Unified Conversion Equations between Olsen and Mehlich-3 Soil Phosphorus Tests

Abstract. Methods for soil test phosphorus (STP) differ globally and even within countries. While soil P tests often correlate, the relationship is often specific to a region or study, making any conversion equation difficult to transfer between contexts. Agronomic recommendations, P transport models, syntheses, and other works lack a strong basis for converting between STP. We fulfil this need for converting between two common STP measurements – Olsen P and Mehlich-3 P – through models which account explicitly for soil properties. Hypothesizing that soil properties at the sample level govern how STP values relate, we built models using a combined dataset of ca. 900 soils across the conterminous US and Canada, spanning 10 soil orders (USDA), 3 to 89 % clay, and pH 4 to 9. Model complexity ranged from conventional ‘region-level’ regressions (no soil data) to models adapting to many facets of soil P chemistry, presenting users several viable options suitable for their data context. Depending on data availability, the user could convert between Olsen P and Mehlich-3 P with half the error or less of conventional ‘region-level’ regressions. This reduction in conversion error impacts agronomic recommendations, environmental risk assessments (e.g., P index), and calibration of P transport models (e.g., SWAT+). While it remains best to simply measure the STP of interest, the conversion models here should prove useful in many contexts where that is not feasible. We provide the models in ready-to-use formats, depending on the covariates available to the user and whether the user wants to apply the equations in a spreadsheet or within model code.