Abstract
Nitrogen (N) and phosphorus (P) are both essential plant nutrients. However, their joint response to plant growth is seldom described by models. This study provides an approach for modeling the joint impact of inorganic N and P fertilization on crop production, considering the P supplied by the soil, which was approximated using the soil test P (STP). We developed yield response models for Finnish spring barley crops (Hordeum vulgare L.) for clay and coarse-textured soils by using existing extensive experimental datasets and nonlinear estimation techniques. Model selection was based on iterative elimination from a wide diversity of plausible model formulations. The Cobb−Douglas type model specification, consisting of multiplicative elements, performed well against independent validation data, suggesting that the key relationships that determine crop responses are captured by the models. The estimated models were extended to dynamic economic optimization of fertilization inputs. According to the results, a fair STP level should be maintained on both coarse-textured soils (9.9 mg L−1 a−1) and clay soils (3.9 mg L−1 a−1). For coarse soils, a higher steady-state P fertilization rate is required (21.7 kg ha−1 a−1) compared with clay soils (6.75 kg ha−1 a−1). The steady-state N fertilization rate was slightly higher for clay soils (102.4 kg ha−1 a−1) than for coarse soils (95.8 kg ha−1 a−1). This study shows that the iterative elimination of plausible functional forms is a suitable method for reducing the effects of structural uncertainty on model output and optimal fertilization decisions.
Highlights
The motivation for using nutrient inputs in agriculture more efficiently has never been greater than it is currently
We evaluated the suitability of the certain functional form for economic optimization by examining whether the following requirements were satisfied: the optimal control trajectory must converge to a finite steady state where the optimal solution for each stage remains approximately the same, and the optimal steady-state fertilizer rates, soil test P (STP) levels, and the yields do not exceed the corresponding sample maximums
After estimating numerous different model formulations for each model element in Equations (2)–(4), by fitting various types of nonlinear functional forms for each dataset, and ranking the obtained model candidates using Akaike information criteria (AIC) (Appendix A, Table A1), we obtained the explicit form for the Cobb−Douglas type yield response model for coarse soils and for clay soils, respectively, as follows: ycoarse θ2,1 P1/2
Summary
The motivation for using nutrient inputs in agriculture more efficiently has never been greater than it is currently. The joint impact of N and P inputs on crop yield was explicitly considered in dynamic crop growth simulation models, such as DAISY [19], HYPE [20], APSIM [21], and EPIC [22,23], and in decision support systems for agrotechnology transfer like DSSAT [24]. These models provide a rich and detailed description of the processes driving the yield response, they are not directly suited to dynamic economic optimization due to the large number of state variables and the extensive data requirements [25]
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