410 E. Nemitz et al. Agricultural and Forest Meteorology 105 2000 405–425
found to be two to five times higher than those of the foliage of the same plants Husted et al., 2000. Direct
daytime measurements of bulk tissue [NH
4 +
] and pH of the litter leaves by the same authors showed a high
temporal and spatial variability. Estimated pH values of leaf litter ranged from 5.1 to 5.4 and [NH
4 +
] from 5.0 to 56.5 mM, probably due to differences in de-
composition stage and humidity. These variations are reflected in the value of the ratio [NH
4 +
][H
+
] of the litter Γ
l
. In the following sections, the single-layer χ
s
–R
w
model is used as the basis for the development of more detailed models including exchange with leaf
litter and siliques, capable of reproducing these mea- surements. Both the original model and the extended
models are then applied to the NH
3
fluxes measured over oilseed rape.
4. Model development
4.1. Parameterizations for the single-layer χ
s
–R
w
model 4.1.1. Stomatal resistance
In the present study, daytime values of R
s
were found from the micrometeorological measurements of
water vapour transfer Sutton et al., 2000b. A light response function that was fitted to these values al-
lows R
s
to be estimated for periods of measurement uncertainty at dawn and dusk. The measurements im-
plicitly include secondary effects of water stress and h
Jarvis, 1976, and it was found that R
s
could be adequately parameterized for the measurements here
solely by the global radiation R R
R
s
as R
s
= min
R
sMax
, R
sMin
1 + α
1
R R
R
s
4 with R
sMax
= 5000 s m
− 1
, R
sMin
= 35 s m
− 1
and α
1
= 180 W m
− 2
. 4.1.2. Cuticular uptake resistance
Sutton and Fowler 1993 suggested a simple parametrization for the h-response of R
w
, the shape of which Sutton et al. 1995 compared with adsorp-
tion data of NH
3
to glass and leaf surfaces Van Hove et al., 1989:
R
w
= R
wMin
exp 1 − h
12 5
with R
wMin
= 2 s m
− 1
. Van Hove and Adema 1996 have recently re-interpreted their values of NH
3
ad- sorption to calculate an effective water-film thickness
on leaf scale M
H
2
O,eff
, which they describe by M
H
2
O,eff
= 18.8 + 105.1 exp
− D
α
2
. 6
where α
2
equals 0.56 kPa, D is the vapour pressure deficit in kPa and M
H
2
O,eff
is given in mm. The re- sulting values for high h seem large e.g. M
H
2
O,eff
= 96 mm for T = 15
◦
C and h = 90, compared with figures obtained from weighing leaves at different h
8–20 mm as well as the typical thickness of the leaf cuticle of 0.5–15 mm. The authors conclude that with
increasing h the cuticle becomes gradually more per- meable, resulting in the extracellular fluid becoming
partially available for pollutant uptake.
Adema and Heeres 1995 measured the uptake con- stant k
+
of NH
3
at a gasliquid interface that can be identified with R
w −
1
for different values of pH and water-film thickness. k
+
was found to be strongly correlated with pH over the range of typical environ-
mental conditions 4.0 pH 8.0 at a constant water-layer thickness of 4600 mm:
R
w
= k
+ −
1
= −
0.00316 pH + 0.0293
− 1
s m
− 1
. 7
In contrast, no obvious relationship could be found with water-layer thickness in a range of 4–4600 mm.
However, the artificial water layers contained T-Pol detergent to ensure continuous films, whereas on hy-
drophobic waxy cuticles water layers may be dis- continuous Cape, 1996. Despite the new estimates
of Eqs. 5 and 7, it remains unclear how the pH changes with the adsorption of NH
3
and other gases as SO
2
and to what degree leaves are covered with water films at different h. The work of Van Hove and
Adema 1996 suggests that the water-layer thickness would be more closely related to D rather than h. The
parametrization
R
w
= minR
wMax
, R
wMin
expα
3
D 8
with R
wMax
= 5000 s m
− 1
, R
wMin
= 1 s m
− 1
and α
3
= 30 kPa
− 1
is of a similar shape as Eq. 5 used by Sutton and Fowler 1993 and leads to good agree-
ment between measured and modelled flux for periods of night-time deposition in this study Section 5.2.
E. Nemitz et al. Agricultural and Forest Meteorology 105 2000 405–425 411
4.1.3. Stomatal compensation point The NH
3
gas-phase concentration in the sub-stomatal cavities, or stomatal compensation point χ
s
, is re- lated to the pH and [NH
4 +
] concentration in the apoplast by the Henry and dissociation equilibria for
NH
3
and NH
4 +
Sutton et al., 1994; modified: χ
s
= 161500
T exp
− 10380
T [NH
4 +
] [H
+
] 9
at 1 atm, where T is the absolute temperature in K and concentrations are in mol l
− 1
. From Eq. 9, the compensation point can be divided into a T-dependent
part and the dimensionless emission potential termed here Γ
s
, which is the ratio of [NH
4 +
] to [H
+
] in the leaf apoplast. At North Berwick, Γ
s
was experimen- tally determined by extraction of the apoplastic liquid
in the field during the period 9–12 June Section 3. 4.2. Two-layer foliage–litter model
χ
s
–R
w
–χ
l
model The leaf litter emission F
l
can be included into the compensation point model as demonstrated in
Fig. 5a, similar to the 2-layer model presented by Shuttleworth and Wallace 1985 to simulate evap-
Fig. 5. Resistance diagrams of extended canopy compensation point models applied to describe NH
3
exchange over oilseed rape. a A 2-layer ‘foliage–litter model’ treats litter leaves at the soil surface with the emission potential χ
l
as a further emission source, with diffusion through the canopy constrained by within-canopy atmospheric and boudary-layer resistance, R
ac
and R
b1
, respectively. b A 3-layer ‘foliage–litter–silique model’ additionally divides the canopy into two layers for the siliques subscript q and foliage subscript f,
respectively. Other resistances are as given in Fig. 1.
oration from sparse crop. Adding a fourth potential χ
l
to the resistance network greatly complicates the solution compared with the χ
c
–R
w
model Eq. 2, and the solving procedure is therefore outlined in
Appendix A. The turbulent resistance in the canopy R
ac
may be parameterized by Raupach, 1989: R
ac
z
1
, z
2
= Z
z
2
z
1
K
H −
1
z dz,
K
H
= T
L
σ
w 2
, 10
where z
1
and z
2
are the heights above the ground between which R
ac
is to be calculated and K
H
z is the eddy diffusivity. T
L
and σ
w
are the Lagrangian time-scale and the standard deviation of the vertical
wind component, respectively, and can be parame- terized by u
∗
, according to the characteristics of the canopy. Whilst a parameterization of σ
w
was obtained from direct measurements Nemitz et al., 2000a, T
L
was parameterized using the formulation by Raupach 1989. Using these expressions, Eq. 10 results in a
simple dependency of R
ac
on u
∗
: R
ac
0, z = αz
u
∗
. 11
The height dependent constant αz is shown in Fig. 6a. For the mean height of the foliar NH
3
exchange taken
412 E. Nemitz et al. Agricultural and Forest Meteorology 105 2000 405–425
Fig. 6. Parametrization of within-canopy turbulent atmospheric resistance R
ac
and quasi-laminar boundary layer resistance R
b1
for the ground surface litter layer. a Parametrization of the constant α used in Eq. 11 as a function of height z. b Partitioning of the total
atmospheric in-canopy resistance into R
ac
1.11 m and R
b1
for different values of u
∗
according to Eqs. 11 and 12, compared with an alternative description of R
ac
Shuttleworth and Wallace, 1985, using an exponential decay parameter of n = 4.
as the zero-plane displacement, d = 1.1 m α equates to 102.3. The resulting values of R
ac
, derived from the measurements at North Berwick, agree very well
with the parameterization of Shuttleworth and Wallace 1985 if a decay constant n of 4 is used in their
expression Fig. 6b. However, these authors neglected the contribution of the boundary layer resistance R
b1
which is here calculated according to Schuepp 1977: R
b1 −
1
= ku
∗ g
Sc − lnδ
z
l
, 12
where k is the von Kármán constant 0.41 and Sc the Schmitt number for NH
3
. δ the distance above
ground where molecular diffusivity D
χ
equals the eddy diffusivity D
χ
∼ = ku
∗ g
δ , and z
l
is the up- per height of the logarithmic wind profile that forms
above the ground and of which u
∗ g
k is the slope.
Since the wind profile was not measured this close to the surface, rough estimates of u
∗ g
and z
l
are based on data presented by Schuepp 1977. Here the val-
ues u
∗ g
= u
1.68 m20 and z
1
= 0.1 m are used.
u 1.68 m is the wind speed at the lowest height above
the canopy canopy height: h
c
= 1.38 m, at which
measurements were carried out continuously. On an average, R
b1
contributed 30 to the total atmospheric in-canopy resistance Fig. 6b.
The NH
3
gas concentration at the surface of the fallen leaf litter χ
l
is calculated as the gaseous NH
3
concentration in equilibrium with [NH
4 +
] and pH of the water in the litter leaves, by analogy to Eq. 9. As
discussed by Nemitz et al. 2000a, χ
l
is affected by the liquid water content of the litter leaves, tempera-
ture, previous emission as well as mineralization and nitrification rates. Because of the high variability in
measured Γ
l
, this was set to an arbitrary value, that led to a reasonable agreement between the modelled and
the measured flux for each whole 24-h period. In an ef- fort to simplify the estimation of Γ
l
, it was found that the fitted Γ
l
could be approximated by one of three values in the range 3000–13 000 which was broadly
similar to the range of available measurements. For 6 and 14 June values had to be chosen which were
greater than the measured values. For Γ
s
a leaf area index L
s
weighted average of the measured values was applied where available, while the initial and final
values were used for other periods. The values derived from this exercise are presented in Fig. 7.
The equilibrium gas concentration χ
l
was cal- culated using Eq. 9 with an average temperature
T
ave
of the temperatures at z
′
T z
′
and the soil T
soil
, z
′
being the notional mean height of the gas exchange e.g. Sutton et al., 1993. This average
was found to match the air temperature above the ground surface T0.06 m, measured over one 24-h
period, much more closely than either T
soil
or T z
′
; T
0.06 m = 0.98T
ave
+ 0.57, R
2
= 0.93, N = 93
E. Nemitz et al. Agricultural and Forest Meteorology 105 2000 405–425 413
Fig. 7. Time series of the values of the ratio Γ = [NH
4 +
][H
+
] of both living Γ
s
and litter Γ
l
leaves as measured and as used for the foliage–litter-model for 6–26 June 1995. The measured values of Γ
s
were used between June 9 and 15 and the first and last measured values were applied beyond this period. Γ
l
was only measured on three occasions, showed high scatter error bars indicate standard deviations and is highly uncertain see text. Γ
l
was therefore set to one of the three values 3000, 6000 or 13 000 to fit the measured flux.
compared with T 0.06 m = 0.61T z
′
+ 4.10,
R
2
= 0.94, N = 93.
4.3. Three-layer model distinguishing different foliage layers χ
s
–R
w 2
–χ
l
model The importance of the silique layer as a further
source can be assessed indirectly through the improve- ment of the model performance after inclusion of a
further layer Fig. 5b. Whilst bulk resistances can be used for models treating the canopy as a ‘big leaf’,
splitting up the canopy into different layers requires the calculation of the different resistances on a leaf
area basis. The total surface area index L
s
of the siliques was estimated to be 3.2 Gammelvind et al.,
1996, whereas the double sided L
s
of the leaves was measured as 4.3 Nemitz et al., 2000a. For Brassica
napus , Jensen et al. 1996 reported adaxial and abax-
ial leaf stomatal densities of 112 and 125 mm
− 2
, re- spectively, together with a stomatal density of the
siliques of 58 mm
− 2
. From direct measurements of the stomatal conductances on leaf area basis g
s
at different heights in the oilseed rape canopy at North
Berwick leaf area averaged values of g
s
of 4.3 and 3.5 mm s
− 1
were found for leaves and siliques, respec- tively. On a canopy-scale these values, combined with
the L
s
values, suggest a 1.8 times higher conductance of the foliage-layer than of the silique-layer. There-
fore the ‘bulk’ stomatal resistances of the foliage-layer R
sf
and the silique-layer R
sq
equate to R
sf
= 2.8
1.8 R
s
, R
sq
= 2.8R
s
. 13
The values for the resistance to cuticular adsorption imposed by foliage R
wf
and siliques R
wq
were cal- culated in a similar way, and the aerodynamic re-
sistances within the canopy R
ac1
and R
ac2
param- eterized by u
∗
according to Eq. 11 and Fig. 6a. The canopy scale boundary-layer resistance of foliage
R
bf
and siliques R
bq
is calculated as Baldocchi, 1988; Schuepp, 1993:
R
bf,q
= r
b
L
s
= l
D
NH
3
L
s
Sh ,
14 where l is a characteristic length assumed to be 5 and
40 mm for siliques and leaves, respectively, D
NH
3
the molecular diffusivity of NH
3
and Sh the Sherwood number. Following the expressions provided by Mon-
teith and Unsworth 1990, Table A.5 and neglecting edge effects, Sh for leaves and siliques is calculated
for flat plates and cylinders, respectively. The physi- cal mean heights of the silique- and foliage-layers are
assumed to be z
q
= 1.2 and z
f
= 0.9 m, respectively,
and the wind speed u at both heights is calculated from the measured wind speed at 1.68 m and the nor-
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
