CALIBRATION AND VALIDATION OF COMPLEX AND SIMPLIFIED TOMATO GROWTH MODELS FOR CONTROL PURPOSES IN THE SOUTHEAST OF SPAIN

Abstract

The tomato crop growth models TOMSIM and TOMGRO have been calibrated and validated for total dry matter production and calibrated for fruit dry matter production in greenhouses located in Southeast of Spain. The parameter estimation was carried out in such a way that the models can be used to simulate the main dynamics of tomato crop growth with differences less than 10% in total dry matter estimation in both models; 2.4% for number of nodes and 6.4% for LAI in TOMGRO; 3.4% for truss appearance in TOMSIM. The dynamic of tomato crop growth is represented by both models in acceptable way. Based on the preliminary results these tomato crop growth models can be used for control purposes. INTRODUCTION In order to apply a three level hierarchical climate greenhouse control strategy in which the middle level is related to control of the crop development, where time scales are governed by physiological processes (Rodriguez et al., 2001), it is important to develop and validate reliable tomato growth models. In this control approach the computational time is important as the control is performed in real time (typical time basis of one minute due to the climate variable control). The models for simulating the dynamic of tomato growth have many state variables; e.g. TOMGRO v1.0 has 69, (Jones et al., 1991), TOMGRO v3.0 has 574 (Kenig and Jones, 1997), the tomato model by De Koning (1994) has more than 300 for a mature plant, TOMSIM reaches 34 for a crop growing by 100 days. The use of many state variables often involves problems with dimensionality or high computational cost. Therefore it is important to use reduced growth models aimed at decreasing the computational cost without affecting significantly the capability of the model to predict the dynamic of tomato growth and yield. On the other hand, a complex model is also required as a reference for accurately describing the dynamic of the growth. In this work the TOMGRO reduced model (Jones et al., 1999) with five state variables and TOMSIM (Heuvelink, 1996, 1999) have been implemented, calibrated and validated for total dry matter and calibrated for fruit dry weight, under the specific conditions (climate conditions, greenhouse structures, agronomical practices and greenhouse management strategies) of Almeria (Spain). These models cited before are representative tomato crop growth models with differences in their underlying hypotheses, and it is important to test the adaptability of them. The main results of the parameters estimation and validation processes of these tomato growth models are shown in this paper. MATERIALS AND METHODS Experimental Data Data from measurements for calibration and validation have been obtained using two experimental sets with plants of Lycopersicon esculentum ‘Ramy’, grown in Rockwool substrate with recirculation of nutrient solution, at two plant densities, 3.04 m and 4.02 m . The experiments were carried out in a controlled climate greenhouse Proc. Int’l. WS on Models Plant Growth & Contr. Prod. Qual. in Hort. Prod. Eds. M. Fink and C. Feller Acta Hort. 654, ISHS 2004 148 of plastic cover with a range of temperature between 11.5 C and 35 C, photosynthetic photon flux density (PPFD) between 50 and 850 μmol m s and without CO2 artificial supply (range between 180 and 394 μmol mol), which are typical conditions of an automated greenhouse in the Southeast of Spain. The tomato crop was planted when plants had an average of 10.8 true leaves. It was grown only with the main stem, pruning the secondary shoots, and flowers were pollinated with the aid of bumble-bees. Electrical conductivity and pH of nutrient solution were maintained within appropriate ranges. The greenhouse roof was whitened with calcium bicarbonate according to the growers practice. Data of temperature, photosynthetic active radiation (PAR) and CO2 were measured with sensors located on the canopy and recorded each minute. In order to calibrate and validate the models, fresh and dry weight of stem, leaves and fruits and leaf area were measured periodically, ten times between 1 and 98 days after planting with a sample of three or six plants each time. Another different data set from a tomato crop grown during 262 days was used to test the model behaviours in a large crop cycle. The range of the climate variables in this experiment were: temperature between 9.8 C and 42.0 C, PPFD between 5 and 1600 μmol m s and CO2 concentration between 290 and 1400 μmol mol. The Simplified and Complex Tomato Growth Models The models tested in this paper are mechanistic ones based on photosynthesis: TOMGRO reduced state-variable (Jones et al., 1999) and TOMSIM aggregated model (Heuvelink, 1996; Heuvelink, 1999). The simplified model used is TOMGRO with the following five state variables to be used for optimal control purposes (Jones, et al., 1999): number of nodes (N), leaf area index (LAI), fruit dry matter (WF), above-ground biomass accumulation (W) and mature fruit biomass accumulation (WM). The main equations corresponding to the dynamics of the number of nodes and leaf area index, which are functions of temperature. The dynamics of the total dry matter production and distribution in fruit and mature dry weight are dependent of photosynthesis and respiration processes, based on temperature, CO2 concentration and PAR radiation. These equations are shown in Table 3. The complex model used was the TOMSIM model (Heuvelink, 1996; Heuvelink, 1999), which estimates the dynamic of growth and development for tomato crop using the following state variables: leaf area index, total dry matter and fruit dry matter. The development and growth can be known in great detail: truss by truss, vegetative units and rate of flowering appearance which let us to model effects of climate variables on the tomato growth, very important for optimal climate control purposes. The model use a pool of assimilates and the distribution to organs of the plant is done according to strength of each sink. The equations in Table 4 represent the dynamic of this model. The constants and equations for photosynthesis were taken from Heuvelink (1996) for TOMSIM and from Jones et al., (1991) for TOMGRO. Models were programmed in Simulink-Matlab and then were run in a computer for calibration and validation purposes. All variables in TOMGRO are calculated each minute. TOMSIM photosynthesis is calculated each minute but state variables are calculated once a day. Calibration and Validation Procedures In a first phase, two sets of data were used, one for calibration and the other for validation purposes with a short crop cycle. The first set (calibration) uses data of an experiment with plant density of 3.04 plants m and the other (validation) of an experiment with 4.02 plants m. The calibration process was made testing parameters to fit the state variables (Table 1 shows the parameters calibrated in TOMGRO). Mature fruit dry weight was not recorded. In order to estimate the fruit dry matter only the calibration process was carried out because only one data set was at hand. Constants were taken from Jones et al. (1999). In TOMSIM, the parameters listed in Table 2 are important to estimate photosynthesis and total dry matter (Bertin and Heuvelink, 1993;