By assuming that ¢T is at isotopic "steady state" (transpired vapour = stem water), there is no condensation, and source contributions do not change over the collection period, the fractional contribution from transpiration, FT is given by:
FT (%)= (dET-dE)/(dT-dE) x100
where dE is the d18O of the water vapour evaporated from the soil surface, dET is the d18O of the water vapour evaporated from the crop surface and dT is the d18O of the water vapour transpired by the foliage of the crop. In our study, similar calculations were made for d2H.
Lagrangian dispersion analysis provides a means of linking canopy sources and sinks with mean concentration profiles using statistics of the turbulence in and above the canopy. Forward Lagrangian dispersion analysis predicts mean concentration profiles generated by given canopy source distributions. As described by Raupach (1989), it uses a Lagrangian (fluid-following) framework to track an ensemble of "marked fluid particles" as they disperse. It recognizes 2 modes of dispersion: near the source, coherence of eddies causes particles to travel in straight lines; far from it, trajectories resemble random walks. This description is called linearised near-field theory. The analysis of Raupach (1989) calculates the contributions of each mode to the concentration at any point in the canopy.
Inverse Lagrangian dispersion analysis does the reverse of the forward analysis; it predicts source profiles from mean concentration profiles. The dispersion equation employed in both analyses uses information on the turbulence and gas concentrations in the canopy to relate the concentrations at any level to the source strengths at all levels. The necessary turbulence statistics are the friction velocity u*, the standard deviation of the vertical velocity sw and the Lagrangian time scale TL (a measure of eddy coherence). The analysis calculates the contributions of the various canopy layers to the net flux.
For stable solutions, the number of concentration measurements (n) should be > number of prescribed source layers (m). This allows for error minimization. Typically, for m=4, n=8; the bottom layer includes contributions from the ground. (The wheat in our study was only 23 cm high. Because the crop was so small, there were only 4 measurement heights in the canopy, and 2 above it, and m was set at 3). sw(z) can be measured, but TL must be inferred from theory or canopy turbulence models such as 2nd order closure. The analysis is dependent on atmospheric stability; corrections need to be applied. For these, we have followed the developments of Leuning (2000). The Inverse Lagrangian technique has been used extensively to identify sources and sinks of heat, water vapour, CO2, ammonia and other gases in forests and crops.
The study was conducted in a wheat field at the Universitaet fuer Bodenkultur in Vienna, Austria. Fluxes of sensible heat, water vapour and momentum above the canopy were measured with a Campbell Scientific CSAT3 sonic anemometer and a LI-COR 7500 H2O/CO2 gas analyser, mounted at a height of 2.5 m above ground. 30-min vertical profiles of water vapour concentration and d2H and d18O were measured with a Picarro analyser drawing air from intakes at heights within the wheat canopy of 0.02, 0.09, 0.16, and 0.23 m above ground and from intakes above the canopy of 0.75 and 1.5 m. The gradients were small over night, but large by day. Evidence of the high quality of the water vapour analyser was that it was able to detect differences between top and bottom of the small 0.23 m canopy from 0.1 to 1.9 hPa during an example day.
Filtering for low wind speeds and extreme atmospheric stability conditions are necessary for successful application of the IL analysis. In this study they removed 44% of a potential total of 421 30-min runs. For the retained runs, the eddy covariance approach (virtually an assumption-free direct method) confirmed the correctness of the inverse Lagrangian analysis for the total water loss from the canopy (to within 6%).
The IL and the isotopic analyses gave essentially the same partitioning of evapotranspiration into E and T: for 3 example days on a dry soil, isotopic analysis using 18O gave E/ET ~ 4% and T/ET ~ 96%, while IL analysis gave corresponding figures of 6% and 94%.
The exercise provided a nice confirmation of the credibility of different approaches, but while validating the predictions of the isotopic analysis in this instance, it should be repeated with a higher LAI and a higher soil moisture content. The IL analysis is a very useful tool for studying canopy gas exchange, particularly when it occurs at all canopy levels (as for H2O), or where there is a 2-way exchange between plant and atmosphere (as for CO2 and NH3), or where the source is the soil (as for N2O & CH4).
Leuning, R., 2000.Estimation of scalar source/sink distributions in plant canopies using Lagrangian dispersion analysi: Corrections for stability and comparison with a multi-layer canopy model. Boundary-Layer Meteorol. 96: 293-314.
Raupach, M.R., 1989. Applying Lagrangian fluid mechanics to infer scalar source distributions from concentration profiles in plant canopies. Agric. For. Meteorol. 47: 85-108.