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
The results presented above clearly indicate that uncertainty propagation analysis should be done as a
standard practice for all cases studied, and not just as a preliminary sensitivity analysis for one or few
sample cases, because errors propagate differently for each crop. An extreme example to illustrate this
point is given in Fig. 8, where calculated yield po- tentials for four consecutive harvests on field No. 2
M. van den Berg et al. Agriculture, Ecosystems and Environment 81 2000 43–55 53
Fig. 8. Simulated effect of maximum rooting depth RDM and available water capacity θ
2d−1.5 MPa
on yield potentials of consecutive sugarcane crops at field 2. Day of planting: 16 February 1980; 1st ratoon, 11 July 1981; 2nd ratoon, 23 September 1982; 3rd ratoon, 13
September 1983–15 September 1984.
are plotted against RDM, for four hypothetical values of θ
2d−1.5 MPa
. Most curves tend to converge with in- creasing RDM, indicating a decreasing sensitivity of
calculated yield potential to θ
2d−1.5 MPa
. The decreas- ing steepness of the curves with increasing RDM and
with increasing θ
2d−1.5 MPa
also indicates decreasing sensitivity. However, the value of RDM where the
curves level off, and the distances between the curves vary greatly among the scenarios. These variations
are related to rainfall distribution, evaporative demand and other growth conditions throughout the growing
season. Horizontal lines at the highest level would be expected in Fig. 8 if rainfall was sufficient and
uniformly distributed, such as under drip irrigation. The divergent relations for the third ratoon are caused
by an extreme drought spell during the summer of 1984, with only 59 mm rain in FebruaryMarch. In
ratoon cane, simulated cane yield potentials for equal values of total available water represented by the
product RDM×θ
2d−1.5 MPa
cm e.g. RDM=50 cm, θ
2d−1.5 MPa
= 0.26 versus RDM=100 cm, θ
2d−1.5 MPa
= 0.13 are generally slightly larger for smaller val-
ues of θ
2d−1.5 MPa
. This is due to the competition between water uptake by roots and evaporation from
the soil surface. When θ
2d−1.5 MPa
is large, a large proportion of infiltrating rainwater is retained in the
surface layer, where it is subject to evaporation. With smaller θ
2d−1.5 MPa
and deep rooting, more infiltrat- ing rainwater will percolate to deeper layers in the
root zone, where it is still available to the roots, but protected against evaporation. This interaction partly
explains why uncertainties in θ
2d−1.5 MPa
have less effect on calculated yield potentials than uncertainties
in RDM, as shown in Table 3, but a more important reason for this is that the estimated uncertainty in
θ
2d−1.5 MPa
is considerably less than in RDM, even though θ
2d−1.5 MPa
is estimated as a simple average value.
It has been recognised for several decades that high Al
3+
concentration inhibits rooting and thereby water
54 M. van den Berg et al. Agriculture, Ecosystems and Environment 81 2000 43–55
availability to crops. However, soil-water availability research on strongly weathered soils has mostly been
concentrated on physical soil properties, partly be- cause different crops and cultivars have different lev-
els of tolerance and expensive crop monitoring field trials are necessary for quantified assessments and
perhaps also because Al
3+
research is traditionally in the domain of soil fertility specialists, who are not
commonly involved with neutron probes and TDRs for soil-water assessment. The results presented here
suggest that systematic interdisciplinary research on these interactions may be rewarding.
Figs. 6 and 7 showed that using different methods to calculate water uptake or to assess available water
capacity resulted primarily in systematic differences of calculated yield potentials. The differences are
considerable, but the strong correlation between the results imply that it is hardly possible to select a supe-
rior method on the basis of yield model results only. The hypothesis that water uptake is primarily condi-
tioned by soil-water status of the wettest zone is insuf- ficiently tested. Almost all plant-soil-water research
at crop level is done by wetting the entire root zone followed by drying by water withdrawal by crops.
This is basically different from rain-fed conditions, where wet and dry soil parts may occur together. The
question of appropriate p
soil
values, which was not ad- dressed in this study, also deserves attention. Thomp-
son 1976 suggests a fixed value of 0.5 for sugarcane, whereas Nable et al. 1999 found a value of 0.15 in
a container experiment. Others prefer to determine p
soil
as a function of atmospheric demand according to the method of Doorenbos and Kassam 1979 or its
follow-up of Allen et al. 1998 as used in this paper.
5. Conclusions
