M. van den Berg et al. Agriculture, Ecosystems and Environment 81 2000 43–55 51
The model was run 100 times for each harvest for configurations 1–7, which adds up to 7×81×100 runs
±7 h run time PC, 266 MHz. The average yield po- tential per harvest, Y
sim
and the pooled standard devia- tion S
Y , sim
root mean of squared standard deviations were calculated from the results of these test runs.
3. Results
A comparison of modelled cane yield potentials and actual yield records expressed in cane dry matter
for model configuration 0 soil data from reference profiles is given in Fig. 4. The correlation between
recorded harvested cane dry matter yields and cal- culated water-limited cane yield potentials is highly
significant, but the correlation coefficient r
2
= 0.43
seems rather small considering the advanced manage- ment applied. The root mean square of residuals from
regression between simulated yield potentials and actual yield records is 4449 kg ha
− 1
. The average difference between simulated yield potentials and
harvested dry cane yields is 16,840 kg ha
− 1
. Part of the difference between the 1:1 line and the trend line
is due to harvest losses and cane tips and basal parts which are included in the modelled yield potentials
but not in the yield records. No quantified data are available for these loss factors, but they are probably
of minor importance, because harvesting is done very carefully, manually, and basal parts and cane tips are
very small compared to the cane stalks of 3 m length or more. Their effect on scatter in Fig. 4 is probably
even smaller.
Table 3 ‘Pooled’ standard deviations of calculated yield potentials S
Y , sim
for studied model configurations
a
Configuration S
Y , sim
kg ha
− 1
1 RDM generated stochastically; θ
2d−1.5 MPa
= 0.17 cm
3
cm
− 3
; method 1 for water uptake
3628 2
Water retention data generated stochastically; RDM set to field average; method 1 for water uptake
1547 3
As 2, but with average θ
2d−1.5 MPa
set to 0.13 instead of 0.17 2264
4 Both water retention data average θ
2d−1.5 MPa
set to 0.17 and RDM are generated stochastically; method 1 for water uptake
3994 5
As 4, but with method 2 for water uptake 3848
6 As 4, but with average θ
2d−1.5 MPa
set to 0.13 instead of 0.17 4436
7 As 4, but disregarding uncertainties in parameters a and b of Eq. 5
3176
a
RDM: maximum rooting depth cm; θ
2d−1.5 MPa
, available soil water retained 2 days after field saturation cm
3
cm
− 3
. Fig. 4. Relation between simulated sugarcane yield potentials and
on-farm yield records for 81 harvest on 15 fields, near Araras. Soil data obtained from reference profiles configuration 0. Thin
line is 1:1 line; bold line: regression line.
The actual yield pooled standard deviation, i.e. the square root of the pooled variance of yields among
plots within a field S
2 Y
k
Eq. 4b was calculated to be 2226 kg ha
− 1
. Table 3 presents the pooled standard deviations of
yield potentials calculated with stochastically gener- ated soil data S
Y , sim
. The values of S
Y , sim
suggest that uncertainties in rootable depth configuration 1 have considerably
greater effect on uncertainties in model outcomes than uncertainties in soil-water relations configurations 2
52 M. van den Berg et al. Agriculture, Ecosystems and Environment 81 2000 43–55
and 3. Calculated yield variances resulting from these two sources of uncertainty exceed the variances in
recorded yields among plots and are large in relation to the root mean square of residuals from regression
between simulated yield potentials and actual yield records 4449 kg ha
− 1
and the residuals from the 1:1 line.
Uncertainties in model results are not homoge- neous. For configuration 4, the smallest standard
deviation among 100 runs was 67 kg ha
− 1
and the largest 8537 kg ha
− 1
. In one case, extreme values of calculated dry cane yield potentials were 7600 and
49,800 kg ha
− 1
Fig. 5 for configuration 4 shows that the propagation of uncertainties is inversely cor-
related with RDM, i.e. sensitivity to RDM becomes greater when it becomes more restrictive within the
range studied. Comparing the differences in S
Y , sim
between configurations 3 and 2 with those of 6 and 4, also shows that uncertainties increase with decreasing
θ
2d−1.5 MPa
. Fig. 6 compares average model results for configu-
rations 4 and 5. They are strongly correlated, but mod- elled yields for configuration 5 method 2 for water
uptake are systematically lower, with an average dif- ference of 1500 kg ha
− 1
. The average results for configurations 4 and 6, pre-
sented in Fig. 7, also show predominantly systematic differences.
Fig. 5. Standard deviations of calculated sugarcane yield potentials in relation to average maximum rooting depth RDM in model
configuration 4. Results of 100 simulation runs were used to estimate each standard deviation.
Fig. 6. Comparison of average simulated sugarcane yield poten- tials, obtained for configuration 4 water uptake method 1: with
compensatory effects and configuration 5 water uptake method 2: no compensatory effects.
Fig. 7. Comparison of calculated sugarcane yield potentials obtained for configuration 4 average available water capacity=
0.17 cm
3
cm
− 3
, and configuration 6 0.13 cm
3
cm
− 3
.
4. Discussion
