Evaluation of simplified water-crop yield models

Abstract

Firstly theoretical considerations on three simplified water-crop yield models are given, which are subsequently used for the analysis of a large number of reported irrigation trials on alfalfa, sorghum and maize. Alfalfa ( Medicago sativa L.), being a crop on which many irrigation trials have been carried out, was first selected for calibrating and testing the three models. Being the first crop for which these simplified relationships are tested, a number of alternative calculation procedures are tried out, using published data from experiments with varying water application. Sorghum ( Sorghum bicolor L. Moench) and maize ( Zea mays L.) were next chosen for calibrating and testing. The most important difference between alfalfa on one hand and sorghum and maize on the other is that the latter crops are not used as forage crops, but for grain production, so that one is interested only in a part of the above-ground dry matter production. This leads to a new parameter in the model, the harvest index, which is the ratio between grain and above-ground dry matter production and depends on the distribution of dry matter in the plant during the growing period. Based on earlier work of De Wit (1965), the concept of standard production is presented as a reference type of potential crop production. Two available simplified water-crop yield models based on the concept of standard production are summarized. The Rijtema model treats the water-yield relationship as a diffusion process, by combining diffusion equations for transpiration and photosynthesis. The method therefore is based on functional relationships for the resistances involved. Respiratory losses are accounted for by a factor expressing photosynthetic efficiency. The original Rijtema model is amended by introducing correction factors for the effect of temperature on plant growth and a conversion factor from total dry matter production to harvestable product. The FKZ model is a Blackman-type production model in which a maximum production level is considered. The effect of the production factor water is accounted for by a simplified transpiration/photosynthesis relationship. Water use efficiency ( P/E) is considered to vary only with crop-type and vapour pressure deficit. A modification is proposed in which water-use efficiency also depends on potential production conditions. A third, Linear model is derived from the Rijtema model. The Linear model is calibrated for alfalfa using 84 data from different regions all over the world. The validation is carried out using 85 data sets. Ninety-two per cent of the observed variation in yields is explained. For the model calibration for sorghum and maize, 58 and 83 data sets, respectively, from different regions were used. The validation of the model was carried out using 42 and 38 data sets, respectively. The calculation of grain production is based on different relationships with the calculated total dry matter production, depending on water stress in sensitive periods. The grain model is calibrated and tested for sorghum using 108 and 76 data sets, respectively, and for maize using 121 and 93 data sets, respectively. The model explains 81% of the observed variations in sorghum and maize grain yields in experiments under different environmental conditions. The simplified transpiration/photosynthesis used in the original FKZ model does not adequately describe the alfalfa data used. An improved version of this relationship, containing the same functional relationships as found for the Linear model, yielded significant results. The modified model explains 95, 80 and 74% of the observed variation in alfalfa, sorghum and maize yields, respectively, using the same data sets as for the Linear model. The functional relationships derived in the calibration of the Linear model are also introduced in the Rijtema model. A number of alternative relationships for photosynthetic efficiency, stomatal and mesophyll resistance are tried for alfalfa. A significant functional relationship is derived between mesophyll and stomatal resistance at a constant value (0.6) of photosynthetic efficiency. Testing the modified model reveals that 87, 72 and 69% of the observed variation in alfalfa, sorghum and maize yields, respectively, can be explained. All three modified models yield satisfactory results for estimating the effects of alternative water management strategies.