State-Space Modeling to Simplify Soil Phosphorus Fractionation
- Xiufu Shuai and
- Russell S. Yost *
Soil P can be fractionated by methods such as the Hedley extraction method to help identify and quantify soil P. Measuring the increases in soil P fractions from P fertilizer does not indicate whether external P can control a P fraction because of transfers among P fractions. Similarly, correlations between soil P fractions and plant P uptake do not directly indicate whether a P fraction affects plant P uptake. The objectives of this research were to describe the transformation among fractions, the effect of P fertilizer on P fractions, and the relationship between plant P uptake and P fractions by a state-space modeling approach, and to minimize the dimension of the state-space model by introducing concepts of controllability and observability and by implementing the General Decomposition Theorem. A P fraction was said to be controllable if its size can be controlled directly by the amount of external P fertilizer, or indirectly through transformations among P fractions. A P fraction was considered observable if it contributed to plant P uptake directly, or indirectly through transformations among P fractions. The jointly controllable and observable P fractions identified by the General Decomposition Theorem were minimum to describe the measured soil P dynamics in selected soil-plant systems, while other fractions were redundant in the cases described. Results showed that only strip-P, inorganic NaHCO3–Pi, organic NaHCO3–Po, and inorganic NaOH-Pi of the seven fractions were necessary and sufficient to describe the P dynamics in example Mollisol, Vertisol, Ultisol, and Oxisol.Please view the pdf by using the Full Text (PDF) link under 'View' to the left.
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