Soil phosphorus quantity–intensity relationships to predict increased soil phosphorus loss to overland and subsurface flow

Soil phosphorus (P) quantity–intensity (q–i) relationships, based on common extraction methods, may potentially be used to estimate the risk of P loss in overland flow and subsurface drainage water. Some workers have used nonlinear q–i relationships to derive thresholds in soil test P (STP; a quantity factor) above which the risk of P loss increases, while others find linear relationships and no threshold. We present here a simple modelling exercise (based on Langmuir adsorption theory) along with data from literature to explain the behaviour of q–i relationships, and to give an explanation for this apparent discrepancy. The data indicate that q–i relationships are dependent upon the soil to solution ratio of the P intensity parameter, adsorption capacity (Qmax) and strength (K) of the soil, and the total range in STP. In turn, this affects the calculation of a threshold in STP. The q–i relationship tends towards linearity under conditions of a narrow total range of STP and/or when using a wide soil to solution ratio for estimating the P intensity parameter. Under such conditions, a threshold is difficult to detect, and uncertain.