Toward the structure of a production function for wheat yields with dated inputs of irrigation water

Abstract

The interdependence between the rate of water used by plants and the available stocks of moisture in the soil, the temporal interdependence between water use at different time points, and the consequences of these interdependencies for the relationship between time profiles as well as the quantities of water used by crop plants and yields have not generally been analyzed in a unified framework. We present one such unified framework for the analysis of optimal use of irrigation water. We have estimated from experimental data the mathematical form of a water use function and have used this function to compute the time profiles of actual water use for two crops: wheat in Delhi and alfalfa in Ohio. The estimated time profiles of consumptive use have been used to determine the relationship between wheat yields and dated inputs 'of water in Delhi.To study the question of economically optimal use of water, we need to know the exact shape of the crop response function to different quantities of water used by the crop throughout its growth cycle. For instance, consider a large reservoir system. The problems of scheduling the operations of the system include decisions on the timing of water releases and the allocation of water among crops. The allocation decision is relevant also for the operation of tube wells or run-ofthe-river irrigation systems. Unless we have the knowledge of the marginal productivity of water allocated to each crop at different stages of its growth, we cannot arrive at an optimal set of decisions. This knowledge is required also in determining the extent of the command area of an irrigation system. A production function for each crop, in which yield is related to dated inputs of water, will provide such knowledge.Moore [1961] in his formal treatment highlights the importance of the timing of irrigation. Deterministic dynamic programing formulations to obtain optimal timing and the amount of irrigation are given by Flinn and Musgrave [1967], Flinn [1968], and Hall et al. [1968]. Dudley et al. [!97!a, b] give stochastic dynamic programing formulations for problems of water management. Dudley' [1972] also poses the problem of the determination of the optimal command area.Moore in his penetrating study assumes that during any period, maximum potential growth will occur when the soil moisture is at field capacity. Using a soil moisture release curve, he estimates the available moisture in the soil profile, used as an indicator of actual yield. His soil moisture release curve assumes that the evapotranspiration (ET) will always be at the potential rate and is independent of the moisture level in the soil. The potential plant growth rate is assumed to be constant, and loss in growth, compared with potential growth, in any period does not depend on actual growth in other periods. His assumptions that the release of moisture is independent of the stock of moisture in the soil and that potential growth in any later period is independent of actual growth in earlier periods insofar as the actual growth is less ...

Modelos agro-meteorológicos na estimativa da produtividade da cultura da soja na região de Ponta Grossa, Estado do Paraná

“…As análises de regressão e correlação, visando verificar o ajustamento da produtividade real com dados climáticos (ETo, ETc, ER, ER/ETc e P), foram realizadas com as equações linear, potencial, exponencial, logarítmica e polinomial de segundo grau, com o auxílio de uma planilha eletrônica. Mediante as recomendações e sugestões apontadas por Moraes et al (1998) e Frizzone et al (2005, foram selecionados os seguintes modelos agrometeorológicos para a análise de regressão e correlação realizada entre os valores, medidos e estimados, de produtividade: -Howell e Hiler (1975): Minhas et al (1974): Camargo et al (1986): 1991-4068,5 1992/1993BR 16 24/11/1992-3565,0 1994/1995BR 16 11/11/19943/4/19953630,0 1995/1996BR 16 22/11/19958/4/19963387,5 1997BR 16 24/10/199719/3/19983254,3 1998/1999BR 16 5/11/19981/4/19993220,0 2000/2001BRS 133 29/11/200012/4/20013873,8 2001/2002BRS 133 1/11/200111/4/20023105,5 2003/2004CD 206 6/11/20038/4/20043631,0 2004/2005CD 206 10/11/20046/4/20053209,3 2006/2007CD 206 27/11/20064/4/2007 A estimativa da ...…”

“…Desta forma, os valores de  i utilizados nos modelos de Jensen (1968) e Minhas et al (1974) foram os mesmos calibrados para cultivares de ciclo semi-tardio a tardio (Tabela 3).…”

Irrigation: Research and development∗

“…Although far preferable to purely physical models of crop response to water of which plenty are available (Vaux & Pruitl, 1983), they are, in the light of the paper presented by Lambrechts & Kassier, hardly appropriate. Dated production functions on which considerable work has already been done (eg Dudley et al, 1971;Flinn & Musgrave, 1967;Hall & Butcher, 1968;Minhas et al, 1974;Moore et al, 1974;Stewart et al, 1976;Dudek et al, 1981) must generally be regarded as preferable to more conventional production function models. The usefulness is illustrated by De Jager (1978), De Jager et al, (1982) and Swaney et al, 1983).…”

Calibração de modelos agrometeorológicos para estimar a produtividade da cultura do trigo, considerando sistemas de manejo do solo, em Ponta Grossa-PR

“…Os modelos agrometeorológicos empregando coeficientes obtidos na literatura (Tabela 3), com exceção do modelo de Minhas et al (1974), também não apresentaram efeito significativo ao nível de 5% de probabilidade entre os valores reais de produtividade registrados para as cinco safras versus produtividades estimadas com os modelos testados. O modelo de Minhas et al (1974) obteve R = 0,81, significativo ao nível de 5%.…”