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
The inverse analysis developed by Raupach 1989a,b, and used in this study, relies on a relatively
simple matrix inversion which provides no a priori constraints on the sourcesink distributions within
the canopy. When applied initially using measured profiles of temperature, water vapour and CH
4
the analysis led to unrealistic cumulative flux profiles as
a result of small irregularities in the concentration
246 R. Leuning et al. Agricultural and Forest Meteorology 104 2000 233–249
Fig. 10. Time series for cumulative fluxes of CH
4
at the top of the rice canopy derived using the Inverse Lagrangian analysis for 8, 11 and 12 August 1996. These fluxes are compared to direct measurements made at 2.2 m using flux the gradient technique. A running 1.5 h
mean has been applied to all time series.
profiles and uncertainties in τ
L
z and σ
w
z. The problem was partially overcome by using smooth
functions for τ
L
z and σ
w
z and by smoothing the temperature and water vapour profiles by using a
quadratic function for the lowest seven data points, and a negative exponential function for all eight CH
4
concentration measurements. No smoothing was ap- plied to the CO
2
profiles which were measured using a single instrument. A major objection to smooth-
ing the concentration profiles is that it may remove structure in the source distributions which actually
exists within the canopy, and that our assessment of ‘unrealistic flux profiles’ is subjective. We accept
this possibility but argue from our prior understand- ing of energy partitioning, and the mechanism of
CH
4
emissions from soils and within crops, that the highly erratic source profiles derived from the raw
measurements are not realistic. Smoothing of profiles does not, of course, guarantee that the resultant in-
ferred sourcesink are correct. We, thus, suggest three possible improvement to the analysis: 1 reducing
measurement errors in profiles of both and concentra- tions; 2 using constrained optimisation techniques;
and 3 introduction of stability corrections to σ
w
and τ
L
. Improvements in the measurements of the tem-
perature and humidity profiles could be obtained by replacing the array of fixed sensors used in this study
with a single transducer which is moved continuously up and down in the vertical, because this would elim-
inate variable relative drifts in the calibration of a set of fixed transducers. Average profiles could then be
constructed by measuring the electrical output signals at a number of measured positions. Success for this
approach is suggested from the CO
2
concentration measurements where a single analyser was used. Air
from the different levels was passed through the anal- yser in turn and this resulted in relatively smooth CO
2
profiles Fig. 4. An identical approach was adopted for measurement of CH
4
concentrations but the resul- tant profiles were somewhat irregular Fig. 8. This
may have resulted from problems of water conden- sation in air lines caused by sampling air with very
high humidity within the rice crop.
It is possible that better solutions for the source strength profile may be obtained by using a con-
strained inverse analysis, whereby prior estimates of the sourcesink strengths are refined by the anal-
ysis. Enting et al. 1993 used this approach in a Bayesian synthesis analysis to estimate magnitudes
R. Leuning et al. Agricultural and Forest Meteorology 104 2000 233–249 247
and uncertainties of regional sourcesink strengths of CO
2
across the globe, while Kandlikar 1997 used a similar approach for estimating sourcesink strengths
for CH
4
at a global scale. In the context of plant canopies, models for the distribution of radiation,
heat, water vapour and photosynthesis e.g. Leuning et al., 1995 could be used to give the prior estimates
of these sources. This class of model requires knowl- edge of various leaf properties as a function of height,
such as leaf area and angle distributions, radiation scattering coefficients and photosynthetic capacity.
Some parameter values in these models are difficult to obtain, and the inverse analysis of concentration
profiles within the canopy can be combined with the model to improve estimates of the parameter values
in an iterative manner. Once the descriptive model of methane transport through soil, water and rice
plants presented by Nouchi 1994 is converted to a process model, it can also be used to provide prior
estimates for CH
4
source strengths for the inverse analysis.
As noted above, fluxes for both CO
2
and CH
4
at the top of the canopy appeared to be overestimated at
night and it was suggested that this resulted from us- ing dispersion coefficients calculated for neutral atmo-
spheric stability, whereas stratification was often sta- ble at night. Assumption of neutral stability leads to
underestimates of the dispersion coefficients, D
ij
re- sistances, and hence, to overestimates of the fluxes.
Leuning 2000 examines whether Monin–Obukhov similarity theory may be used to adjust τ
L
z and σ
w
z within and above plant canopies to provide corrections
for stability.
6. Conclusions
