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A new method for analysing spatial patterns was designed based on the variance of moving window averages (VMWA), which can be directly calculated in geographical information systems or a spreadsheet program (e.g. MS Excel). Different types of artificial data were generated to test the method. Regardless of data types, the VMWA method correctly determined the mean cluster sizes. This method was also employed to assess spatial patterns in historical plant disease survey data encompassing both airborne and soilborne diseases. The results obtained using the VMWA method were generally different from those obtained with Lloyd's index of patchiness and beta-binomial distribution methods, were in partial agreement with the results from spatial analysis by distance indices, and were highly consistent with the results from semivariogram and spatial autocorrelation analysis methods. Results demonstrated that the VMWA method can be applied to many types of data, including binomial diseased or healthy plant counts, incidence, severity, and number of diseased plants or pathogen propagules although directional and edge effects may limit its application.

The effect of solute concentration on sorption kinetics may be a factor in determining bioavailability and transport of organic pollutants in soils and sediments, but there is conflict in the literature over whether sorption is concentration-dependent. Sorption of phenanthrene and pyrene to seven soils ranging in organic carbon (OC) content from 0.18 to 43.9% was studied. Careful analysis revealed that experimentally the normalized rate of approach to equilibrium for compounds exhibiting a concave-down (with respect to the solute concentration axis) nonlinear isotherm increases with concentration. However, the effect is rather small and is most apparent when the fraction of total solute finally taken up by the solid (F) is low. The explanation is rooted in the nonlinearity of the isotherm and the finite-bath condition of the experiment and can be expressed in terms of two opposing effects. On the one hand, the apparent diffusivity of a (concave-down) nonlinearly sorbing compound within particles increases with concentration because its affinity for the solid phase decreases with increasing concentration. On the other hand, rates in finite-bath reactors carried out at the same liquid/solid ratio will suffer from a batch process temporal bias called the "shrinking gradient" effect. It is an artifact of the methodology and is due to gradient driving forces that slow the sorption rate as F declines. In nonlinear cases F declines as concentration increases. The shrinking gradient effect vanishes as the liquid/solid ratio approaches infinity. Although this effect is self-correcting when an appropriate nonlinear diffusion model is applied, consensus about such models has not yet been achieved. To provide bounds for the shrinking gradient effect in finite-bath systems semiempirically, two models that give lower and upper bounds of the characteristic sorption time tau in the limit of infinite bath have been employed: (a) a wetting front model, which assumes sorption is rate-limited by molecular migration, and (b) a fast diffusion model, which assumes a mass-transfer resistance at the sorption site. The results are consistent with an intrinsic positive concentration dependence of sorption kinetics.

Open flow-through systems coupled to infrared gas analyzers have been frequently employed in the study of CO(2) exchange transients such as the postillumination burst observed in leaves of C(3) plants. A major limitation associated with use of such systems is their non-steady state response to rapid changes in leaf CO(2) exchange rate. A previous publication outlined a numerical approach to model the analyzer response as a function of CO(2) exchange rate and thus permit estimation of the postillumination burst (Peterson 1983 Plant Physiol 73: 978-982). The model is critically analyzed within the framework of the physics of solute dispersion as previously described for linear flow systems. Thus, the numerical simulation is validated on the basis of physical principle. Additional improvements to the previous model are described which enhance the accuracy and efficiency of use of this technique for estimation of photorespiration.