Multiscale modelling of nutrient and water uptake by plants - Köry, Jakub (2018)
Growing populations in combination with the effects of climate change make the task of ensuring global food security in the future challenging. Water and various nutrients contained in soils are essential for the growth and survival of crop plants. Processes governing the dynamics of these substances are often highly complex and occur at various spatial scales. Because of that, and also due to limited possibilities for direct studies of soil processes in general, the ability to model such processes across these scales will most likely be crucial to address the food security challenge. Therefore, in this thesis, we model water and nutrient uptake by plant roots at various spatial scales. As all our models will be simulated numerically, we first test whether the software used throughout this thesis (FEniCS) gives us reliable numerical results (Chapter 2). We then proceed with the central part of this thesis, where we study nutrient uptake by root hairs using the method of homogenisation (introduced in Section 1.4.4). In Chapter 3, we first rederive the homogenisation result from [80] using a framework of periodic arrays of uptaking cylinders (hairs). Noticing that this framework can also be used to model nutrient or water uptake by a field of crops, we further study how well the homogenisation result compares with full-geometry numerics using various continuity equations and boundary conditions. In Chapter 4, we study the case where the radius of the root hair is much smaller than the inter-hair distance, which eventually leads us to a distinguished limit. In Chapter 5, we first establish that the framework from Chapters 3 and 4 is a suitable geometry for modelling nutrient uptake by root hairs, if the hair length is much smaller than the root radius. However, this is rarely the case. Therefore, we then investigate the effects of root surface curvature and hair length on the homogenised equation, and obtain a better approximation for the case where the hair length is comparable to the root radius. In the final two chapters, we introduce different complex problems relating to uptake by plants, and show how even simple multiscale techniques can provide us with useful insights into these problems. In Chapter 6, we show how to upscale nitrate uptake kinetics from a single transporter level to a root segment level, and then propose a model for nitrate uptake via low and high affinity transporters (see Section 6.1.2). Model predictions for the time of depletion, and a threshold nitrate concentration at which uptake ceases, are both in accordance with empirical values (Section 6.3.6). Finally, we demonstrate that under certain conditions, three-dimensional descriptions of the root system architecture are not necessary to estimate overall water and nitrate uptake, and that simple one-dimensional models can be used instead (Chapter 7).