State‐Space Modeling to Simplify Soil Phosphorus Fractionation

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 NaHCO 3 –Pi, organic NaHCO 3 –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.