Crop Water Production Function Research Articles

Downscaling Crop Water Sensitivity Index Using Monotone Piecewise Cubic Interpolation

Crop-water production functions quantitatively describe the relationship between crop yield and field evapotranspiration. The crop water sensitivity indexes of crop-water production functions, a key factor for optimizing irrigation scheduling in case of water scarcity, are usually obtained from field experiments or other sources for crop growth stages, while their values in shorter intervals are preferred for practical irrigation scheduling. We proposed a method to downscale the sensitivity index from growth stages to shorter intervals by monotone piecewise cubic interpolation of the cumulative sensitivity index curve. This method was used to estimate sensitivity indexes in irrigation intervals of about 10 d for corn and wheat in central Shanxi Province of China. Results showed that the downscaled sensitivity index could reflect the impact of water stress on crop growth both at different growth stages and within each stage. Scenario analysis of water stress at a single growth stage of wheat showed the rationality of downscaling water sensitivity index from growth stages to shorter intervals through interpolation of cumulative sensitivity index, and this proposed downscaling method was superior to the traditional linear downscaling method.

A root zone model for estimating soil water balance and crop yield responses to deficit irrigation in the North China Plain

The development of water-conserving and sustainable agricultural management practices is essential and significant to alleviate the rapid depletion of groundwater resources in the North China Plain (NCP). Estimating drainage out of the root zone and improving water use efficiency could provide a basis to assist in reasonable utilization of groundwater resources for agricultural irrigation in the NCP. This study proposed a new soil water balance model to quantify drainage out of the root zone by incorporating the Darcy's law. This model was connected with the Jensen crop water production function to simulate soil water components and relative crop yield under deficit irrigation. Field experiments with the winter wheat and summer maize crop rotation were conducted in Beijing area in the NCP (2007–2009) to evaluate the model. The model could give quite reasonable predictions of soil water content in the root zone with the average root mean square error (RMSE), mean relative error (RE) and model efficiency (EF) of 0.02cm3cm−3, 6.69% and 0.78, respectively. The predicted soil water flux through the bottom of root zone agreed well with the measured ones supported by the values of RMSE (0.10mmd−1) and EF (0.92). The simulations indicated that the accumulated drainage out of root zone accounted for −27% to 19% of the applied water (irrigation and precipitation) among different crop seasons. As an application, the model was used to obtain the optimal irrigation management schedules for the hydrologic years of 75%, 50%, and 25% in the study area. The average amount of irrigation saving and reduction of water losses through drainage under optimal irrigation alternative were about 175mm and 101.9mm, respectively. This study shows that the developed root zone model has minimal input requirement, robust physical meaning and satisfactory simulation performance, which is more applicable and feasible for agricultural water management in the semi-arid area.

Simulation and optimization for crop water allocation based on crop water production functions and climate factor under uncertainty

In this paper, the uncertainty methods of interval and functional interval are introduced in the research of the uncertainty of crop water production function itself and optimal allocation of water resources in the irrigation area. The crop water production functions in the whole growth period under uncertainty and the optimal allocation of water resources model in the irrigation area under uncertainty are established, and the meteorological factor is considered in the model. It can promote the practical application of the uncertain methods, reflect the complexity and uncertainty of the actual situation, and provide more reliable scientific basis for using water resources economically, fully improving irrigation efficiency, and keeping the sustainable development of the irrigated area. This approach has important value on theoretical and practical for the optimal irrigation schedule, and has very broad prospects for research and development to other related agriculture water management.

Sustainable management of a coupled groundwater–agriculture hydrosystem using multi-criteria simulation based optimisation

In this paper we present a new simulation-based integrated water management tool for sustainable water resources management in arid coastal environments. This tool delivers optimised groundwater withdrawal scenarios considering saltwater intrusion as a result of agricultural and municipal water abstraction. It also yields a substantially improved water use efficiency of irrigated agriculture. To allow for a robust and fast operation we unified process modelling with artificial intelligence tools and evolutionary optimisation techniques. The aquifer behaviour is represented using an artificial neural network (ANN) which emulates a numerical density-dependent groundwater flow model. The impact of agriculture is represented by stochastic crop water production functions (SCWPF). Simulation-based optimisation techniques together with the SCWPF and ANN deliver optimal groundwater abstraction and cropping patterns. To address contradicting objectives, e.g. profit-oriented agriculture vs. sustainable abstraction scenarios, we performed multi-objective optimisations using a multi-criteria optimisation algorithm.

Water and Pollution Discharge Permit Allocation to Agricultural Zones: Application of Game Theory and Min-Max Regret Analysis

This paper presents a new game theoretic methodology for water and discharge permit allocation to agricultural zones in shared rivers. The methodology consists of four main steps: (1) initial allocation of water rights and pollutant discharge permits, (2) forming possible coalitions and optimal water and discharge permit reallocation to water users participating in a coalition to increase their total net benefit, (3) equitable benefit reallocation by utilizing some solution concepts in cooperative game theory, and (4) identifying the best water and pollutant discharge permit allocation strategies by minimizing the maximum regret in the system. A new linear form for crop water production function is used in the objective function of the water allocation optimization models. To show the efficiency and applicability of the methodology, it is applied to the Karoon-Dez river system in Iran.

Impact of water stress on citrus yield

Water shortage is becoming a severe problem in arid and semi-arid regions worldwide, reducing the availability of agricultural land and water resources. Deficit irrigation strategies can improve water-use efficiency and the sustainability of agro-ecosystems, although it is important to model the effects on yield loss due to irrigation water restrictions. This work estimates the water production function in citrus trees, determining the relationship between plant water stress and yield depression, as well as establishing a mathematical model for each phenological stage considered (flowering, fruit growth and ripening), and for the entire productive process. For three consecutive years (2006–2008), four regulated deficit irrigation treatments plus a control (100% crop water evapotranspiration (ETC)) were implemented in 13-year-old citrus trees (Citrus sinensis L. Osb. cv. Navelina). Different water production functions were determined for each phenological stage, establishing the relationship between the irrigation water stress and crop yield. Our results show that the fruit growth and flowering stages were the most sensitive periods in relation to irrigation water deficit and yield loss. Water stress close to 50% of ETC during the flowering stage would impose a yield loss of up to 20%, whereas this same water stress level during the fruit growth or ripening stages would result in yield losses of nearly 10% and 6%, respectively. The adjustment with cross terms (r 2 = 0.87) estimated the yield loss with good accuracy, being very similar to data measured in each study season. Consequently, the combined effect of deficit irrigation in different stages would be an additive–multiplicative model, considering that the effect of water stress in previous periods determined the crop yield response. Our model indicated that the crop water production function under deficit irrigation programmes would have a quasi-linear relation for water deficits below to 40% ETC. The previous model functions did not enable us to establish an accurate relationship when the water stress was applied in different phenological stages. Thus, this new interpretation is valuable to improve our knowledge and predict the impact of regulated deficit irrigation and have potential application in precision water stress and sustainable irrigation scheduling for citrus.

Erratum to: Sensitivity analysis of FAO 33 crop water production function

Erratum to: Sensitivity analysis of FAO 33 crop water production function

Evaluation of Crop Models for Simulating and Optimizing Deficit Irrigation Systems in Arid and Semi-arid Countries Under Climate Variability

The variability of fresh water availability in arid and semi-arid countries poses a serious challenge to farmers to cope with when depending on irrigation for crop growing. This has shifted the focus onto improving irrigation management and water productivity (WP) through controlled deficit irrigation (DI). DI can be conceived as a strategy to deal with these challenges but more knowledge on risks and chances of this strategy is urgently needed. The availability of simulation models that can reliably predict crop yield under the influence of soil, atmosphere, irrigation, and agricultural management practices is a prerequisite for deriving reliable and effective deficit irrigation strategies. In this context, this article discusses the performance of the crop models CropWat, PILOTE, Daisy, and APSIM when being part of a stochastic simulation-based approach to improve WP by focusing primarily on the impact of climate variability. The stochastic framework consists of: (i) a weather generator for simulating regional impacts of climate variability; (ii) a tailor-made evolutionary optimization algorithm for optimal irrigation scheduling with limited water supply; and (iii) the above mentioned models for simulating water transport and crop growth in a sound manner. The results present stochastic crop water production functions (SCWPFs) that can be used as basic tools for assessing the impact on the risk for the potential yield due to water stress and climate variability. Example simulations from India, Malawi, France and Oman are presented and the suitability of these crop models to be employed in a framework for optimizing WP is evaluated.

Optimal planning and operation of irrigation systems under water resource constraints in Oman considering climatic uncertainty

In this contribution, we introduce a stochastic framework for decision support for optimal planning and operation of water supply in irrigation. This consists of (1) a weather generator for simulating regional impacts of climate change on the basis of IPCC scenarios, (2) a tailor-made evolutionary optimization algorithm for optimal irrigation scheduling with limited water supply, (3) a mechanistic model for simulating water transport and crop growth in a sound manner, and (4) a kernel density estimator for estimating stochastic productivity, profit, and demand functions by a nonparametric method. As a result of several simulation/optimization runs within the framework, we present stochastic crop-water production functions (SCWPF) for different crops which can be used as a basic tool for assessing the impact of climate variability on the risk for the potential yield for specific crops and specific agricultural areas. A case study for an agricultural area in the Al Batinah region of the Sultanate of Oman is used to illustrate these methodologies. In addition, microeconomic impacts of climate change and the vulnerability of the agro-ecological system are discussed.

Novel simulation-based algorithms for optimal open-loop and closed-loop scheduling of deficit irrigation systems

The scarcity of water compared with the abundance of land constitutes the main drawback within agricultural production. Besides the improvement of irrigation techniques a task of primary importance is solving the problem of intra-seasonal irrigation scheduling under limited seasonal water supply. An efficient scheduling algorithm has to take into account the crops' response to water stress at different stages throughout the growing season. Furthermore, for large-scale planning tools compact presentations of the relationship between irrigation practices and grain yield, such as crop water production functions, are often used which also rely on an optimal scheduling of the considered irrigation systems. In this study, two new optimization algorithms for single-crop intra-seasonal scheduling of deficit irrigation systems are introduced which are able to operate with general crop growth simulation models. First, a tailored evolutionary optimization technique (EA) searches for optimal schedules over a whole growing season within an open-loop optimization framework. Second, a neuro-dynamic programming technique (NDP) is used for determining optimal irrigation policy. In this paper, different management schemes are considered and crop-yield functions generated with both the EA and the NDP optimization algorithms compared.

Sensitivity analysis of Doorenbos and Kassam (1979) crop water production function.

Doorenbos and Kassam’s (1979) equation and the multiplicative and additive forms of it that were developed by Rao et al. (1988) were extensively used in optimization models and deficit irrigation planning. Although these equations were validated and successfully used by several investigators to predict crop yield at several locations, however, some signs of anomalies exist. This paper present the results of sensitivity analysis of these equations for potato crop in relation to three parameters namely maximum evapotranspiration (PET), actual evapotranspiration (AET) and crop yield response factor (Ky). Results show that plus error of PET and Ky and minus error of AET results in over predicting of relative yield (Yr). For a specific error value of Ky, when water shortage increases, error percentage of estimated Yr by Doorenbos and Kassam (1979) equation and by multiplicative and additive forms of Rao et al. (1988) equation increases. For a specific error value of PET or AET, however, when water shortage increases, error percentage of estimated Yr by Doorenbos and Kassam (1979) equation and by multiplicative form of Rao et al. (1988) equation decreases while error percentage of estimated Yr by additive form of Rao et al. (1988) equation increases. Sensitivity of Doorenbos and Kassam (1979) equation and additive form of Rao et al. (1988) equation is equal for plus or minus error of Ky and AET but their sensitivities are greater for minus error of PET than plus error. However, sensitivity of multiplicative form of Rao et al. (1988) equation is greater for minus error of Ky and PET and plus error of AET. It was shown that error percentage on estimation of Yr by multiplicative form of Rao et al. (1988) equation arising from error of PET, AET or Ky is less than additive form. In addition, calculated Yr by multiplicative equation is higher than additive form and the difference between two forms of this equation increases severely when water shortage increases. According to the results, it is recommended that multiplicative form of Rao et al. (1988) equation instead of additive form be used in optimization models and deficit irrigation planning. Key words: Sensitivity analysis, Doorenbos and Kassam (1979) equation, multiplicative and additive equations, Rao et al. (1988) equation.

Field crop water-yield models and their applications

In this paper,crop water-production functions,namely crop water-yield models,of wheat,maize and cotton were analyzed and intrinsic relations among the different models advanced.Models of water-production function of different crops were fitted based on least-square theory using field experimental data from various irrigation regions,with quadratic model used for the whole growth period and Jensen model for growth stages.Water sensitivity index resulting from the fitting shows a low-high-low trend during the growth period.The results could provide agricultural irrigation practice with vital reliable academic hits to optimize irrigation systems in water deficient regions.

Modeling the potential for closing quinoa yield gaps under varying water availability in the Bolivian Altiplano

In the Bolivian Altiplano, the yields of rainfed quinoa are relatively low and highly unstable. We use a validated crop water productivity model to examine the potential of closing quinoa yield gaps in this region. We simulate the expectable yields under rainfed cultivation and under different deficit irrigation (DI) strategies using the AquaCrop model for the Northern, Central and Southern Bolivian Altiplano. Simulated DI scenarios include a reference strategy avoiding stomatal closure during all sensitive growth stages and allowing drought stress during the tolerant growth stages (DI 0) and various restrictive deficit irrigation strategies (DI i ) representing cases when water resources are limited. We obtain a logistic crop water production function for quinoa by plotting the seasonal actual evapotranspiration versus total grain yield. Due to the large scatter, this function only indicatively provides expectable yields. From the scenario analysis, we derive yield probability curves for the 3 agro-climatic regions. DI, without restriction in irrigation water during the drought sensitive growth stages, is able to close the yield gaps in the Northern, Central and Southern Bolivian Altiplano, and would guarantee a high and stable level of water productivity (WP). The yields of quinoa under rainfed cultivation during dry years are only 1.1, 0.5 and 0.2 Mg ha −1 in the Northern, Central and Southern Bolivian Altiplano, whereas under DI 0 they are 2.2, 1.6 and 1.5 Mg ha −1, respectively. Under limited water availability for irrigation, these stable yield levels decrease, most drastically in the Southern Bolivian Altiplano. Below a minimum water availability of 600 m 3 per ha and 700 m 3 per ha in the Central and Southern Bolivian Altiplano, respectively, the application of DI for quinoa is not significantly effective and should be avoided to save valuable resources. The yield probability curves we derive can serve as input for stochastic economic analysis of DI of quinoa in the Bolivian Altiplano.

Potential impact of climate change on durum wheat cropping in Tunisia

The potential effect of climate change on durum wheat in Tunisia is assessed using a simple crop simulation model and a climate projection for the 2071–2100 period, obtained from the Meteo-France ARPEGE-Climate atmospheric model run under the IPCC (International Panel on Climate Change) scenario A1B. In the process-oriented crop model, phenology is estimated through thermal time. Water balance is calculated on a daily basis by means of a simple modelling of actual evapotranspiration involving reference evapotranspiration, crop coefficients and some basic soil characteristics. The impact of crop water deficit on yield is accounted for through the linear crop-water production function developed by the FAO (Food and Agriculture Organization of the United Nations). Two stations are chosen to study the climate change effect. They are representative of the main areas where cereals are grown in Tunisia: Jendouba in the northern region and Kairouan in the central region. In the future scenario, temperature systematically increases, whereas precipitation increases or decreases depending on the location and the period of the year. Mean annual precipitation declines in Jendouba and raises in Kairouan. Under climate change, the water conditions needed for sowing occur earlier and cycle lengths are reduced in both locations. Crop water deficit and the corresponding deficit in crop yield happen to be slightly lower in Kairouan; conversely, they become higher in Jendouba.

Field water supply:yield relationships of grain sorghum grown in three USA Southern Great Plains soils

Field water supply (FWS) combines the three sources of water used by a crop for evapotranspiration (ET), and consists of available soil water at planting (ASWP), rainfall, and irrigation. Examining the grain yield and FWS relationship ( Y g:FWS) may provide insight into the reported variability in crop water production functions such as water productivity (WP) and irrigation water productivity (IWP). Since water is most productive when entirely consumed in ET, diversion of FWS into non-ET losses such as drainage and excessive soil water evaporation results in declines in WP and IWP. The objective of this experiment was to examine the Y g:FWS and Y g:ET relationships of grain sorghum grown under a range of irrigation treatments (0, 25, 50, and 100% replacement of ET), beginning soil water contents, evaporative demands, in the Amarillo, Pullman, and Ulysses soils of the Great Plains. The purpose was to determine the amount of FWS beyond which declines in WP and IWP began to occur due to non-ET losses as indicated by a change in the slope and intercept of the Y g:FWS and Y g:ET relationships. Large amounts of non-ET irrigation application losses occurred in the finer-textured soils in the T-100 irrigation treatment. In both years, the T-100 irrigation application amounts and ASWP resulted in a FWS ranging from 750 to 870 mm which exceeded the maximum ET requirement of 530–630 mm and which reduced WP and IWP. Piecewise regression analysis of the Y g:FWS and Y g:ET relationships for the crops in the Pullman and Ulysses soils identified the knot point, or change in slope and intercept, in the FWS where both WP and IWP tended to be optimized. This was about 500 mm in both soils, and involved the utilization of about 250 mm in ASWP, irrigation applications averaging about 250 mm, and about 60–130 mm remaining in the soil at harvest. For the coarser-textured Amarillo soil, the yield response to increasing FWS was linear, because non-ET application losses such as drainage gradually increased with the irrigation application amount. The linear Y g response in the sandy Amarillo soil and the piecewise Y g responses in the clay and silt loams of the Pullman and Ulysses soils to FWS also reflected the difference in water-holding capacities of the soils that affected the amount of available water as irrigation increased. Irrigating without considering FWS resulted in non-ET irrigation application losses and declines in WP and IWP.

Optimization model of an irrigation reservoir for water allocation and crop planning under various weather conditions

This paper develops a non-linear programming optimization model with an integrated soil water balance, to determine the optimal reservoir release policies, the irrigation allocation to multiple crops and the optimal cropping pattern in irrigated agriculture. Decision variables are the cultivated area and the water allocated to each crop. The objective function of the model maximizes the total farm income, which is based on crop–water production functions, production cost and crop prices. The proposed model is solved using the simulated annealing (SA) global optimization stochastic search algorithm in combination with the stochastic gradient descent algorithm. The rainfall, evapotranspiration and inflow are considered to be stochastic and the model is run for expected values of the above parameters corresponding to different probability of exceedence. By combining various probability levels of rainfall, evapotranspiration and inflow, four weather conditions are distinguished. The model takes into account an irrigation time interval in each growth stage and gives the optimal distribution of area, the water to each crop and the total farm income. The outputs of this model were compared with the results obtained from the model in which the only decision variables are cultivated areas. The model was applied on data from a planned reservoir on the Havrias River in Northern Greece, is sufficiently general and has great potential to be applicable as a decision support tool for cropping patterns of an irrigated area and irrigation scheduling.

Evaluation of selected crop water production functions for an irrigated maize crop

This paper presents the performance evaluation of four selected crop water production functions (CWPF). The general objective of the study was to test the capability and suitability of the models in predicting grain yield of a maize crop for a study area giving the models’ input parameters. The four functions evaluated were Jensen [Jensen, M.E., 1968. Water consumption by agricultural plants. In: Kozlowski, T.T. (Ed.), Water Deficits in Plant Growth, vol. 1. Academic Press, New York, pp. 1–22], Minhas et al. [Minhas, B.S., Parkhand, K.S., Srinivasan, T.N., 1974. Towards the structure of a production function for wheat yields with dated input of irrigation water. Water Resour. Res. 10, 383–386], modified Stewart et al. [Stewart, J.L., Danielson, R.E., Hanks, R.J., Jackson, E.B., Hagon, R.M., Pruit, W.O., Franklin, W.T., Riley, J.P., 1977. Optimizing Crop Production through Control of Water and Salinity Levels in the Soil. Utah Water Res. Lab. PR. 151-1, Logan, UT, 191 pp.], and modified Bras and Corodova [Bras, R.L., Corodova, J.R., 1981. Intra-seasonal water allocation in deficit irrigation. Water Resour. Res. 17 (4), 886–874] models. Field experiments were carried out during the year 2004 and 2005 irrigation seasons of June–October at Igurusi ya Zamani irrigation scheme in the Mkoji sub-catchment of the Great Ruaha River basin in Tanzania. The moisture stress sensitivity indices of the crop water production models were determined using field data from the 2004 season. The grain yields simulated by the crop water production functions were compared with the field-measured data for the 2005 season. The base moisture stress sensitivity indices obtained for the vegetative, flowering and grain-filling growth stages of the maize crop were 0.29, 1.07, and 0.54, respectively, for the Jensen model, and 1.24, 3.36, and 1.69, respectively, for the Minhas et al. model. The moisture stress sensitivity indices for the vegetative, flowering, and grain-filling growth stages for the modified Bras and Cordova model were 0.21, 0.86, and 0.49, respectively; and 0.21, 0.86, and 0.49, respectively, for the modified Stewart et al. model. The indices for the different growth stages were considered as appropriate weights of the moisture sensitivity of the different growth stages of the maize crop. The Jensen model over predicted relative yield by 10%, the modified Bras and Cordova, Stewart et al., and Minhas et al. over predicted relative yield by 6, 15, and 18%, respectively. Although these performances of the models were considered fairly adequate, bearing in mind that empirical models rarely perfectly simulate field data due to some inherent variability in field data that models may not capture, the performance of the Jensen and modified Bras–Cordova models were considered better compared to the Minhas et al. and modified Stewart et al. models. The Jensen [Jensen, M.E., 1968. Water consumption by agricultural plants. In: Kozlowski, T.T. (Ed.), Water Deficits Plant Growth, vol. 1. Academic Press, New York, pp. 1–22] and the modified Bras–Cordova models with their moisture stress indices obtained in this study are recommended as the multiplicative and additive CWPF for the maize crop in the study area.

Consideration of Climate Variability and Change in Agricultural Water Resources Planning

Although agriculture and its use of water resources are obviously sensitive to climatic conditions, past research has seldom identified the effects of climate variability and climate change on the fully developed relationship between crop yield and irrigation. There is potentially great value in understanding the role of climatic uncertainty on this relationship because of the dependence of agriculture on irrigation and the scale of water consumption for irrigation. Probability distributions of crop-water production functions (CWPF-PDs) are demonstrated as being useful encapsulations of the climate-yield-irrigation relationship for decisions at various levels of time and space. Combined with reliable climate teleconnections or climate forecasts, CWPF-PDs can be a central decision support tool for questions of risk and reliability. For long planning horizons, potential climate change predicted by multiple general circulation models (GCMs) can be assessed in the context of agricultural water resources. By analysis of changes in the CWPF-PDs, conclusions regarding the efficacy and sustainability of water resources and agricultural policies can be made. A semihypothetical case study for the Lake Victoria Basin in East Africa is used to illustrate these methodologies, and potential future climate impacts as predicted by the CGCM1, ECHAM3, and HadCM2 GCMs are discussed.

Optimizing water and fertilizer input using an elasticity index: A case study with maize in the loess plateau of china

Matching fertilizer rates with available water supplies in water-scarce environments remains a major challenge for improving water use efficiency and crop yield. The objectives are to (i) develop a new approach to characterizing interrelations of yield ( Y), evapotranspiration (ET), water use efficiency (WUE), and soil fertility using an elasticity index, and (ii) to further derive optimal-coupling domains of water and fertilizer inputs using maize data of 1997 and 1998, as an example. The experiment was an incomplete factorial design with two factors (water supply and fertilizer input) with five levels each, and had a total of 13 treatments with three replicates each. A maize cultivar (Zhongdan 2, Zea mays L.) was grown in a loessial silt loam in the hilly region of the Loess Plateau of China. Irrigation was hand applied at predetermined amounts as needed, and fertilizers including nitrogen, phosphate, and yard manure were applied at planting and jointing at predetermined rates. Approaches on how to use the crop–water production function and elasticity index (EI) to characterize the interrelations of Y, ET, and WUE were presented, and further extended to derive the optimal-coupling domains of water and fertilizer inputs. Yield responses to water and fertilizer inputs followed a quadratic function with a positive interactive term. When constrained by local maximum yields, the optimal-coupling domain took a half-ellipse form with the global maximum WUE and Y (or maximum ET) corresponding to the left and right end points on its long axis. As water supply increased, WUE reached its maximum before yield did. If water supply is limiting, fertilizer rates that maximize WUE rather than yield should be used; otherwise, seeking maximum yield may be desirable. For irrigation management, total water supply to maize should not exceed 550 mm in the region. Furthermore, the optimal domain can be used to determine optimal fertilizer rates for any given water supply, which may be estimated from seasonal climate forecasts in the case of dryland farming or based on available water supply for future irrigation. For a given water supply, fertilizer rates should be between the rate of reaching local maximum WUE and the rate of reaching local maximum yield.

Determining crop-water production functions using yield–irrigation gradient algorithms

Crop-water production functions (CWPFs) are a useful tool for irrigation planning, but derivation of CWPFs by field experimentation is expensive, and traditional analytical techniques are not well suited to derivation of CWPFs. Physiologically based crop models provide a useful tool for simulation of agricultural experiments, but they have not been extensively applied to the task of CWPF determination. A new algorithm type based upon differential crop yield response to irrigation (“yield–irrigation gradients” [YIG]) is presented that uses these crop models to determine planning-level irrigation schedules and CWPFs. Three specific algorithms are developed within this type, varying in complexity, performance, and computational costs. Performance of the YIG methods is compared against a standard reference evapotranspiration method. In particular, the randomized iterative YIG (RIYIG) algorithm provides near-optimal results but at the highest computational costs of all the methods specified. All of the techniques presented have general applicability and are not limited to any one crop or location.