant parameters. Uniform distributions
of soil surface humidity within a class of humidity and the parameterisations of soil reflectance–humidity re-
lationships in Table 1 were used for the soil parame- ters. For a given soil texture and a given class of sur-
face humidity, series of 250 spectral reflectance in the green, red and near-infrared bands were simulated for
a range of 10 LAI values from 0.05 to 6.0, by draw- ing parameter values from the distributions estimated
from field measurements. The absolute errors on re- flectance estimate E=ρ
real
− τ
simulated
using options
Table 3 Parameters defining contrasted emergence conditions and crop
establishment results Emergence
conditions SEMERG
◦
C day LAI
init
10
− 4
m
2
m
− 2
Good 75
27.0 Intermediate
110 13.9
Poor 150
2.9
1 and 2 were computed for each situation and each spectral band.
Option 2 allowed the estimation of SAIL parame- ters using prior knowledge of regional variability and
this had many advantages over the standard estimates Fig. 3. Option 1, with its standard values, overesti-
mated reflectance for small values of LAI when soil reflectance has strong influence, while option 2 pro-
vided estimates closer to the actual values.
The errors might be even larger for higher or lower soil surface humidity. When expressing the errors in
terms of relative RMSE Eq. 2:
RRMSE= 250
P
250 1
ρ
real
1 250
250
X
1
ρ
real
− ρ
simulated 2
0.5
2 for all the range of soil surface humidity, the errors
appeared to be considerably reduced with our method of estimating SAIL parameters Fig. 4, especially in
the early part of the growing cycle from 30 to 15.
The next major problem was to quantify the effects of the propagation of these errors due to variations
in soils and crops on the results of the crop model recalibration using the assimilation of remote sensing
data. This is the objective of the present work.
3. Method
A realistic scenario was simulated for estimating re- gional sugar beet yields using the crop model and the
programming of five remote sensing data acquisitions during canopy establishment. The challenge was to
assimilate the remote sensing data into the combined SUCROS+SAIL model and to re-estimate the sowing
date DAYSOW and the emergence parameters SE- MERG, LAI
init
. A Monte Carlo type approach was also used.
3.1. Creation of virtual regional crop situations and associated reflectance
A set of virtual crop establishment situations was created, covering the likely variations over a sugar
factory area in the considered region. Three possi- ble sowing dates 15 and 30 March, 15 April were
considered and three crop emergence results: good
62 M. Gu´erif, C.L. Duke Agriculture, Ecosystems and Environment 81 2000 57–69
Fig. 3. Absolute errors in simulated reflectances for two spectral bands red and near-infrared on a silty loam of intermediate surface humidity: a red reflectance, option 1; b red reflectance, option 2; c nir reflectance, option 1 and d nir reflectance, option 2.
rapid, intermediate, and poor slow, characterised by three sets of SEMERG, LAI
init
parameters Guérif et al., 1998 Table 3. SUCROS was run
for the nine resulting combinations of sowing date and emergence parameters and for a given climatic
year 1995, and provided a wide range of LAI time changes Fig. 5. The differences in LAI between ex-
treme situations reached as much as 4.4 around Day 150 during canopy establishment.
The schedule for remote sensing data acquisitions consisted of five dates within this period, beginning
5 May Day 125, ending 24 June Day 175, with around 12 days intervals cf. Fig. 5. For each of the
nine crop situations and the five dates, virtual spectral reflectances were calculated, by running SAIL model.
Each crop situation×date was characterised by a LAI value, given a soil type and a soil surface humidity
class which allowed to draw the SAIL parameter values from the distributions of crop and soil charac-
teristics, as above. In that way, 250 temporal profiles of five spectral reflectances in the green, red, and
near-infrared bands were calculated for each crop situation. A vegetation index, TSAVI, combining of
red and near-infrared reflectance Baret and Guyot, 1991, was also calculated using Eq. 3:
TSAVI = aρ
nir
− aρ
r
− b
aρ
nir
+ ρ
r
− ab + 0.081 + a
2
3 where a and b are the coefficients of the soil line
ρ
soil×nir
= aρ
soil×r
+ b, the subscripts ‘nir’ and and
‘r’ represent, respectively, the spectral reflectance in the near-infrared and the red bands.
3.2. Assimilation of the virtual reflectance to recalibrate the SUCROS+SAIL model
The 250 profiles of spectral reflectance or TSAVI were assimilated into the SUCROS+SAIL model for
M. Gu´erif, C.L. Duke Agriculture, Ecosystems and Environment 81 2000 57–69 63
Fig. 4. Relative RMSE of simulated reflectances for the three spectral bands on a silty loam: a option 1 and b option 2.
each of the nine crop situations, using the two ways of estimating SAIL parameters options 1 and 2.
The criterion ‘crit’, which was minimised Eq. 4, was the root mean square difference between the
spectral reflectance three bands simulated by the SUCROS+SAIL model and the ‘real’ spectral
reflectance:
crit = 1
3 × 250
750
X
1
ρ
real
− ρ
simulated 2
0.5
4 Constraints were imposed on the sowing date and
emergence parameters estimated from this process of minimisation, so that they did not have ‘unreasonable’
values. As a result, 250 sets of DAYSOW, SEMERG,
Fig. 5. LAI time changes for nine contrasted crop establishment situations, 1995. Time is expressed as the day number since 1
January. The vertical lines represent the dates at which remote sensing data are supposed to be available.
LAI
init
values were estimated. These new parameter values were then used to estimate LAI growth as well
as the final yield. The errors introduced in the estimate of spectral
reflectance by estimating SAIL parameters, as well as the intrinsic error of the method, led to errors in the
DAYSOW, SEMERG, LAI
init
estimates. The errors concerning DAYSOW and SEMERG were quantified
by RMSE. The errors concerning LAI
init
, LAI and root dry mass were quantified by a relative RMSE Eq. 5:
RRMSE = 1
LAI
init×real
× 1
250
250
X
1
LAI
init×real
− LAI
init×simulated 2
0.5
5 For the nine crop situations, the ‘real’ values for
DAYSOW were 15 and 30 March or 15 April, the ‘real’ values for SEMERG and LAI
init
were those presented in Table 3. The ‘real’ LAI and root dry mass
were those obtained by simulation with SUCROS model, using these sowing dates and emergence
parameters.
4. Results
