A novel simple soil-plant-atmospheric continuum model that emphasizes the vegetation's role in controlling water transfer (v-SPAC) has been developed in this study. The v-SPAC model aims to incorporate both plant and soil hydrological measurements into plant water transfer modeling. The model is different from previous SPAC models in which v-SPAC uses (1) a dynamic plant resistance system in the form of a vulnerability curve that can be easily obtained from sap flow and stem xylem water potential time series and (2) a plant capacitance parameter to buffer the effects of transpiration on root water uptake. The unique representation of root resistance and capacitance allows the model to embrace SPAC hydraulic pathway from bulk soil, to soil-root interface, to root xylem, and finally to stem xylem where the xylem water potential is measured. The v-SPAC model was tested on a native tree species in Australia, Eucalyptus crenulata saplings, with controlled drought treatment. To further validate the robustness of the v-SPAC model, it was compared against a soil-focused SPAC model, LEACHM. The v-SPAC model simulation results closely matched the observed sap flow and stem water potential time series, as well as the soil moisture variation of the experiment. The v-SPAC model was found to be more accurate in predicting measured data than the LEACHM model, underscoring the importance of incorporating root resistance into SPAC models and the benefit of integrating plant measurements to constrain SPAC modeling.
A root system, considered as a collection of sources and sinks, is simulated as a submodel in many larger models that describe either crop–environment relationships or matter transfer (water, carbon, or nutrients) in the soil–plant–atmosphere continuum (SPAC). In such cases, root biomass, as a proportion of plant biomass, root density distribution (in space), and root length density distribution, are all used to control water and⧸or mineral uptake. A secondary assumption also needs to be made: that the spatial distribution of the roots is homogeneous in the soil layer and the uptake is similar among all roots. Root distribution is assessed in terms of the penetration and proliferation of roots down to the penetrated depth, with consideration of the effects of one or more environmental factors on root growth (Asseng et al., ). There are some models that describe temporal development of root distribution as a diffusion process (Acock and Pachepsky, ; de Willigen et al., ; Gerwtiz and Page, ). For example, Acock and Pachepsky () developed a two-dimensional convective-diffusive root system model in which the proliferation and growth of roots in all directions are considered to result from a diffusion-like gradient, whereas the convection-like propagation of roots downward is perceived to be caused by geotropism. Mmolawa and Or () reviewed some expressions for these parameters as applied to root-zone solute dynamics under drip irrigation. Because root growth differs in terms of direction, spacing, elongation rate, and functional activity, such assumptions represent an oversimplification (Rengel, ). These models are not discussed here, as they ignore root architecture.
With the development of computer hardware and software, various root system architecture models have been developed over the last three decades. Pioneering work in the simulation of root systems was carried out by Lungley (). Some models purely simulate root static structure (Henderson et al., ), root system growth and development in two dimensions (Lungley, ; Porter et al., ; Rose, ), or root architecture in three dimensions (Bernston, ; Diggle, a; Fitter et al., ; Pagès et al., ). Other models involving the root system relate to water uptake (Clausnitzer and Hopmans, ; Doussan et al., ; Tsutsumi et al., ), nutrient uptake (Grant and Robertson, ), and uptake-dependent growth (King et al., ; Somma et al., ).
There are different approaches to the description of root systems in the models. The most common is topology of the branching process (Acock and Pachepsky, ; Clausnitzer and Hopmans, ; Diggle, a; Fitter et al., ; Hackett and Rose, ; Lungley, ; Lynch et al., ; Pagès et al., ). Roots are classified according to branching order, and each order has its own characteristics in terms of growth rate, life span, and branching ability. Fractal geometry has also been used in connection with root architecture simulation (Ozier-Lafontaine et al., ; Shibusawa, ). In this method, the network of a root system is described as being self-similar or following scale-invariant branching rules. This is achieved by deducing properties of the entire root system from basic rules governing individual bifurcations and the geometry of each segment or branch. A stochastic (as opposed to deterministic) approach has also been practiced for the description of root system architecture and development (Jourdan and Rey, ). Stochastic processes (e.g., automata, probability, and graphic models) have been used to simulate the topology of branched structures and root development (growth, mortality, and branching). Because biological hypotheses are not quantified, such a model is purely descriptive.
The current chapter builds on an earlier review (Pagès, ) to present an in-depth, systematic review of individual models and their equations. At this level of detail, it becomes clear that published models often use different terminology to describe processes of root growth and development, and a number of different mathematical expressions have been used to describe the same process. It has been found to be helpful, when considering further development of such models, to formalize the process descriptions and to distinguish those that are essential to the main processes of the models. In this chapter, seven existing models are discussed and compared. These models have been developed in various different areas of the world, cover a range of different plant species, and have been frequently cited in the literature. Although some of the reviewed models have submodels to simulate water flow, nutrient transport, and carbohydrate allocation to various plant components, we limit the analysis here to processes directly associated with the root system.