R. Leuning et al. Agricultural and Forest Meteorology 104 2000 233–249 239
various heights within the canopy to measure σ
w
. Friction velocity, u
∗
, was measured using another 3-D sonic anemometer with path length of 0.15 m
and installed at a height of 2.2 m Solent 1021R, Gill Instruments Ltd., Lymigton, UK. The two
sets of measurements were combined to develop a composite profile of σ
w
u
∗
. as a function of zh
c
, where z is measurement height above water when
the paddy was flooded or above ground when it was drained.
Fluxes of sensible heat, H, water vapour, E, and CO
2
, F
CO
2
at 2.2 m above the ground were mea- sured using the eddy covariance method Miyata
et al., 2000. Fluctuations of the three wind velocity components and of air temperature were measured
with a Solent RS3A sonic anemometer. Sonic virtual temperature fluctuations were corrected for variation
in the speed of sound with air density according to Hignett 1992. A fast response, open-path infrared
gas analyser with a 0.20 m span E009, Advanet Inc., Okayama, Japan was installed at the same
height as the sonic anemometer with a horizontal separation of 0.17 m to measure the fluctuations in
the CO
2
and water vapour concentrations. Miyata et al. 2000 provide details of corrections to account
for the high-frequency losses in eddy covariance measurements resulting from path-averaging and
instrument separation Moore, 1986; Leuning and Moncrieff, 1990. Corrections to eddy fluxes aris-
ing from density fluctuations due to H and E Webb et al., 1980, and for the cross-sensitivity of the CO
2
gas analyser to water vapour Leuning and Mon- crieff, 1990; Leuning and Judd, 1996 were also
applied. Methane fluxes above the canopy were estimated
using classical flux-gradient relationships as de- scribed in detail by Miyata et al. 2000. In that
paper, both the friction velocity and CO
2
were used as ‘tracers’ to evaluate the eddy diffusivity, K,
required in
F
CH
4
= − ρ
a
K M
CH
4
M
a
ds
CH
4
dz 14
where s
CH
4
is the mixing ratio of CH
4
relative to dry air and ρ
a
is the density of dry air, and M
a
and M
CH
4
are the molecular masses of dry air and CH
4
, respec- tively.
4. Results
4.1. Temperature and humidity profiles Profiles of temperature and water vapour pressure
for half-hourly periods commencing at 01:00 and 13:00 hours local standard time on 8 and 11 August
1996 are shown in Fig. 2. The profiles display the measured data points as well as smooth curves ob-
tained by fitting a quadratic function to the lowest seven data points. Without this smoothing, the inverse
analysis resulted in highly erratic source profiles, in- cluding clearly spurious sinks for water vapour within
the canopy during the day results not shown. We consider that errors were introduced into the measured
Fig. 2. Half-hourly average profiles for temperature and water vapour pressure measured in rice at Okayama at starting times of
01:00 and 13:00 hours on 8 and 11 August 1996. Data points are shown, along with smooth curves formed by fitting a quadratic
function to the lowest seven data points. Canopy height was 0.72 m.
240 R. Leuning et al. Agricultural and Forest Meteorology 104 2000 233–249
Fig. 3. Profiles of cumulative fluxes of sensible and latent heat obtained through the inverse Lagrangian analysis of the smoothed
scalar profiles shown in Fig. 2. Fluxes measured above the canopy at 2.2 m using the eddy covariance technique are also shown at
0.8 m for reference. Note differences in vertical scale compared to concentration plots.
temperature and humidity profiles through the use of a set of instruments, despite careful intercomparison
of sensors before and after the field campaign. The issue of smoothing is addressed further in Section 5.
Fig. 3 shows cumulative profiles through the canopy for fluxes of sensible heat and latent heat correspond-
ing to the scalar profiles in Fig. 2 note the change in vertical scale between the two figures. The anal-
ysis indicated that nocturnal fluxes of both sensible and latent heat were negligible throughout the lower
part of the canopy, and thus, did not account for the ground heat flux which was typically 20–30 W m
− 2
upwards at this time. This discrepancy may have been caused by smoothing the temperature profiles andor
by the very small u
∗
and hence σ
w
and τ
L
which leads to low diffusivities at these times. The small up-
ward evaporative flux in the top 20 of the canopy was well matched by a downward flux of sensible heat
from the atmosphere. This energy closure indicates good internal consistency between the measurements
of temperature and water vapour pressure gradients within and above the canopy. At night, both sensible
and latent heat fluxes derived from the inverse anal- ysis were within 50 W m
− 2
of those measured above the canopy at 2.2 m using the eddy covariance tech-
nique shown at 0.8 m for reference in Fig. 3. This is well within measurement errors associated with both
approaches. During the daytime, sensible heat fluxes were small and uniformly positive on 8 August and
negative on 11 August and evaporation dominated the energy flux from the rice paddy on both days. Accord-
ing to the inverse analysis, each layer contributed ap- proximately equally to the total water vapour flux on
8 August when the paddy was drained, but on 11 Au- gust the upper 20 of the canopy made only a small
contribution to λE.
Estimates of evaporation from the soilwater using energy balance calculations were 78 and 86 W m
− 2
at 13:00 hours on the 8 and 11 August, respectively. These values were estimated using net radiation
available at the surface derived from radiation pen- etration calculations, plus measured soil heat fluxes
and changes in energy storage in the soilwater. Mid- day values of λE for the lowest layer were typically
80–100 W m
− 2
, which compares favourably with en- ergy balance calculations. To obtain these results, we
used the exponential function in Eq. 9 to describe the σ
w
profile within the canopy so that σ
w
→ 0.2
at the ground. In a separate analysis, Eq. 10 was used to decrease σ
w
linearly through the bottom half of the canopy to ensure that σ
w
= 0 at the ground.
This resulted in peak evaporative fluxes at 0.14 m of 35 W m
− 2
, values which are substantially lower than the energy balance calculations, and thus pro-
vides some a posteriori justification for using Eq. 9. We presume that the presence of vegetation contin-
ues to ensure significant turbulent mixing and σ
w
except within a very thin layer above the soil surface. In future, measurements should be made close to the
ground to resolve the behaviour of σ
w
and τ
L
close to the ground.
4.2. Carbon dioxide profiles Profiles of differential CO
2
concentrations relative to the reference height at 2.5 m are presented in Fig. 4
for four half-hourly periods straddling dawn on 8 and 11 August 1996. There was a transition from nega-
tive gradients throughout the canopy at 06:00 hours to positive gradients above the canopy and negative
gradients close to the ground later in the morning. No profiles are available for 09:00 and 10:00 hours be-
cause instruments were calibrated at those times.
Fig. 5 shows cumulative flux profiles for CO
2
corresponding to the scalar profiles in Fig. 4 note the change in vertical scale between these figures.
R. Leuning et al. Agricultural and Forest Meteorology 104 2000 233–249 241
Fig. 4. Profiles of CO
2
for four half-hourly periods straddling dawn on 8 and 11 August 1996. The measurements are differential
concentrations relative to the reference height at 2.5 m. Note the transition from negative gradients throughout the canopy at 06:00
hours to positive gradients above the canopy and negative gradients close to the ground later in the morning. No profiles were available
at 09:00 and 10:00 hours because of instrument calibrations.
There is a good correspondence between the height of the turning points in the concentration profiles in
Fig. 4 with the height of zero net flux in Fig. 5. On 8 August, positive fluxes are predicted by the inverse
analysis throughout the canopy until 07:00 hours, followed by negative fluxes in the top of the canopy
and positive fluxes in the lower canopy later in the morning. The profiles show that both the soil and
canopy contributed to the total respiratory flux until 07:00 hours, and that the soil plus the lowest canopy
layer continued as a source of CO
2
during the day. The second lowest canopy layer was also respiring
at 08:00 hours but was a net sink for CO
2
by 11:00 hours, consistent with the deeper penetration of light
during the middle hours of the day. Similar patterns
Fig. 5. Cumulative flux profiles for CO
2
obtained through the inverse Lagrangian analysis of the concentration profiles shown in
Fig. 4. Fluxes measured above the canopy at 2.2 m using the eddy covariance technique are also shown at 0.8 m for reference. Note
differences in vertical scale compared to concentration plots.
were observed on 11 August except that the transition from respiration to photosynthesis occurred about
half an hour earlier. There is some suggestion that the upper 20 of the canopy was a small source of CO
2
during the day, rather than the expected sink. This is probably an artefact of the analysis arising from
errors in concentration measurements and the speci- fied profiles for σ
w
and τ
L
. It is, thus, likely that the sink strength of the fourth layer from the bottom has
been overestimated by 20–30, especially during the daytime.
Fluxes of CO
2
measured above the canopy at 2.2 m using the eddy covariance technique are also shown
at 0.8 m in Fig. 5. While there is good agreement between cumulative fluxes at the top of the canopy
with eddy covariance measurements during the day, the agreement at night was generally poor. Possible
242 R. Leuning et al. Agricultural and Forest Meteorology 104 2000 233–249
reasons for the discrepancies are discussed below in conjunction with discussion of the methane fluxes.
Some authors Dolman and Wallace, 1991; McNaughton and van den Hurk, 1995; van den Hurk
and McNaughton, 1995 have applied the LNF the- ory to the calculation of canopy energy balances of a
two layer canopy using a modified resistance network which includes a ‘near-field resistance’ in series with
the boundary-layer resistance to account for near-field effects. In this approach, normally used aerodynamic
resistances were replaced by ‘far-field resistances’ calculated using the diffusive part of the LNF. The
near-field resistance was found to be small, and thus, had only a small effect on the canopy microclimate
and hence on the calculated evaporation rates. These findings could lead to the conclusion that traditional
K-theory is satisfactory for describing within canopy transport. To test this hypothesis, the inverse anal-
ysis was repeated but with the contribution of the near-field dispersion omitted in the calculation of the
dispersion coefficients. Results for two typical CO
2
profiles presented in Fig. 6 show convincingly that the near-field dispersion cannot be ignored in the inverse
analysis. Neglect of the near-field contribution greatly amplified the inflections in the cumulative flux profile
for 11 August, and thus led to spurious sources and sinks. Respiration in the lower canopy and photosyn-
thesis in the upper canopy was overestimated for 8 August when near-field component was omitted.
Fig. 6. Typical profiles of CO
2
concentration at 08:00 hours on 8 and 11 August and the resultant cumulative flux profiles derived
from the inverse Lagrangian analysis with near-field dispersion included squares and with it omitted circles.
Resolution of these apparent discrepancies lies in the nature of the ‘forward’ and inverse dispersion prob-
lems. In the forward mode, the objective is to calculate fluxes from the canopy plus underlying surface soil,
water using bulk resistances between a ‘big-leaf’ and a reference point. In this case, near-field dispersion
provides distortions to the local concentration profiles within the canopy but does not contribute substan-
tially to the overall resistance to transport between the canopy and the reference point. In contrast, the
inverse analysis is used to estimate source and sink distributions within the canopy and then details of lo-
cal dispersion are critical. A similar conclusion con- cerning the forward and inverse problems was made
by Katul et al. 1997. Raupach 1989a has pointed out that while the overall level of the concentration
profile is set by the far field sources, the local struc- ture of the profile is closely linked to the distribution
of the near-field sources. Ignoring this local structure means it is impossible to deduce the source distribu-
tion as this information is, by definition, lost in the far field.
4.3. Time series for heat, water vapour and CO
2
Time series for half-hourly fluxes at the top of the canopy derived from the inverse analysis for 8 and
11 August are compared in Fig. 7 to fluxes mea- sured using eddy covariance techniques. These two
methods for estimating above-canopy fluxes are es- sentially independent, except for a weak link through
the vertical velocity fluctuations used to estimate u
∗
. Sensible heat fluxes from the inverse analysis are sys-
tematically lower than those measured using the eddy covariance technique by ≈40 W m
− 2
on both days. We are unable to resolve whether these discrepancies
are due to systematic errors in the temperature gradi- ents or in the eddy covariance measurements. Latent
heat fluxes at the top of the canopy were ≈60 W m
− 2
lower than the eddy covariance measurements during the morning of 8 August, but agreement between
the two methods was excellent for the rest of that day and on 11 August. These results are typical of
measurements made on all other days.
Maitani and Miyashita 1999, personal communica- tion measured fluxes of sensible heat, latent heat and
CO
2
above the canopy at 1.05 m and within the canopy at 0.45 m using eddy covariance techniques. The
R. Leuning et al. Agricultural and Forest Meteorology 104 2000 233–249 243
Fig. 7. Time series for cumulative fluxes of sensible heat, latent heat and CO
2
at the top of the rice canopy derived using the inverse Lagrangian analysis. These fluxes are compared to direct
measurements made at 2.2 m using the eddy covariance technique. Evaporative fluxes at 0.42 m and CO
2
fluxes at 0.14 m are also shown. Note the differing scales for H and λE.
diurnal variations in their latent heat fluxes above the canopy on 8 and 11 August were very similar to those
shown in Fig. 7, peaking around 400 W m
− 2
on each day. However, measured latent heat fluxes at 0.45 m
peaked at ≈80 W m
− 2
, whereas peak fluxes from the inverse analysis at 0.42 m were ≈210 and 280 W m
− 2
on 8 and 11 August, respectively Fig. 7. It is possi- ble that path averaging and instrument separation may
have caused the within-canopy eddy covariance mea- surements to have underestimated the flux at 0.45 m.
The sonic anemometer used had a 50 mm path-length, the open-path infrared analyser for water vapour and
CO
2
had a path length of 100 mm, and the two instru- ments were separated by 150 mm. Any errors in the
prescribed turbulence field and the measured humidity profiles used in the inverse Lagrangian analysis may
also have contributed to the observed discrepancies. Cumulative fluxes of CO
2
at the top of the canopy derived from the inverse Lagrangian analysis were in
close agreement with eddy covariance measurements during daylight hours on both days shown in Fig. 7.
However, nocturnal fluxes from the inverse Lagrangian analysis were two to three times greater than those
measured directly, particularly on 8 August. Night time values of u
∗
were 0.1 m s
− 1
on 7 and 8 August while they were higher on other nights and during the
daytime. Given the good agreement between noctur- nal fluxes estimated by the inverse analysis and the
eddy covariance technique on other nights e.g. 11 Au- gust, Fig. 7, and data not shown, we conclude that the
inverse technique overestimated the nocturnal fluxes during 7 and 8 August. This is probably because we
have ignored atmospheric stability when calculating the dispersion coefficients in the inverse Lagrangian
analysis. We shall discuss this complication below.
Miyata et al. 2000 observed a reduction in the net downward flux of CO
2
to the whole canopy when the field was drained compared to when it was flooded.
Assuming similar photosynthetic activity by the crop with or without flooding, the reduced net CO
2
uptake may be due in part to a greater upward CO
2
flux from the drained soil than from the floodwater, as suggested
by Fig. 7. Average fluxes of CO
2
at 0.14 m were 0.318 S.E. 0.036, n=45 mg CO
2
m
− 2
s
− 1
for 8 August when the field was drained, more than double the value
of 0.134 S.E. 0.015 mg CO
2
m
− 2
s
− 1
for 11 Au- gust when the paddy was flooded. While the CO
2
flux from aerobic drained soil will be inherently greater
than from the anaerobic, flooded soil, the water layer will also act as a barrier to diffusion of gases. This
barrier is enhanced by algal photosynthesis during the day which reduces the partial pressure of CO
2
within the water to low levels Ohtaki, 1999, personal com-
munication and causes a downward diffusion of CO
2
from the air to the water the inverse analysis will not yield this downward diffusion with the air sampling
heights used because respiration by the lower leaves is also included in the 0–0.14 m layer.
4.4. Methane Profiles of differential CH
4
concentrations relative to the reference height at 2.5 m are presented in Fig. 8
for four half-hourly periods straddling dawn on 8 and 11 August. Concentrations within the canopy were
244 R. Leuning et al. Agricultural and Forest Meteorology 104 2000 233–249
Fig. 8. Measured and smoothed profiles of CH
4
for four half hourly periods straddling dawn on 8 and 11 August 1996. The
measurements are differential concentrations relative to the refer- ence height at 2.5 m. A negative exponential function of the form
c=a
1
+ a
2
exp−a
3
z was used to smooth the data.
very high 50 ppb near the ground, even during the day when atmospheric mixing was relatively strong.
Gradients for CH
4
were usually positive between mea- surement heights except on some occasions where the
concentration closest to the ground was lower than that at the next level, thereby suggesting a possible local
sink for CH
4
. Before examining the results of the inverse La-
grangian analysis for methane, we first discuss quali- tatively the expected source distributions within rice
canopies. Methane produced by methanogenic bac- teria in the soil is transported through the overlying
water to the atmosphere by three main pathways Nouchi, 1994: 1 through the formation of bubbles;
2 a slow, diffusive exchange across the water–air interface; and 3 transport through the rice plant
aerenchyma and then through micropores which are arranged on the culm an aggregation of leaf sheaths
of the rice plant and on the leaf sheaths. The latter is the dominant mechanism of transport. Note that the
micropores are always open and are independent of the stomata. While some of the CH
4
produced in the anaerobic flooded soil is oxidised at the soil–water
interface and in the water column by methanotrophic bacteria Schutz et al., 1989; Sass et al., 1992, we ex-
pect a net CH
4
source at the soilwater surface as well as sources, rather than sinks, distributed throughout
the canopy. To ensure continuous, negative concen- tration gradients within the canopy, and hence smooth
source profiles, an exponential function of the form c=a
1
+ a
2
exp−a
3
z was used to fit the concentra-
tion data. The coefficients were estimated using the Levenberg–Marquardt algorithm given in Press et al.
1992 and the fitted profiles are also shown in Fig. 8. This approach can be criticised on the basis that prior
expectations or prejudices have been incorporated into the analysis. We accept that possibility, but con-
sider that measurement errors are mainly responsible for the somewhat erratic concentration profiles ob-
served and that it is valid to constrain general trend of the analysis using extra, prior knowledge.
Cumulative inverse Lagrangian flux profiles for CH
4
are shown in Fig. 9 for periods corresponding to the concentration profiles in Fig. 8 note the change
in vertical scale between these figures. Sensitivity of the derived cumulative flux profiles to small changes
in the concentration profile is evident when the results from smoothed and measured concentration profile
are compared cf. Figs. 8 and 9. It is clear that the inverse Lagrangian analysis using the unsmoothed
data over-estimates source strengths in some layers and predicts sinks in others. Within the uncertain-
ties in the analysis, the results from the smoothed concentration profiles appear more plausible in that
cumulative fluxes increase monotonically or remain approximately constant through the canopy space.
This is consistent with the expected source distribu- tion predicted above.
There was often poor agreement between individ- ual half-hourly estimates of CH
4
fluxes between the inverse Lagrangian analysis and micrometeorological
measurements above the canopy Fig. 9. To reduce variability, a running mean of 1.5 h duration was ap-
plied to both time series and the results are compared for 8, 11 and 12 August in Fig. 10. Daytime CH
4
fluxes at the top of the canopy from the inverse Lagrangian
R. Leuning et al. Agricultural and Forest Meteorology 104 2000 233–249 245
Fig. 9. Cumulative flux profiles for CH
4
obtained through the Inverse Lagrangian analysis of the concentration profiles shown
in Fig. 8. Fluxes measured above the canopy at 2.2 m using the eddy covariance technique are also shown at 0.8 m for reference.
Note differences in vertical scale compared to concentration plots. Square symbols indicate cumulative fluxes derived from the mea-
sured concentrations while circles are cumulative fluxes derived from the smoothed profiles.
analysis are similar, but less variable than results from the flux-gradient approach. This suggests that flux es-
timates are improved by using information from the whole profile in the inverse Lagrangian analysis, rather
than just the top two concentration measurements in the flux-gradient approach.
Daytime CH
4
fluxes above the canopy as estimated by both methods were higher on 8 August when the
paddy field was drained than on 11 and 12 August when it was flooded. Miyata et al. 2000 postulate
that the diffusion barrier caused by the floodwater will cause fluxes from the flooded paddy to be lower
than from initially saturated, drained soils. As time progresses, fluxes from the drained soil will decrease
as methanotrophic bacteria consume CH
4
as it passes through the upper oxygenated soil. Results from the
inverse Lagrangian analysis provide some support for these suggestions; fluxes across the lowest plane
at 0.14 m were a little higher on 8 August, with a mean value of 0.459 S.E. 0.059, n=45 mg CH
4
m
− 2
s
− 1
, compared to 0.318 S.E. 0.040 and 0.388 S.E. 0.030 mg CH
4
m
− 2
s
− 1
for 11 and 12 August, respectively.
As with CO
2
fluxes, the inverse analysis overesti- mates CH
4
fluxes at night relative to the flux-gradient estimates. Methane production is determined by
microbial activity in the soil and production rates increase strongly with temperature Seiler et al.,
1984; Chapman et al., 1996. Because soil tempera- tures peak late in the afternoon and are at a minimum
before dawn Miyata et al., 2000, it is unlikely that the high nocturnal CH
4
emission rates obtained from the inverse analysis can be correct. These high flux
estimates correspond to periods when the friction velocity, u
∗
0.1 m s
− 1
Fig. 10 and any errors in de- termining u
∗
at night will propagate directly through the inverse analysis through estimates of σ
w
and τ
L
and hence the dispersion coefficients D
ij
. Periods of low u
∗
also correspond to times of stable thermal stratification within and above the canopy positive
temperature gradients, Fig. 2. The current version of the inverse analysis assumes neutral stability when
estimating the D
ij
, and it, thus, is likely that they have been underestimated for stable, nocturnal conditions,
causing overestimates of the fluxes. These problems are less severe during the day when u
∗
0.1 m s
− 1
. The effects of atmospheric stability on turbulence
statistics and transport within maize canopies have been discussed by Jacobs et al. 1992, 1994, 1996
and within forests by Shaw et al. 1988.
5. Discussion
