414 E. Nemitz et al. Agricultural and Forest Meteorology 105 2000 405–425
malized within-canopy profile of uzu1.68 m pre- sented by Nemitz et al. 2000a.
4.4. Modelling diurnal variability in Γ
l
In order to investigate the possible effect of diurnal cycles of Γ
l
, a simple dependence on h is suggested and compared with the measurements:
Γ
l
= Γ
l,max
exp −
1 − h a
, 15
where Γ
l,max
is the value for Γ
l
from Fig. 7, neces- sary to obtain the night-time emission under humid
conditions and a is a constant, which is obtained by fitting the modelled to the measured flux. This pa-
rameterization would clearly fail in the foliage–litter model using the measured values of Γ
sf
, since neither stomatal emission nor ground litter emission could ac-
count for the observed high daytime emission. There- fore the h dependency of Γ
l
was only used in the foliage–litter–silique model.
5. Results: application of resistance models to NH
3 3
3
exchange measurements with oilseed rape
5.1. Single-layer model The application of the χ
s
–R
w
model to an exam- ple period using the measured estimates of Γ
s
with a
Fig. 8. Application of the foliage–litter-model Fig. 5a to the four day period 10–13 June 1995, covering a variety of meteorological conditions. Measured and modelled net-flux F
t
are shown together with the modelled exchange through the stomata of the living leaves F
s
.
mean of 390, contrasted with an arbitrarily assumed constant value of Γ
s
= 1200, is shown alongside the
measured flux in Fig. 3. For 10 June the model, us- ing the apoplastic estimate of Γ
s
, reproduces the mea- sured flux fairly closely, whereas hardly any emission
is predicted for all other days, during which χ
s
re- mains below χ
a
. Arbitrarily raising Γ
s
to a value of 1200 leads to a better fit for some daytime periods 12
and 13 June, but the emission on 10 June is overes- timated. During night-time, when stomata are closed
and adsorption to the leaf cuticle is the only other ex- change process described in this model, periods of de-
position are accurately dealt with, whereas periods of emission cannot be explained.
5.2. Two-layer model The model result of the 2-layer model for the same
example period considered in Fig. 3 is shown in Fig. 8. The fit over a wide range of meteorological situations
is encouraging. During nights of high h and low wind speed nights of 10 and 11 June, deposition is shown
to have taken place to the leaf cuticle. In contrast, dur- ing windy nights 11 and 12 June, the model correctly
predicts the leaf litter emission to have penetrated the canopy, although it still underestimates the magnitude
of the net emission. This effect was not eliminated by the fitting of Γ
l
, because it was already set to the maximum value 13 000 and chosen to reproduce the
E. Nemitz et al. Agricultural and Forest Meteorology 105 2000 405–425 415
Fig. 9. The foliage–litter–silique model applied to the example period of Fig. 3 10–13 June 1995, using experimental values of the foliar [NH
4 +
][H
+
] ratio Γ
sf
, a value of 1500 for the siliques Γ
sq
and for the litter Γ
l
according to Eq. 15 with a = 30 and Γ
l, max
from Fig. 7. a Measured and modelled net flux with the atmosphere F
t
as well as stomatal from the silique stomata F
sq
and the litter layer F
l
. b Diurnal variability in modelled Γ
l
in relation to the relative humidity measured just above the canopy hz = 1.68 m.
whole day. There are several possible mechanistic ex- planations: adsorption of NH
3
to water layers F
w
could be overestimated in this case, because contin- uous adsorption to the leaf cuticle is likely to raise
both [NH
4 +
] and pH of the water-layer, resulting in a non-zero concentration at the leaf surfaces. This effect,
however, can only be accounted for in dynamic models e.g. χ
d
, Sutton et al., 1998. As with the 6–9 June, the 10 June could be modelled with Γ
1
= 6000, whereas
for the following days, this value had to be increased to 13 000. A possible explanation could be increased
microbial activity after the very humid night from 10 to 11 June see Fig. 9b. In contrast, the apoplastic
measurement indicated that Γ
s
was relatively stable over this period. As a consequence, the daytime ex-
change through leaf stomata shows emission until 10 June and considerable adsorption afterwards, domi-
nated by uptake of NH
3
emitted by the leaf litter Fig. 8.
5.3. Three-layer model The 3-layer model was applied with values for Γ
l
and Γ
sf
from Fig. 7 and various constant values of Γ
sq
to explore the sensitivity to this term. Both the average values and correlation coefficients of the modelled vs.
the measured flux are presented in Table 1. The correlation coefficients R in Table 1 for
cases 4 and 5 are only slightly larger than for the foliage–litter model and are also potentially mislead-
ing: for values of Γ
sq
yielding the highest correlation coefficient of 0.69, the model largely over-estimates
the net emission, whereas for Γ
sq
= 1260 case 3, the
mean net flux matches the measured value. In contrast to the inverse Lagrangian sourcesink analysis, a large
part of the daytime net emission is still predicted to originate from the ground, which can be seen from
Table 1 in the values of the stomatal daytime flux from the siliques F
sq
being much smaller than the
416 E. Nemitz et al. Agricultural and Forest Meteorology 105 2000 405–425
Table 1 Results of applying the foliage–litter–silique model Fig. 5b to the period 6–26 June demonstrating the model sensitivity to assumed
values of the apoplastic ratio [NH
4 +
][H
+
] in the siliques Γ
sq a
Case Γ
sq
R F
t
all data ng m
− 2
s
− 1
F
t
daytime ng m
− 2
s
− 1
F
sq
daytime ng m
− 2
s
− 1
Measured flux –
1 15.7
24.9 –
Foliage–litter model –
0.65 13.4
19.8 F
s
= − 9.1
1 500
0.59 9.6
14.1 1.2
2 1000
0.66 13.7
20.2 8.3
3 1260
0.67 15.7
23.8 12.0
4 1500
0.68 17.7
26.4 15.5
5 2000
0.69 21.8
32.5 22.6
6 h-dependent Γ
l
2000 0.62
13.5 22.1
23.3
a
Overall mean and daytime mean of measured flux F
t
are compared with the mean modelled flux and modelled stomatal exchange of the siliques F
sq
. The correlation coefficient R is shown for the comparison of overall F
t
. The results of the foliage–litter model Fig. 5a are presented for comparison including the mean stomatal flux F
s
. Values of Γ for leaves Γ
l
and foliage Γ
sf
are from Fig. 7, except for case 6, which considers diurnal variability in Γ
l
as a function of relative humidity h from Eq. 15.
total emission flux F
t
. In the foliage–litter–silique model, the high Γ
l
values of Fig. 7 are still necessary to reproduce the night-time emission measured.
Two likely sources of error can be identified in the model parameterization: first Γ
l
might be larger dur- ing night-time than for daytime, and second the trans-
fer resistance for the litter emission R
b1
+ R
ac1
is expected to be over-estimated when free convection
contributes to the transport within the canopy during night. In particular, R
ac1
is based on a parameterization of σ
w
u
∗
that was obtained during daytime conditions. However, night-time emission usually coincided with
relatively strong turbulence see Fig. 4, conditions under which the error associated with R
b1
and R
ac1
is expected to be similar to the daytime situation. Diur-
nal variability in Γ
l
is therefore the most likely expla- nation of these discrepancies, with chamber measure-
ments in the field indicating a larger Γ
l
for nocturnal high humidity conditions Nemitz et al., 2000a.
5.4. Humidity dependence of Γ
l
Next, the 3-layer model was applied with a h
-dependent Γ
l
according to Eq. 15. Whilst an op- timum value of Γ
sq
of 1260 had been found in the model run using a constant Γ
l
Table 1, the suppres- sion of Γ
l
during dry daytime conditions necessitated the use of a greater Γ
sq
2000 in order to reproduce the measured daytime emission. Applying a value
of a = 30 yields a correlation coefficient between measured and modelled F
t
of R = 0.62, and an average model flux of 13.5 ng m
− 2
s
− 1
that compares well with the measured value of 15.7 ng m
− 2
s
− 1
Ta- ble 1. At the same time the average daytime stomatal
emission from the siliques of 23.3 ng m
− 2
s
− 1
was comparable with the average daytime net emission
of 22.1 ng m
− 2
s
− 1
, which would be in agreement with the prediction of the ILT. The application of the
foliage–litter–silique model to the example period used for the other models Figs. 3 and 8 is shown in
Fig. 9, with a scatter plot in Fig. 10. The modelled daytime net emission is virtually identical to the emis-
sion from the silique layer. Consequently, the litter
Fig. 10. Scatter plot of the daytime and night-time averages of the measured and modelled net exchange flux F
t
for 10–13 June 1995.
E. Nemitz et al. Agricultural and Forest Meteorology 105 2000 405–425 417
emission, which is of the same order of magnitude as predicted by the ILT, is found to be recaptured in
the foliage litter Fig. 9. For this example period, the night-time emission predicted to originate from the
litter layer is underestimated, although the inclusion of a h-dependent Γ
l
improves the model fit on other days. A possible explanation is the underestimation of
h at the ground surface by the measurement estimate
applied just above the canopy z = 1.68 m. Further uncertainties in Eq. 15 are addressed in Section 7.3.
5.5. Application of the models to the whole measuring period
In the past, resistance models describing the bi-directional exchange of NH
3
have been mainly compared with measurements for periods of a few
days e.g. Sutton et al., 1995, 1998; Wyers and Erisman, 1998. Application to longer periods is
necessary to assess the adequacy of mechanistic model descriptions more rigorously Plantaz, 1998;
Flechard et al., 1999. Here both the foliage–litter and the foliage–litter–silique model were applied to the
whole of the data set. Fig. 11 shows the time-series
Fig. 11. Time series of averaged fluxes as measured full symbols and predicted by the foliage–litter model Fig. 5a open symbols for daytime 04:30–20:00 GMT and night-time 20:00–4:30 GMT periods for 8–26 June 1995. The model is based on the Γ values of Fig. 7,
and other resistances from Eqs. 5, 9, 12 and 13.
of the comparison between measured and predicted flux modelled with the foliage–litter model sepa-
rating daytime 04:30–20:00 GMT and night-time 20:00–04:30 GMT periods, while Fig. 12 a shows
the corresponding scatter plot. Although Γ
l
has been set to one out of three values, this is kept constant
over a whole 24-h period Fig. 7. Hence Figs. 11 and 12a show i how well the same value fits both
daytime and night-time measurements, ii the in- fluence of gaps in the measurement data on the
measured average and iii the adequacy of using just three different values of Γ
l
. The model slightly underestimates the daytime emission and night-time
deposition, and, although there are a few outliers 17 and 23 June, the overall fit is very encouraging. The
modelled flux tends to a lower standard deviation σ
F
of 10 min fluxes for each day than the measured flux Fig. 12b. This is not surprising, considering
that the model is parameterized using only the av- erage
of the NH
3
concentrations measured at the different heights, whereas the measured flux is depen-
dent on the NH
3
concentration gradient. Hence the measured flux is more heavily influenced by analyser
noise.
418 E. Nemitz et al. Agricultural and Forest Meteorology 105 2000 405–425
Fig. 12. Comparison of a the daily net exchange flux F
t
and b the standard deviation σ
F
of daily measured and modelled net NH
3
flux from 10 min values using the foliage–litter model. The 1:1 relationships solid lines and the linear regressions dotted lines are also shown.
Table 2 Contribution of different component exchange fluxes to net NH
3
exchange fluxes F
t
over oilseed rape as predicted by the foliage–litter and the foliage–litter–silique models
a
Measured Foliage–litter model constant Γ
l
Foliage–litter–silique model h-dependent Γ
l
All Day
Night All
Day Night
All Day
Night n
2081 1316
765 2214
1414 800
2214 1414
800 F
t
15.7 24.9
1.4 13.4
19.8 2.1
13.5 22.1
− 2.8
F
s
− 5.8
− 9.1
− 0.1
12.8 18.9
1.0 F
sf
− 2.9
− 4.4
− 0.0
F
sq
15.7 23.3
1.1 F
w
− 6.4
− 4.0
− 10.7
− 8.9
− 6.2
− 14.0
F
wf
− 2.6
− 1.5
− 4.8
F
wq
− 6.4
− 4.8
− 9.2
F
l
25.6 32.8
12.9 9.7
9.4 10.1
χ
a
1.07 1.21
0.85 χ
z 1.17
1.43 0.71
1.01 1.29
0.52 χ
c
, χ
cf
0.91 1.19
0.43 0.95
1.18 0.62
χ
cq
1.11 1.55
0.36 χ
s
, χ
sf
0.58 0.73
0.30 0.60
0.75 0.31
χ
sq
4.09 5.10
2.10 χ
l
12.22 14.00
8.82 5.87
5.13 7.31
a
The foliage–litter–silique model was run with Γ
s
= 2000 and Γ
l
according to Eq. 15 with a = 30 using values of Γ
l,max
from Fig. 7. Values are means of 10 min estimates for the period 8–26 June 1995. All symbols are used as shown in Fig. 5, fluxes are given in
ng m
− 2
s
− 1
and concentrations in mg m
− 3
. Daytime: 04:30–20:00 GMT. n: number of observations.
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.
6. Sensitivity and error analysis