Source/sink distributions of heat, water vapour, carbon dioxide
and methane in a rice canopy estimated using Lagrangian
dispersion analysis
R. Leuning
a,∗, O.T. Denmead
a, A. Miyata
b, J. Kim
caCSIRO Land and Water, P.O. Box 1666, Canberra, ACT 2601, Australia bNational Institute of Agro-Environmental Research, Tsukuba, Ibaraki 305-8604, Japan
cDepartment of Atmospheric Science, Yonsei University, Seoul 120-749, South Korea
Received 5 January 1999; received in revised form 1 June 1999; accepted 20 March 2000
Abstract
Source distributions for heat, water vapour, CO2and CH4within a rice canopy were derived using measured concentration profiles, a prescribed turbulence field and an inverse Lagrangian analysis of turbulent dispersion of scalars in plant canopies. Measurements were made during IREX96, an international rice experiment in Okayama, Japan. Results for the cumulative fluxes of heat, water vapour and CH4at the canopy top were satisfactory once their respective concentration profiles were smoothed using simple analytic functions. According to the inverse analysis, water vapour was emitted relatively uniformly by each of five equi-spaced layers within the canopy, whereas sensible heat fluxes were small (<100 W m−2) and of either sign. Methane fluxes were predicted to be emitted most strongly in the lower 50% of the canopy, as expected from the distribution of micropores along leaves and leaf sheaths, the major pathway for CH4loss from the soil–crop system. No smoothing was required for CO2concentration profiles and the inverse analysis provided close correspondence between the turning point in the concentration profile is the changeover from respiration by the soil/paddy water and lower canopy to net photosynthesis by the upper canopy. These results could only be obtained by including both the near- and far-field contributions of sources to the total concentration profile. Neglect of the near-field contribution in the inverse analysis led to spurious source distributions.
Excellent agreement was obtained between cumulative fluxes of heat, water vapour, CO2and CH4at the top of the canopy from the inverse analysis and direct eddy covariance measurements when the friction velocityu∗>0.1 m s−1, and atmospheric
stability was approximately neutral. Nocturnal fluxes of CO2and CH4from the inverse method exceeded micrometeorological measurements above the canopy by a factor of 2–3 whenu∗<0.1 m s−1and stable atmospheric conditions prevailed within
and above the canopy. Neglect of these stability effects will lead to an underestimate of the dispersion coefficients (dimension of resistances) in the transport model and hence an overestimate of the fluxes. Further work is required to establish the correct procedure for incorporating stability effects into the inverse analysis. © 2000 Elsevier Science B.V. All rights reserved.
Keywords:Lagrangian dispersion analysis; Plant canopy source/sink distributions; Rice
∗Corresponding author.
1. Introduction
Information on the partitioning of sources and sinks of quantities such as heat, water vapour, CO2
and CH4 within plant canopies and the underlying 0168-1923/00/$ – see front matter © 2000 Elsevier Science B.V. All rights reserved.
soil is required for many practical problems. For example: (1) researchers concerned with water use efficiency of crops (Condon et al., 1990) need to separate transpiration from soil evaporation when assessing the effectiveness of various breeding strate-gies, such as selection of varieties for early canopy closure; (2) source/sink distributions of sensible heat, water vapour and CO2 within the canopy and at
the soil surface are required to validate multi-layer soil–vegetation–atmosphere-transfer models (e.g. Wang and Jarvis, 1990; Baldocchi and Harley, 1995; Leuning et al., 1995); (3) separate contributions of soil and plants to net ecosystem carbon exchanges are needed because soils and plants respond differently to such factors as temperature, moisture and rising atmospheric CO2 concentrations (Wang and
Pol-glase, 1995), with strong implications for response of ecosystems to climate change (Schimel et al., 1994); and (4) rice cultivation is one of the major biogenic sources of atmospheric CH4(Houghton et al., 1995).
Methane is produced anaerobically by bacteria in the soil and the CH4 is transported to the atmosphere
by bubble formation, water–air–gas exchange, and transport through the aerenchyma of the rice plants (Nouchi, 1994). Rice cultivation is one of the few biogenic sources where management of methane emissions is possible (Sass, 1994), and accurate esti-mates of the relative contributions of CH4fluxes from
rice plants and from paddy water will contribute to the design of effective emission control strategies.
Various techniques exist for partitioning fluxes between plants and soil. Most current estimates of CO2 emission from soils and CH4 emissions from
soils and vegetation are based on chamber studies (Denmead, 1979; Neue et al., 1994). Advantages of chambers for trace gas fluxes include the ability to measure very small fluxes and to examine emissions as a function of soil temperature, oxygen, nitrogen and carbon levels and microbial activity. However, chambers alter the microclimate, possibly causing systematic errors in CO2and CH4flux measurements
(Denmead, 1994). Chambers are totally unsuitable for measuring soil evaporation because they alter the humidity deficit compared to undisturbed conditions. In this case, alternatives such as miniature lysimeters may be used (e.g. Leuning et al., 1994).
The distribution of source/sink strengths within canopies can also be measured using
micrometeoro-logical methods such as eddy covariance and eddy accumulation (see review by Denmead, 1994). While these approaches are suitable for use within tall canopies such as corn (Wilson et al., 1982) and forests (Denmead and Bradley, 1987), they have been used relatively infrequently within short, dense canopies such as rice, because current instruments are too bulky. This may cause errors in flux measurements due to loss of covariance resulting from path averag-ing and instrument separation (Moore, 1986; Leunaverag-ing and Judd, 1996), and to vertical flux divergence across the space occupied by the instruments.
In addition to the eddy covariance and eddy ac-cumulation methods, fluxes above canopies can been measured using flux-gradient techniques, but this approach is not applicable within the canopy where there is no simple relationship between fluxes and the local scalar gradient (Denmead and Bradley, 1985; Finnigan and Raupach, 1987; Raupach, 1987). This is unfortunate because concentration gradients within canopies are often large and relatively easy to measure. Raupach (1987) developed a Lagrangian ‘Localised Near Field’ (LNF) theory of dispersion in plant canopies which showed that the scalar con-centration at a point within the canopy is a result of contributions from both local and distant sources; hence the non-local relationship between fluxes and gradients.
In its inverse form (Raupach, 1989a,b), the theory does allow us to deduce source/sink strengths from measured concentration profiles and knowledge of the turbulence field within the canopy. The inverse theory has been used to quantify the sources and sinks of water vapour and CO2in wheat and sugarcane crops
(Denmead and Raupach, 1993; Denmead, 1995) and for CO2in a loblolly pine forest (Katul et al., 1997),
but before the new technique can be applied routinely to a variety of ecosystems, its strengths and limitations should be carefully examined.
The aim of this study was to evaluate the perfor-mance of the inverse Lagrangian method for inferring net fluxes and source strengths of heat, water vapour, CO2 and CH4 in a rice canopy. This was done by
above the canopy as reported in a companion paper by Miyata et al. (2000).
2. Theory
2.1. Localised near-field dispersion
The scalar concentration field within a canopy can be viewed as the linear superposition of contributions from all sources. Raupach (1987, 1989a,b) divided the concentration field into a ‘near-field’ part,Cn(z),
dom-inated by the contribution of nearby sources, and a ‘far-field’ part,Cf(z), resulting from the contribution
of distant sources. The near-field is defined as the dis-tance from the source that fluid particles move in a timeτL, the characteristic Lagrangian time scale of
the turbulence, whereas the far-field is the distance from the source a fluid particle travels in times≫τL.
Atmospheric turbulence causes transport of the scalar from the source to the observation point. In the near-field, transport is dominated by coherent eddies, while in the far-field transport is essentially diffu-sive. The LNF theory of Raupach (1987) assumes: (1) that the canopy is horizontally homogeneous at each height so that net transport occurs only in the vertical direction; (2) that near-field transport can be described as if it occurred in homogeneous tur-bulence with standard deviation of vertical velocity
σw(z) and Lagrangian time scaleτL(z) equal to that
at the source height; and (3) the contribution to the concentration field from distant (far-field) sources obeys the diffusion equationFf(z)=−Kf(z) dCf(z)/dz.
The concentration field at any height is the average across an area extending over many canopy elements (Kaimal and Finnigan, 1994).
In the discrete form of the LNF analysis, the canopy is divided into m horizontally homogeneous layers with thickness 1zj and source strengthSj. By sum-ming the emissions from all source layersj(j=1,m), contributions, andCR is the concentration at a
refer-ence height above the canopy. The coefficientsDij of
the dispersion matrix,DDD, describe the turbulent trans-port within and above the canopy. Once theDij are known, the set of linear equations (Eq. (1)) can be in-verted to solve for the source profileSj. The LNF the-ory, which solves the forward problem of predicting concentration profiles from known profiles of sources and turbulence within the canopy, is used to calculate the elements of the matrixDDDas follows.
The near-field concentration profile is determined by the vertical distribution and strength of the sources, and the vertical profiles of σw andτL. Designating the height of a given source aszs, the near-field con-centration profile is given by
Cn(z)=
kernel’ whose analytical approximation is given by Raupach (1989a) as
kn(ζ )= −0.3989 ln(1−e−|ζ|)−0.1562 e−|ζ| (3)
An image source and turbulent flow are introduced into Eq. (2) to ensure a zero-flux boundary condition at the ground for the scalar (Raupach, 1989a).
The far-field concentration profile obeys the gradient-diffusion relationship
F (z)= −Kf(z)dCf(z)
dz (4)
whereKf =σw2(z)τL(z)and where the source strength is related to the flux at heightzby
F (z)=F (0)+
for dispersion from layerjto concentration at height i, i.e.
Dij =
ci −cR s 1zj
(8)
Each element of DDD has a near-field and a far-field component because ci=cni+cfi. We assume a unit source strength in each layer and use Eqs. (2)–(6) to estimate cni andcfi, and hence, the coefficients Dij from Eq. (8).
We can simplify the procedure considerably if we assume that the turbulent structure (and hence the Dij) scales withu∗. In this case, once the scalar sam-pling heights and the normalised profiles for σw(z)
and τL(z) have been adopted (see Fig. 1), we need
only calculate the dispersion coefficients once us-ing the above integration procedures. From then on Dij (with dimensions of resistance) scale according to Dij=Dij ,refu∗,ref/u∗, where the Dij ,ref have been
computed using a reference valueu∗,ref. 2.2. Profiles forσw,τLand Kf
To evaluate the dispersion coefficients required in Eq. (1), the profiles of σw(z) and τL(z) within and
above the canopy must be specified for a Lagrangian
Fig. 1. Normalised profiles of the standard deviation of verti-cal velocity,σw/u∗, the Lagrangian time scale, τLu∗/hc, and the
far-field diffusivityKf/(u∗hc) as a function of normalised height,
z/hc. Theoretical profiles of the latter two quantities for neutral
stratification in the inertial sublayer above the canopy are also shown. The measured composite profile ofσw/u∗and the standard
deviations of the measurements obtained using a miniature sonic anemometer are indicated by circles.
Table 1
List of variables and parameter values used to describe normalised profiles of the Lagrangian time scale,τLu∗/hc, and the standard
deviation of vertical velocity,σw/u∗a
z/hc x y θ a b d
≥0.25 z/hc−0.8 τLu∗/hc 0.98 0.256 0.40 +1
<0.25 4z/hc τLu∗/hc 0.98 0.850 0.41 −1
>0.8 z/hc σw/u∗ 0.98 0.850 1.25 −1
aSee Eq. (10).
(moving) coordinate frame, but measurements are made relative to fixed coordinates. Finding τL(z) is difficult and will be considered below, but there is no problem forσw(z), because it is the same in both
co-ordinate systems and hence can be measured directly. To describe the normalised profiley=σw/u∗, an ex-ponential function (Eq. (9)) was used up toz/hc=0.8,
and a non-rectangular hyperbola (Eq. (10)) above that height, i.e.
y=c1ec2x, z <0.8hc (9)
y= (ax+b)+d p
(ax+b)2−4θabx
2θ , z≥0.8hc
(10)
wherex=z/hcis the normalised height,hcthe canopy height, and θ is the parameter describing the curva-ture of the hyperbola. Good agreement was obtained between direct observations and the fitted functions (Fig. 1) using the parameter values given in Table 1 and with c1=0.2, c2=1.5. The limiting value of σw/u∗ well above the canopy was set to 1.25, which is appropriate for the inertial sublayer under neutral conditions (Kaimal and Finnigan, 1994), even though this is a little higher than the mean of the measure-ments. With the hyperbolic formulation,σw/u∗=1.25 is not attained until z/hc=2.5, in conformity with
the summary of observations reported by Raupach (1989b), and consistent with the mixing-layer hy-pothesis for canopy flow developed by Raupach et al. (1996). Note also that asz→0 Eq. (9) results inσw(0)→c1rather thanσw(0)→0. This was done to ensure that turbulent fluxes are not forced to zero at the ground, and we discuss later the sensitivity of estimated source/sink strengths to the choice of the
σwprofile close to the ground.
The shape of theτLu∗/hcprofile remains somewhat
ofτL(z). We know that in the inertial sublayer (which
typically begins at z/hc>≈2, Kaimal and Finnigan,
1994) we are outside the near-fields of any canopy sources and thus the diffusion equation (Eq. (4)) applies. In this region, turbulent transport in the neu-trally stratified atmosphere is well described by the Monin–Obukhov similarity relationships (Kaimal and Finnigan, 1994), and Kf=ku∗(z−d). Matching this withKf=τLσw2, the expected form of the Lagrangian
time scale in the inertial sublayer is
τLu∗
whered is the zero-plane displacement andk is the von Karman constant (0.4).
In the roughness sublayer (z/hc<≈2), turbulent
transport is dominated by coherent eddies associated with the strong inflection in the mean velocity profile at the top of the canopy (Kaimal and Finnigan, 1994; Raupach et al., 1996). This produces a single dom-inant turbulence length scale, Ls ∝ U (hc)/U′(hc),
whereU(hc) is the mean velocity athcandU′=dU/dz.
According to Raupach et al. (1996), the correspond-ing Lagrangian time scale isτL≈0.7Ls/σw. Using the
observed value ofσw/u∗=0.9 at the top of the canopy (Fig. 1) and a typical value of Ls/hc=0.5 (Raupach et al., 1996), we obtain τLu∗/hc=0.4. At heights z/hc<0.25, the turbulent time scale is influenced by
the presence of the ground, and the normalised time scale is allowed to decrease from 0.4 atz/hc=0.25 to
0 atz/hc=0. To avoid discontinuities at the transition
between the these regions, Eq. (10) was again used to describe the three sections of the profile. The ap-propriate x variable and parameter values are given in Table 1, with the resultant profile shown in Fig. 1. Except for the linear reduction in τLu∗/hc below z/hc=0.25, this profile is a smoothed version of the
linear-piecewise form adopted by Raupach (1989b). Use of the Lagrangian time scale profile shown in Fig. 1 leads to good qualitative agreement between the predicted shape of theKf profile (Fig. 1) and the wind tunnel results of Brunet et al. (1994; Fig. 6) for z/hc<2.5 (wind tunnel results above this height are in
doubt because the wind tunnel boundary layer was insufficiently deep relative to canopy height). Finally, excellent matching of fluxes for sensible heat, water vapour and CO2 as measured using eddy covariance
and those deduced from the inverse analysis (see
below) provides further indirect, a posteriori support for theτLu∗/hcprofile adopted.
2.3. Number of source layers
Matrix algebra may be used to invert Eq. (1) to determine source strength profiles, Sj, from mea-sured profiles ofCi, and the calculatedDij. However, both Ci, and Dij contain errors, and instabilities in the solution arise when we attempt to infer source strengths for the same number of layers as the num-ber of heights at which concentrations are measured. To overcome this problem, Raupach (1989b) recom-mended that redundant concentration data be included so that source densities Sj in m layers are sought fromnconcentration measurements, withn>m.
The maximum number of source layers that can be extracted from concentration measurements at n heights is determined by the ‘information content’ of the dispersion matrixDDD, information which can be obtained using the technique of singular value decomposition (SVD, Press et al., 1992). This anal-ysis decomposes then×mmatrixDDDinto the product of an n×m column-orthogonal matrix,UUU, an m×m diagonal matrixWWW with diagonal elements wj (the singular value matrix), and the transpose of anm×m orthogonal matrixVVV according to
D
DDn×m=UUUn×mWWWm×mVVVTm×m (12)
The singular values are positive and are arranged down the diagonal of WWW in decreasing magnitude according to the indexj, withwj ≥wj+1.
In terms of the SVD components, the solution of Eq. (1) for the source vectorSSS is given by (Press et
Note that the singular values appear in the denomi-nator of Eq. (13), and thus, the sensitivity of the so-lution to errors in wj (i.e. to errors in the disper-sion coefficients) increases with the indexjdue to the increasingly small values ofwj. The absolute mini-mum in the residuals of the solution (Eq. (13)) is ob-tained by inclusion of allwj, but Press et al. (1992) recommend including only those equations such that
the best least-squares fit and sensitivity of the solution to errors in the matrix operatorDDD. Using the criterion
α=0.01, six is the maximum number of source lay-ers that can be obtained from the eight concentration measurement heights used in this study. However, the number of layers finally adopted was reduced to five because errors in the measured scalar concentrations also contributed to instability of the inversion analysis.
3. Experimental site and methods
3.1. Study site
Measurements were made in a rice paddy located at the agricultural station of Okayama University (34◦32′N, 133◦56′E) from 6 to 13 August 1996. The field measured ∼300 m×300 m and was surrounded by similar rice fields in all directions, providing a fetch of >400 m in the prevailing SE wind direction. Average plant height was 0.72 m during the obser-vation period, row spacing was 0.29 m and leaf area index measured using a canopy analyser LAI-2000 (LiCor Inc., Lincoln, NE, USA) was 3.1±0.3 (S.D.). The normal weekly irrigation cycle consisted of flood-ing for 4 days followed by a drained period of 3 days. The field was drained on the afternoon of 6 August until midday on 9 August, and the mean water depth during flooding thereafter was 0.08–0.10 m.
3.2. Measurement of temperature, water vapour, CO2and CH4profiles
Temperature and relative humidity profiles were measured using Humitter sensors (Vaisala Oy, Helsinki, Finland) housed in double-walled radi-ation shields ventilated at >3 m s−1. Air inlets to
the radiation shields were located at eight heights above the water, 0.12, 0.24, 0.36, 0.48, 0.60, 0.72, 1.10 and 2.40 m The sensors were calibrated using a high-precision temperature/humidity chamber to a precision of 0.05◦C in both temperature and dewpoint. Before the experiment, the sensors were also placed at the same height to provide an inter-calibration of the instruments.
Concentrations of CO2 and CH4 were measured
using non-dispersive infrared analysers, an LI-6251 (LiCor Inc., Lincoln, NE USA) for CO2, and a
GA-360E (Horiba, Kyoto, Japan) for CH4(Miyata et al.,
2000). The latter instrument was equipped with an air pre-conditioner to minimise the interference of non-methane hydrocarbons and water vapour in non-methane analysis (Harazono et al., 1998). The methane analyser was calibrated between 09:00–10:00 and 17:00–18:00 hours each day using a reference cylinder of high grade air containing 1.7 ppmv CH4 (Takachiho, Tokyo,
Japan). The CO2analyser was calibrated at the same
time using two reference cylinders with 350 and 400 ppmv CO2in N2(Takachiho, Tokyo, Japan).
Air was sampled for gas analysis at the same eight heights as the temperature sensors, plus an extra line for reference air at 2.50 m. For each line, a diaphragm pump sampled air continuously through 10 mm i.d. nylon tubing, through an ice-trap to reduce moisture content, into a cylindrical PVC buffer (70 dm3in
vol-ume), and then to a T-junction. A tube connected to the second arm of the T junction was immersed in a water tank 600 mm deep to control the air pressure and flow rate in the sampling line, and to vent excess air when not required for gas analysis. The third arm of each T-junction was connected to a solenoid valve and man-ifold to permit selection of each sampling line in turn for gas analysis. Air from a selected line was passed through flow meters, dried to a dew point of 2◦C us-ing a Peltier cooler condenser, before beus-ing split and passed through the CO2and CH4analysers. For CO2
analysis, reference and sample air lines were brought to the same pressure before the analyser by venting excess air through water bubblers 60 mm deep. For CH4, reference and sample air were passed to the
pre-conditioning unit. A full sampling sequence was completed in 30 min. The standard error of concen-trations measured by the CH4analyser was 2.5 ppbv
when it was used in fast-response mode and 1.0 ppbv in slow-response mode. The corresponding figure for the CO2 analyser is 0.2 ppmv. These error estimates
are more relevant than the absolute errors induced by uncertainties in the calibration gases because the anal-ysis of source/sink distributions utilises profiles of the difference in concentration between each level and a reference level (Eq. (6)).
3.3. Turbulence measurements
various heights within the canopy to measure σw.
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 σw/u∗. as a function of z/hc,
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 CO2, FCO2 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 CO2 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 toHandE(Webb et al., 1980), and for the cross-sensitivity of the CO2
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 CO2 were
used as ‘tracers’ to evaluate the eddy diffusivity, K, required in
FCH4 = −ρaK
MCH4
Ma
dsCH4
dz (14)
wheresCH4 is the mixing ratio of CH4relative to dry
air andρais the density of dry air, andMa andMCH4
are the molecular masses of dry air and CH4,
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. 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 and/or by the very small u∗ (and hence σw andτL) 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−2of 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 toλE.
Estimates of evaporation from the soil/water 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 soil/water. Mid-day values ofλEfor 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 σw profile within the canopy so that σw→0.2
at the ground. In a separate analysis, Eq. (10) was used to decreaseσw linearly through the bottom half
of the canopy to ensure that σw=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 σw)
except within a very thin layer above the soil surface. In future, measurements should be made close to the ground to resolve the behaviour ofσw (andτL) close
to the ground.
4.2. Carbon dioxide profiles
Profiles of differential CO2concentrations 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 CO2
Fig. 4. Profiles of CO2 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 CO2 during the day.
The second lowest canopy layer was also respiring at 08:00 hours but was a net sink for CO2by 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 CO2 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 CO2
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 forσw andτL. 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 CO2measured above the canopy at 2.2 m
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 CO2
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 CO2 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 critilo-cal. 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 informadistribu-tion is, by definidistribu-tion, lost in the far field.
4.3. Time series for heat, water vapour and CO2
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 estimateu∗. 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 measuremgradi-ents. 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 CO2above the canopy at 1.05 m and within the canopy
Fig. 7. Time series for cumulative fluxes of sensible heat, latent heat and CO2 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 CO2 fluxes at 0.14 m are also
shown. Note the differing scales forHandλE.
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 CO2had 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 CO2at 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 ofu∗were<0.1 m s−1on 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 anoctur-nalysis 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 CO2to 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 CO2uptake
may be due in part to a greater upward CO2flux from
the drained soil than from the floodwater, as suggested by Fig. 7. Average fluxes of CO2at 0.14 m were 0.318
(S.E. 0.036, n=45) mg CO2 m−2s−1 for 8 August
when the field was drained, more than double the value of 0.134 (S.E. 0.015) mg CO2 m−2s−1 for 11
Au-gust when the paddy was flooded. While the CO2flux
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 CO2within
the water to low levels (Ohtaki, 1999, personal com-munication) and causes a downward diffusion of CO2
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 CH4concentrations relative
Fig. 8. Measured and smoothed profiles of CH4 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=a1+a2exp(−a3z) 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 CH4were 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 CH4.
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 CH4produced 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 CH4source at the soil/water 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=a1+a2exp(−a3z) 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 CH4are 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 CH4 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 CH4fluxes
Fig. 9. Cumulative flux profiles for CH4 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 CH4fluxes 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 CH4as 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 CH4
m−2s−1, compared to 0.318 (S.E. 0.040) and 0.388
(S.E. 0.030)mg CH4m−2s−1for 11 and 12 August,
respectively.
As with CO2 fluxes, the inverse analysis
overesti-mates CH4fluxes 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 CH4emission 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-terminingu∗ at night will propagate directly through the inverse analysis through estimates ofσw andτL
and hence the dispersion coefficientsDij. 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 theDij, and it, thus, is likely that they have beenunderestimatedfor stable, nocturnal conditions, causingoverestimates 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 source/sink distributions within the canopy. When applied initially using measured profiles of temperature, water vapour and CH4 the
Fig. 10. Time series for cumulative fluxes of CH4 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 τL(z) and σw(z). The
problem was partially overcome by using smooth functions forτL(z) andσw(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 CH4
concentration measurements. No smoothing was ap-plied to the CO2profiles 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 partitionunderstand-ing, and the mechanism of CH4 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 source/sink 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 σw
andτL.
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 CO2 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 CO2
profiles (Fig. 4). An identical approach was adopted for measurement of CH4concentrations 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.
and uncertainties of regional source/sink strengths of CO2across the globe, while Kandlikar (1997) used a
similar approach for estimating source/sink strengths for CH4 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 CH4 source strengths for the inverse
analysis.
As noted above, fluxes for both CO2 and CH4 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,Dij (re-sistances), and hence, to overestimates of the fluxes. Leuning (2000) examines whether Monin–Obukhov similarity theory may be used to adjustτL(z) andσw(z)
within and above plant canopies to provide corrections for stability.
6. Conclusions
Source distributions for heat, water vapour, CO2
and CH4 within a rice canopy were derived using
an inverse Lagrangian analysis of turbulent disper-sion of scalars. Results for the cumulative fluxes of heat and water vapour and CH4 were plausible
once their respective concentration profiles were smoothed using simple analytic functions. Accord-ing to the inverse analysis, water vapour was emitted relatively uniformly by each of five layers within the canopy, whereas sensible heat fluxes were small (<100 W m−2) and of either sign. Methane fluxes
were predicted to be emitted most strongly in the lower 50% of the canopy, as expected from the dis-tribution of micropores along leaves and leaf sheaths, the major pathway for CH4 loss from the soil–crop
system. No smoothing was required for CO2 and the
inverse analysis provided close correspondence be-tween the turning point in the concentration profile and the changeover from respiration of the lower canopy to net photosynthesis of the upper canopy. Fluxes of CO2 in the lowest layer were always
posi-tive (net respiration), with values being higher when the soil was drained rather than flooded. Part of the enhancement is attributed to removal of the diffusion barrier caused by the floodwater.
Excellent agreement was obtained between cumu-lative fluxes of heat, water vapour, CO2 and CH4 at
the top of the canopy from the inverse analysis and direct eddy covariance measurements when the fric-tion velocityu∗>0.1 m s−1, and atmospheric stability was approximately neutral. Nocturnal fluxes of CO2
and CH4from the inverse method exceeded
microme-teorological measurements above the canopy by a fac-tor of 2–3 whenu∗<0.1 m s−1and stable atmospheric conditions prevailed. Neglect of these stability effects will lead to an underestimate of the dispersion coeffi-cients (resistances) in the transport model and hence an overestimates of the fluxes.
Acknowledgements
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