A Two-dimensional, Dynamic Model for Root Growth Distribution of Potted Plants

A two-dimensiona l mathematical model was developed to describe the time course of root growth and its spatial distribution for container-grown plants, using chrysanthemum (Dendranthema ×grandiflorum (Ramat.) Ki- tamura) as the model system. Potential root growth was considered as consisting of several concurrent processes, including branching, extension, and death. Branching rate was assumed to be related sigmoidally to existing root weight density. Root growth extension rate was assumed to be proportional to the existing root weight density above some threshold root weight density in adjacent cells. The senescence rate of root weight density was assumed to be proportional to existing root mass. The effects of soil matric potential and temperature on root growth were quantified with an exponential function and the modified Arrhenius equation, respectively. The actual root growth rate was limited by the amount of carbohydrate supplied by the canopy to roots. Parameters in the model were estimated by fitting the model to experimental data using nonlinear regression. Required inputs into the model included initial root dry weight density distribution, soil temperature, and soil water potential data. Being a submodel of the whole-plant growth model, the supply of carbohydrates from canopy to roots was required; the total root weight incremental rate was used to represent this factor. Rather than linking to a complex whole-plant C balance model, the total root weight growth over time was described by a logistic equation. The model was validated by comparing the predicted results with independently measured data. The model described root growth dynamics and its spatial distribution well. A sensitivity analysis of modeled root weight density to the estimated parameters indicated that the model was more sensitive to carbohydrate supply parameters than to root growth distribution parameters. The principal functions of roots are the uptake of water and nutrients, the transport of these materials into the vascular sys- tem, and anchorage of the plant in the root medium. Root dis- tribution and growth are important in determining water and nutrient uptake, and in affecting plant water and nutrient bal- ance. Despite this importance, few models for root growth dy- namics have been developed, probably because the processes involved are not well understood and are difficult to observe. Several whole-plant models that include the representation of below-ground processes have been developed for field crops (see Luxmoore and Stolzy, 1987). Greenwood et al. (1974) and Barnes et al. (1976) developed models of nutrient uptake and growth for prediction of vegetable crop response to fertilizer application under varying weather and soil conditions. Huck and Hillel (1983) developed a model for root growth and water up- take of field crops that accounted for the C balance, water bal- ance, and vertical distribution of roots. Lambert and Baker (1982) combined current knowledge of soil water physics and data on root growth with hypotheses concerning root growth and water and nitrate uptake to form a two-dimensiona l dynamic simula- tion model (RHIZOS) that Acock et al. (1983) incorporated into their comprehensive soybean (Glycine max (L.) Merr.) model GLYCIM. Brugge and Thornley (1985) and Brugge (1985) de- veloped a theoretical model using the diffusion analogy for grass root mass and its vertical distribution. All of these models were developed for plants growing in field soil. The applicability of these models to the individual potted plant is limited, since container configuration, irrigation practices, and rooting me-