A plant may experience stress under adverse circumstances for development, such as water excess or deficit, extreme temperatures, or high soil salinity. Water stress, i.e. water excess or deficit, can be particularly damaging: water excess may restrict the plant’s gaseous exchange with its environment, while deficit may jeopardise its growth or productivity (Luna-Flores et al. 2015).
Agricultural management and irrigation, especially in semi-arid and arid regions, depend to a large degree on early, precise characterisation of the temporal dynamic and spatial distribution of soil moisture, especially around the roots, due to their impact on soil salinisation and plant production and health (Kumar et al. 2013). Mulching is a beneficial practice in soil preparation for blueberry crops (Gough 1980; Spiers 1983, 1986). It improves weed control efficiency, insulates the soil from high temperatures in summer, allows more uniform distribution of soil moisture, increases the organic matter content in the soil, and improves soil structure and the availability of nitrogen and micronutrients (Eusufzai and Fujii 2012).
A basic problem of agronomy is to determine growing conditions, which will minimise stress or its negative impact on the plant, while taking into consideration uncontrollable environmental factors such as drought, pests, forest fires, and frost.
Several papers have demonstrated that blueberry is a plant sensitive to water stress (Egea et al. 2017, Vargas et al. 2015, Bryla 2011, Bryla et al. 2006). In fact, increases in soil water tension cause an increase in the gradient of the water potential between the plant and the soil to maintain the flow of water to the roots. To achieve this, the plant consumes a greater amount of energy and could cause a lower fruit production or affect its vegetative development. Laboratory measurements show that leaf water potential of − 2.1 MPa produces reductions of 50% in the hydraulic conductance of the stems (Sperry et al. 1988). However, in evaluations on the field, it has been observed that the reduction in conductance is lower, possibly due to adjustments in the conductance of the stomata. The study of the effect of the soil water potential on the development of the crop has received little attention. One of the few studies published on this regard reports the incorporation of electronic sensors to control the onset and duration of irrigation (Egea et al. 2017).
The framework for this research is the agronomic problem of determining suitable irrigation conditions for a blueberry crop under conditions of water stress due to drought-induced water deficit. Various studies have addressed this problem, and others related with blueberry-growing, but without recourse to fitting mathematical models to the soil-water-plant-atmosphere continuum (Estrada et al. 2015; Inostroza-Blancheteau et al. 2014; Lobos et al. 2016; Valenzuela-Estrada et al. 2009).
Studies on blueberry water use mainly focus on water demand, comparison of irrigation methods, and sensitive period to water stress and less attention has been given to the interaction between the root of the plant and the soil water. However, this has been changing due to the increasing availability of instruments and their practical application to irrigation automation. On the other hand, the articles that report the physiology of the crop have determined critical values of processes related to water. Just recently, Masseroni et al. (2016) and Egea et al. (2017) reported studies on irrigation management related to soil variables. Based on the previous comments, our research explicitly incorporates the variables of water stress into mathematical modelling, which allows us to preliminarily evaluate the differences empirically observed in the management of blueberry in soils of different textures.
The mathematical modelling cycle has been developed from the application of scientific method to the study and comprehension of quantitative aspects of complex systems. It is based on fitting continuous, discrete, stochastic or other mathematical models such as neural networks and fuzzy logic (Singh 2008; Teh 2006). For example, the works of Salvo et al. (2011) and Holzapfel et al. (2015) fit the data from Chilean blueberry crops to statistical regression models.
One of the main advantages of this method is the possibility of creating a computer simulation of various scenarios of interest when experimental implementation is complex for reasons of time, or due to financial or human limitations. In the case of continuous models, differential equations are usually used; they are proposed after the application of the laws of conservation of mass, momentum, or energy to control volumes representing the phenomenon to be modelled. Continuous models of this kind have been widely used to model various agronomic phenomena, including water stress studied here (Albasha et al. 2015; Gou and Miller 2014; Gong et al. 2006; Qin et al. 2016; Šimůnek and Hopmans 2009).
González et al. (2015) used the HYDRUS-1D model (Šimůnek et al. 2008) to simulate the dynamics of water in the soil for a maize plantation protected from the rain. Four irrigation treatments were applied: one which avoided water stress and three which simulated different stress levels. Soil evaporation and crop transpiration data were collected. The hydraulic properties of the soil were calculated using inverse estimation. González et al. (2015) stated that the HYDRUS-1D model successfully simulated the temporal variability of the dynamics of water in soil for the four treatments, i.e. with and without water stress, and considered that the results of their research would make it possible to perfect computer programmes for large-scale irrigation planning such as those currently used in Brazil.
Kumar et al. (2013) reviewed the main mathematical models used with a macroscopic approach to model water consumption by the plant root in different agroclimatic regions and assessed their appropriateness based on a field study. One of their main conclusions is that the plant root’s water extraction pattern is neither constant nor linear.
In a work related with the present investigation, Peters (2016) used numerical simulations in HYDRUS-1D, without considering experimental data, to assess a conceptual modification of the compensated model of water consumption by the root.
The works of González et al. (2015), Kumar et al. (2013), and Peters (2016), among others, illustrate the existence and effectiveness of an integrated agronomic methodology, focusing on fitting mathematical models. This technique has not previously been applied to a blueberry crop subjected to water stress conditions caused by drought. In order to start to fill this gap, and as a first methodological step, this work reports the results obtained after carrying out a set of computer simulations considering realistic environmental situations, a generic blueberry plant and soils representative of those generally used in Chile, i.e. one clay soil and one sandy loam. The mathematical models used in this research have been validated against experimental data in various international studies (Albasha et al. 2015; González et al. 2015; Qin et al. 2016; Marquez et al. 2017; Šimůnek and Hopmans 2009). However, the authors of the present work are unaware of any experimental validation studies for this particular species, at least for this type of model.
The computer simulations reported here consider a porous medium consisting of a solid matrix (soil) and a single active fluid phase (water) which partially occupies the pore space. An inactive gaseous phase is assumed. The phenomenological focus is macroscopic; this usually gives rise to the continuity equation after the application of the law of conservation of mass to the fluid phase (Bear 1988).
Given that the existing empirical knowledge of the physiology of water absorption by blueberry root is limited (Davies and Flore 1986; Valenzuela-Estrada et al. 2009; Keen and Slavich 2012; Egea et al. 2017), the mathematical modelling reported in this paper considers an average condition of adult plants, and the numerical simulations were carried out using physical properties of two types of soils representative of the south central zone of Chile, a clay soil and a sandy loam soil.
The root of the blueberry plant is explicitly represented in the differential equation by an algebraic term, which models the rate at which the root consumes a fraction of the water available in the soil. Specifically, the water flow inside the soil surrounding the root was modelled using the Richards equation, while the root water uptake, and therefore the water stress, was modelled using the functional expressions proposed by Feddes et al. (1978) and Jarvis (1989). The mathematical model was solved numerically using the HYDRUS-1D software (Šimůnek et al. 2008). Below, we present the mathematical model used in all the computer simulations reported here.
https://link.springer.com/article/10.1007%2Fs42729-019-0015-y
Claudio Inostroza-Blancheteau, Emilio Cariaga, Jorge Jerez, Leonardo Vásquez
