Sensitivity and error analysis
E. Nemitz et al. Agricultural and Forest Meteorology 105 2000 405–425 419
Table 3 Sensitivity analysis for the 3-layer model: a single parameter is changed within the bounds specified in brackets, while all other parameters
are kept constant
a
Modified value Γ
sq
constant 2270 Γ
sq
fitted for F
t
model = F
t
measured R
F
measured
vs. F
model
Mean F
t
ng m
− 2
s
− 1
F
sq
F
t
daytime Best fit Γ
sq
R F
measured
vs. F
model
F
sq
F
t
daytime Unmodified model
0.62 15.7 = F
t
measured 1.07
2270 0.62
1.07 F
t
measured ∓25 0.620.62
15.715.7 1.071.07
17852755 0.610.63
1.041.09 χ
a
measured ∓25 0.650.59
18.612.9 0.991.17
19202619 0.650.60
0.961.17 Γ
sf
∓25 0.620.63
15.216.2 1.101.04
23302209 0.620.63
1.101.03 Γ
sq
∓25 0.610.63
11.120.3 1.031.09
NA NA
NA Γ
l,max
∓25 0.600.64
14.117.4 1.160.99
24762063 0.610.64
1.160.97 R
ac
+ R
b1
∓ 50
0.660.61 21.314.0
0.861.16 15532482
0.630.61 0.731.15
R
sf
∓ 50
0.610.63 14.916.2
1.121.04 23702212
0.610.63 1.131.03
R
sq
∓ 50
0.620.63 29.912.4
1.121.04 14743065
0.600.63 1.081.06
T z
′
∓ 25
0.560.62 7.130.4
1.101.05 41121221
0.630.61 1.140.96
a
The sensitivity to each parameter is assessed a by applying the model with a constant value of the silique [NH
4 +
][H
+
] ratio Γ
sq
= 2270, and b by choosing a new value of Γ
sq
to fit the predicted net exchange flux to the measured average. The correlation coefficient R and the net flux F
t
provide a means to test the sensitivity of the model performance, while the ratio of silique flux to total flux F
sq
F
t
is indicative of the partitioning of the exchange between plant parts. T z
′
is the temperature of the mean canopy height in
◦
C, all other parameters are defined in Fig. 5b.
Although Figs. 11 and 12 show the comparison of the measurements with the foliage–litter model, these
could equally be shown for the foliage–litter–silique model. While the latter model is considered to be a
more realistic mechanistic representation of the ex- change process, the comparison shows that the simpler
foliage–litter model is adequate to predict the main features of net fluxes. A comparison of the overall
performance of the two models is shown in Table 2. This shows the mean component fluxes through dif-
ferent plant parts as predicted by a the foliage–litter model and b the foliage–litter–silique model with
h
-dependent Γ
l
. The measured net-flux F
t
is slightly underestimated by both models. However, the aver-
ages do not cover exactly the same periods: short gaps of up to 2 h in the χ
a
data were interpolated and still used as model input, although measured fluxes could
not be calculated. By contrast, for a few periods the flux could be measured, but there are parameters miss-
ing, which are essential for the model application.
Whereas the foliage–litter model predicts deposi- tion to the leaf stomata F
s
of −9.1 ng m
− 2
s
− 1
for daytime, the inclusion of a silique-layer into the model
suggests that the deposition to the leaf stomata of −
4.4 ng m
− 2
s
− 1
is more than balanced by the emis- sion from the silique stomata of 23.3 ng m
− 2
s
− 1
. At night-time stomata are, as expected, inactive, with
small fluxes being induced by some duskdawn ef- fects. Surprisingly, the suppression of Γ
l
during dry daytime conditions as a consequence of Eq. 15 leads
to the litter emission flux F
l
being on an average the same during day and night about 10 ng m
− 2
s
− 1
; the increased turbulence at daytime, favouring the ground
level emission coming through the canopy, and in- creased T are exactly compensated for by the smaller
daytime value of Γ
l
. If Γ
l
is kept constant over the day, as in the foliage–litter model, the night-time emission
is only 40 of its daytime value. Both models sug- gest that the night-time leaf litter emission is roughly
balanced by deposition to leaf water-layers F
w
, with the ratio of the deposition to siliques F
wq
and leaves F
wf
in the foliage–litter–silique model being 2:1. The leaf litter emission is mainly captured by the lower
leaves, whereas atmospheric deposition takes place to the aerodynamically more exposed siliques.