Footprint prediction of scalar fluxes from analytical solutions of the diffusion equation

The use of analytical solutions of the diffusion equation for footprint prediction is explored. Quantitative information about the footprint, i.e., the upwind area most likely to affect a downwind flux measurement at a given height z, is essential when flux measurements from different platforms, particularly airborne ones, are compared. Analytical predictions are evaluated against numerical Lagrangian trajectory simulations which are detailed in a companion paper (Leclerc and Thurtell, 1990). For neutral stability, the structurally simple solutions proposed by Gash (1986) are shown to be capable of satisfactory approximation to numerical simulations over a wide range of heights, zero displacements and roughness lengths. Until more sophisticated practical solutions become available, it is suggested that apparent limitations in the validity of some assumptions underlying the Gash solutions for the case of very large surface roughness (forests) and tentative application of the solutions to cases of small thermal instability be dealt with by semi-empirical adjustment of the ratio of horizontal wind to friction velocity. An upper limit of validity of these solutions for z has yet to be established.     

Turbulent transfer at the ground: On verification of a simple predictive model

Observations on heat transfer from ground-based plates and evaporation from free water surfaces in the laboratory and in the field are compared with predictions from a simple model. The model relates the convective transfer coefficient (or boundary-layer resistance) at any point on a surface to the momentum transfer (friction velocity) in the boundary layer immediately above it and should be applicable to practically any soil surface, open or vegetated.Heat-transfer data showed a standard deviation of 25%; between predictions and observations. Evaporation data provided only order-of-magnitude confirmation of the model because of uncertainty in effective water vapor density above small free-water surfaces.     

Studies of forced-convection heat and mass transfer of fluttering realistic leaf models

The forced-convection mass transfer - and by analogy, heat transfer - of various realistic leaf models at Reynolds numbers 2 x 10³<Re<4 x 104 was studied with an electrochemical method. The results are compared with similar measurements on plates and with transfer coefficients calculated from the laminar boundary-layer theory. In this way the validity of the commonly-used analytical expressions which represent the leaf by a rigid plate and neglect the effects of leaf curvature, fluttering, surface roughness and fluid turbulence, can be tested.The measurements show that for fluttering single leaves, the convective mass-transfer coefficients must be expected to be higher by a factor of 1.4 ± 0.1 than the ones calculated for rigid plates of equal size and shape. For a leaf in a crop, the increase might be as high as a factor of 2. The high transfer coefficients measured for elements of cedar foliage are also discussed.     

The impact of using area-averaged land surface properties —topography, vegetation condition, soil wetness—in calculations of intermediate scale (approximately 10 km) surface-atmosphere heat and moisture fluxes

It is commonly assumed that biophysically based soil-vegetation-atmosphere transfer (SVAT) models are scale-invariant with respect to the initial boundary conditions of topography, vegetation condition and soil moisture. In practice, SVAT models that have been developed and tested at the local scale (a few meters or a few tens of meters) are applied almost unmodified within general circulation models (GCMs) of the atmosphere, which have grid areas of 50–500 km². This study, which draws much of its substantive material from the papers of Sellers et al. (1992c, J. Geophys. Res., 97(D17): 19033–19060) and Sellers et al. (1995, J. Geophys. Res., 100(D12): 25607–25629), explores the validity of doing this. The work makes use of the FIFE-89 data set which was collected over a 2 km × 15 km grassland area in Kansas. The site was characterized by high variability in soil moisture and vegetation condition during the late growing season of 1989. The area also has moderate topography.

The 2 km × 15 km ‘testbed’ area was divided into 68 × 501 pixels of 30 m × 30 m spatial resolution, each of which could be assigned topographic, vegetation condition and soil moisture parameters from satellite and in situ observations gathered in FIFE-89. One or more of these surface fields was area-averaged in a series of simulation runs to determine the impact of using large-area means of these initial or boundary conditions on the area-integrated (aggregated) surface fluxes. The results of the study can be summarized as follows:

1. 1. analyses and some of the simulations indicated that the relationships describing the effects of moderate topography on the surface radiation budget are near-linear and thus largely scale-invariant. The relationships linking the simple ratio vegetation index (SR), the canopy conductance parameter (_F) and the canopy transpiration flux are also near-linear and similarly scale-invariant to first order. Because of this, it appears that simple area-averaging operations can be applied to these fields with relatively little impact on the calculated surface heat flux.

2. 2. The relationships linking surface and root-zone soil wetness to the soil surface and canopy transpiration rates are non-linear. However, simulation results and observations indicate that soil moisture variability decreases significantly as an area dries out, which partially cancels out the effects of these non-linear functions.In conclusion, it appears that simple averages of topographic slope and vegetation parameters can be used to calculate surface energy and heat fluxes over a wide range of spatial scales, from a few meters up to many kilometers at least for grassland sites and areas with moderate topography. Although the relationships between soil moisture and evapotranspiration are non-linear for intermediate soil wetnesses, the dynamics of soil drying act to progressively reduce soil moisture variability and thus the impacts of these non-linearities on the area-averaged surface fluxes. These findings indicate that we may be able to use mean values of topography, vegetation condition and soil moisture to calculate the surface-atmosphere fluxes of energy, heat and moisture at larger length scales, to within an acceptable accuracy for climate modeling work. However, further tests over areas with different vegetation types, soils and more extreme topography are required to improve our confidence in this approach.

     

Laboratory studies on dry deposition of submicron-size particles on coniferous foliage

The deposition of 0.03 m particles to an assembly of 10 spruce shoots and a synthetic juniper shoot was studied by electrochemical transfer under conditions of Re and Sc similarity at flow velocities corresponding to wind speeds of 0.1 to 3 m s^–1.The concept of representing transfer to needle-type foliage by that to cylinders in crossflow, with adjustment factors for angle of incidence and for mutual interference of cylinders (needles), however imprecise, appears to be sufficient to interpret the results. The transfer data follow approximately a Re^1/2 relationship with respect to flow velocity and the mass transfer coefficient calculated for cylinders in crossflow with a shelter factor of the order of 2, to account for reduction in transfer due to mutual interference of needles, can be expected to be a reasonable first approximation of the deposition velocity.Applications of the results to forest stands show very little absorption by stands of limited extension; distances of the order of kilometers would be required to reduce airborne concentrations to 1/e of their initial value for aerosol with negligible sedimentation and inertial impaction.     

Aircraft measurements of CO2 exchange over various ecosystems

The National Aeronautical Establishment's Twin Otter Atmospheric Research Aircraft has been equipped with open-path CO₂ analyzers in order to obtain estimates of CO₂ exchange over a corn field, a forest and a lake using the eddy correlation technique. On the 18th of August 1980, mean uptakes obtained over corn and forest were 12 and 8 kg CO₂ ha^-1 hr^-1, respectively. On the 28th of August, mean uptakes obtained over corn, forest and the lake were 36, 14, and 1 kg CO₂ ha^-1 hr^-1, respectively. The data are discussed in the light of general conditions on the two days.     

Observations on the use of analytical and numerical models for the description of transfer to porous surface vegetation such as lichen

Convective deposition of submicron-size aerosol to porous surface vegetation was studied by electrochemical simulation, under Reynolds and Schmidt similarity, to a rectangular array of closely-packed lichen and artificial wire roughness layers. Results, showing an approximate tenfold increase in deposition velocity over that of a flat plate placed at the same position, were compared with predictions made on the basis of various rough-surface transfer models, including those based on statistical eddy renewal, as well as with numerical solutions of the diffusion equation in statistically-renewed surface cavities. Most analytical models could be made to fit the observed data, at least for a limited range of flow velocities, but poorly known and poorly defined parameters limit their usefulness for predictive purposes; and their validity across a large variation in molecular diffusivity (or Schmidt number Sc) is generally not assured. Numerical models also depend on poorly substantiated physical assumptions but the effect of such assumptions on transfer can be calculated for a wider range of conditions than those permitting an analytical solution. This allows more direct feedback between model assumptions and calculated or observed transfer. Numerically calculated values for deposition velocity in air for Sc from 0.7 to 7000 and flow velocities from 0.2 to 5 m s^-1 are presented for different model assumptions, with values ranging from < 0.01 to > 1 cms^-1.