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
Figs. 6 and 7 show the results given by the method for one of the nine crop situations: a medium sowing
64 M. Gu´erif, C.L. Duke Agriculture, Ecosystems and Environment 81 2000 57–69
Fig. 6. Estimated root dry mass and simulated LAI time changes as resulting of the 250 processes of reflectance assimilation into
SUCROS+SAIL model for a particuliar crop situation medium sowing date, poor emergence, silty loam, intermediate soil surface
humidity, and the two options for estimating SAIL parameters estimation. The solid line on LAI graphs represents the real LAI
change with time, the dotted lines the simulated one. The vertical arrow on root dry mass graphs represents the ‘real’ value of yield.
RRMSE values are reported.
date 30 March, with poor crop establishment con- ditions, assuming it was on a silty loam soil with an
intermediate soil surface humidity, with the errors in reflectance estimates given in Fig. 3. The results ob-
tained during the 250 processes of reflectance assim- ilation into the SUCROS+SAIL model are given in
Figs. 6 and 7.
In order to compensate for the bad SAIL param- eter estimates by option 1 cf. Fig. 3, which led to
an over-estimation of reflectance particularly in the near-infrared band, the assimilation process led to so-
lutions that decreased ‘nir’ reflectance, and therefore, underestimated LAI Fig. 6: most of the simulations
are below the solid line which represents the real LAI change with time. Consequently, light interception,
biomass production and root dry mass were underes- timated with option 1. In comparison, the use of more
accurate estimates of SAIL parameters option 2 in- stead of standard values option 1, reduced greatly the
errors in LAI and yield estimates: RRMSE dropped from 43 to 29 for LAI and from 7 to 4 for root
dry mass, and there was no more bias.
Fig. 7. Sowing dates and emergence parameters as resulting of the 250 processes of reflectance assimilation into SUCROS+SAIL
model for a medium sowing date, poor emergence soil condition: silty loam, intermediate surface humidity. The vertical arrow rep-
resents the ‘real’ parameter value. RMSE or RRMSE values are reported. The abscissa extreme values are the constraints applied
during the minimisation process.
Fig. 7 shows the associated estimates of sowing date and emergence parameters. With option 1, the
tendency for the assimilation process to underestimate LAI was achieved by estimating very late sowing dates
estimated DAYSOW are always later than the real value. In comparison, the use of option 2 provided a
better estimate of the sowing date there is less bias and the RMSE is 3 days less than for option 1. The im-
provement was not so clear for LAI
init
and SEMERG, particularly because of compensatory effects between
sowing date and these parameters on the response of the model choosing a late sowing date is somewhat
equivalent to choose a large SEMERG or to choose a little LAI
init
. The precision of estimates depends on the type of
crop situation. The results of using the best option No. 2 for a medium sowing date 30 March, but with op-
timal crop establishment conditions Fig. 8 indicate
M. Gu´erif, C.L. Duke Agriculture, Ecosystems and Environment 81 2000 57–69 65
Fig. 8. LAI change with time, histograms of root dry mass, DAYSOW, SEMERG and LAI
init
values as resulting of the 250 processes of reflectance assimilation into SUCROS+SAIL model for a medium sowing date, good emergence crop situation soil condition: silty loam,
intermediate surface humidity, and option 2 for SAIL parameters estimation. The solid line on LAI graphs represents the real LAI change with time, the dotted lines the simulated one. The vertical arrows on the histograms represents the ‘real’ values. RMSE and RRMSE values
are reported.
that the overall performances were better: RRMSE on LAI and root dry mass were significantly lower 2.2
and 10 and the LAI growth curves were closed to the ‘real’ curve. This improvement in performance
seemed to be linked to more appropriate remote sens- ing data acquisition dates, which provided complete
cover of the fast growing period of LAI see the ver- tical bars on the LAI graph on Fig. 8 and compare to
the same features on Fig. 6. The estimates of sow- ing date and emergence parameters were not so good,
again due to compensatory effects of these parameters in the minimisation process.
In summary, it appeared that the use of more ac- curate estimates of SAIL parameters obtained from a
prior knowledge of regional variability instead of stan- dard values allowed better estimates of yield, which
is the main objective. These results were even better when the timing of remote sensing data fit well the
LAI growing period. More contrasted results were ob- tained on the retrieval of sowing dates and emergence
parameters; they still needed to be improved.
Such an improvement could be achieved by using the vegetation index TSAVI to calculate the criterion
to be minimised in the assimilation process, instead of using the spectral reflectance in the three bands; on
the same type of crop situation Fig. 9, the precision on sowing date and emergence parameters estimates
was significantly improved an RMSE of 4.9 days for sowing date, 7.2
◦
C days for SEMERG, which corre- spond roughly to 1 day at this period of the year, and
an RRMSE of 11 for LAI
init
. At the same time, the errors on the root dry mass and LAI estimates were
greatly reduced, reaching very low values RRMSE of 0.8 and 4. The improved ability of TSAVI to min-
imise the contribution of soil reflectance to the canopy reflectance Baret and Guyot, 1991 resulted in better
performance of the crop model recalibration. Because of these interesting properties, TSAVI was therefore
used as the best way of predicting both sowing and emergence parameters and crop growth variables and
to compare the results for the whole range of crop situations.
The results of the 250 processes of TSAVI assimi- lation into the crop model for the nine crop situations
are summarised in Table 4. The errors on the estimates of sowing date and emergence parameters are quite
high, except for early or intermediate sowing dates and good emergence conditions columns 1 and 4.
66 M. Gu´erif, C.L. Duke Agriculture, Ecosystems and Environment 81 2000 57–69
Fig. 9. LAI change with time, histograms of root dry mass, DAYSOW, SEMERG and LAI
init
as resulting of the 250 processes of model recalibration using TSAVI and option 2 for SAIL parameters estimation, for a medium sowing date, good emergence crop situation soil
condition: silty loam, intermediate surface humidity. The solid line on LAI graphs represents the real LAI change with time, the dotted lines the simulated one. The vertical arrows on the histograms represents the ‘real’ values. RMSE and RRMSE values are reported.
Compensatory effects among these parameters made it difficult to interpret correctly the ranges and sense
of the errors. The LAI dynamics simulated using the retrieved
parameters Fig. 10 confirmed that the results were
Table 4 Results of the 250 assimilation processes on the nine crop situations
Sowing date Emergence parameters
Crop growth RMSE
RRMSE RRMSE
DAYSOW day SEMERG
◦
C day LAI
init
LAI RDM
a
15 March G
b
1.6 1.8
7.8 4.1
0.6 I
c
10.4 31.2
73.6 12.2
1.4 P
d
13.3 33.1
170.1 42.9
2.6 30 March
G
b
4.9 7.2
11.1 3.5
0.8 I
c
3.1 9.6
30.2 10.2
1.0 P
d
3.9 9.9
64.6 20.0
1.6 15 April
G
b
16.6 47.5
34.8 9.4
2.6 I
c
11.5 36.3
25.8 10.6
1.9 P
d
6.1 6.5
23.8 14.3
2.0
a
Root dry mass.
b
Good emergence.
c
Intermediate emergence.
d
Poor emergence.
better for early sowing dates and good emergence: these favourable conditions are characterised by a fast
growth of LAI during a period that is well covered by the remote sensing data acquisition schedule see the
relative position of the vertical bars and the LAI curve
M. Gu´erif, C.L. Duke Agriculture, Ecosystems and Environment 81 2000 57–69 67
Fig. 10. LAI changes with time as resulting of the 250 processes of reflectance assimilation into the SUCROS+SAIL model for the nine crop situations
{emergence good, medium, poor}×{sowing date 15 and 30 March, 15 April} soil condition: silty loam, intermediate surface humidity using TSAVI, option 2 for SAIL parameters estimation. RRMSE values are reported.
on the graphs. The remote sensing dates are too early for the poor emergence results to give a correct fitting
to the LAI curve and accurate estimates of the initial parameters; the simulated curves are widely scattered
round the ‘real’ LAI curve solid line.
The consequences on yield estimates at harvest are shown in Fig. 11: the relative RMSE of root dry
mass ranged from 0.6 for early sowing and good emergence to 2.6 for poor emergence results or late
sowing. The very high relative RMSE for LAI sim- ulations, had very little effects on yield estimate: the
errors in high LAI have a major influence on the in- crease in the RRMSE of LAI, but these errors caused
very little differences in light interception and hence biomass production. The differences in yield root dry
mass between the extremes for sowing dates ranging from 15 March to 15 April and emergence ranging
from good to poor, were about 25; from 19.5 tha for late sowing and poor emergence to 25.5 tha for
early sowing and good emergence, with a ‘mean’ value of 22.9 tha for medium sowing and intermedi-
ate emergence. Without any information, this mean value would be a sensible predictor of the regional
yield. The great uncertainty associated to this predic- tor which could be even greater, if sowing dates were
even later can be greatly reduced using this technique of crop model recalibration using five remote sensing
data acquisitions during crop establishment.
68 M. Gu´erif, C.L. Duke Agriculture, Ecosystems and Environment 81 2000 57–69
Fig. 11. Histograms of root dry mass estimates as resulting of the 250 processes of reflectance assimilation into SUCROS+SAIL model for the nine crop situations
{emergence good, medium, poor}×{sowing date 15 and 30 March, 15 April} soil condition: silty loam, intermediate surface humidity using TSAVI, option 2 for SAIL parameters estimation. The vertical arrows on the histograms represents
the ‘real’ values. RMSE and RRMSE values are reported.
5. Discussion
