Oxygen Transport to Plant Roots: Modeling for Physical Understanding of Soil Aeration

Although there appears to be some evidence to suggest that the concentration of CO2 in the soil may have A model that couples the diffusion of O2 to plant roots at the an effect on plant growth, the major effect of poor microscale to diffusion of O2 through the soil at the macroscale is derived. The solution is complex, but if the length scales (Zr and Zm; aeration on plant growth is the lack of O2 (Gliński and see APPENDIX for list of symbols) are equated a simple analytical Stępniewski, 1985). Like field capacity, soil aeration is expression can be obtained. This model is used to investigate relationa term that has an empirical basis and many different ship between a critical air-filled porosity ( m) and the other paramedefinitions. There are a number of different indices for ters; viz temperature (T ), O2 concentration in the bulk soil (C*), O2 defining the aeration status of a soil. These include: gasconcentration at the root surface (Cr), root length density (L ), the filled porosity (Wesseling and van Wijk, 1957; Jayawarratio of root radius (a ) to the water film radius (R ), microbial respiradane and Meyer, 1985; Gliński and Stępniewski, 1985), tion (Mo), and length scales (Zm and Zr) related to the depth to which the ODR (Lemon and Erickson, 1952; Letey and Stolzy, microbial and plant respiration are active in the model using sensitivity 1967; McIntyre, 1970; Armstrong and Wright, 1976; Blackanalysis. The model shows that m is not very sensitive to the O2 well, 1983), and O2 concentration or partial pressure concentration at the root surface (Cr), or the ratio of root radius (a )/ water film radius (R ), but is sensitive to all the other parameters in (Grable, 1966; Armstrong and Gaynard, 1976; Blackwell some part of their range. The results indicate that indices used to define and Wells, 1983; Meyer and Barrs, 1991). However, soil aeration; O2 diffusion rate (ODR) or O2 flux, O2 concentration, or there has not been a good theoretical basis for investiair-filled porosity, which have been previously used, are related and gating the validity of these indices for assessing the a single critical value for these is unlikely. If a constant critical value aeration status of a soil or their correlation. Traditionexists for one of these indexes it cannot exist for the other two. It is ally, the concept of soil aeration has been based on a also shown that it is highly unlikely that a universal critical parameter correlation between plant performance and these varirelated to soil aeration exists for any of these parameters. It is conous indices of the O2 status of the soil. cluded that more parameters than ODR, O2 concentration, or air-filled At a physiological level, the minimum aeration status porosity need to be measured if progress in soil aeration research is occurs when the flux of O2 to the root surface, especially to be made. the root tip, is just able to meet the O2 demand of the root tissues. The transport of O2 to a plant root occurs first through diffusion from the atmosphere via the gasT concept of a nonlimiting water range (NLWR) filled porosity of the soil to the depth of the root, and was introduced by Letey (1985). This has been rethen through a boundary layer surrounding the root. cently called the least limiting water range by da Silva Most previous studies in this area have considered this and Kay (1997a, 1997b). For the NLWR to be identified boundary layer around the root to be liquid-filled porosthe water content at which O2 supply to plants becomes ity, because as Bernstein et al. (1959) stated, otherwise limiting needs to be known or measured. The introducthe plant would have to have a refrigeration system if tion and attempted uses of the NLWR concept has again water was transported to it via a vapor gap. This liquid highlighted the lack of a good definition for soil aerafilled boundary layer was considered by Letey and Stolzy tion. Here we will attempt to put such a definition on (1967) to be cylindrical. This assumption of a circular a sounder physical basis. boundary layer was criticized by McIntyre (1970) as For most plants to grow in soil, a proportion of the being highly unlikely given the heterogeneity of pore pore space needs to be gas-filled. The gas-filled proporsize found in soil (Fig. 1). In this study the boundary tion of the pore space allows the influx of O2 into, and layer will be assumed cylindrical, as without such an the efflux of CO2 from the soil. The consumption of O2 assumption the mathematics becomes very difficult. The in the soil and production of CO2 is because of the value of this radius is taken as that which gives the same oxidative demands of plant roots, microorganisms, and radial gas flux through the boundary layer as would chemical reactions. The status of a soil in relation to be measured. the proportion of gas-filled pores and the concentration In this study we will derive the relationships between of O2 and CO2 in the soil is often referred to as the respiration rate of roots and the transport processes at aeration status of the soil. The effect of aeration on the microscale (root scale) and couple this with the plant growth has been reviewed recently by Gliński and transport of O2 with root and microbial respiration as Stępniewski (1985). distributed sinks at the macroscale (bulk soil). The resulting solutions of the differential equations will be F.J. Cook, CSIRO, Land and Water, 120 Meiers Road, Indooroopilly used to define soil aeration in terms of the physical and QLD 4068, Australia and CRC for Sustainable Sugar Production; J.H. Knight, CSIRO, Land and Water, P.O. Box 1666, Canberra ACT biological parameters of the system and to determine 2601, Australia. Contribution from CSIRO Land and Water. Received 11 Dec. 2000. *Corresponding author ([email protected]). Abbreviations: NLWR, nonlimiting water range; ODR, O2 diffusion rate. Published in Soil Sci. Soc. Am. J. 67:20–31 (2003).