Evaluation of residual nutrient effects in soils

Abstract

Some nutrients applied to soils remain available to plants well beyond their time of application. Efficient use of fertilizers requires better definition of these residual effects. In this paper the behaviour of nutrients applied to soils is expressed as a mechanistic model comprising two differential equations:A / dt = F(t) + K₃U − (K₁ + K₂) − P(t) dU / dt = K₁A − K₃U, where A and U are the available and and unavailable soil nutrient levels and K₁, K₂ and K₃ are the fixation, loss and release coefficients respectively. The applied nutrient F(t) and the nutrient removed in harvested plant products P(t) are considered as impulses to the system. The solved form of these equations can be fitted to appropriate field experimental data by using iterative least squares procedures and parameters estimated. The model has been fitted to 6 years' experimental data where pasture responses to 16 different superphosphates regimes were measured on a soil with a high phosphate retention capacity. The estimated rates of fixation (K₁), loss (K₂) and release (K₃) of available phosphorus as percentages per month on this soil were 1.29, 1.48 and 0.072 respectively, with release extremely low. To maintain pasture production on this soil the model suggests that high rates of phosphorus will be required for a long time, that it is wasteful to apply phosphorus above a specified maintenance level (as such phosphorus is either fixed or lost) and that biennial application is more efficient than annual. From the model the theoretical maximum residual available nutrient, c, in a soil at time t after application, is c(t) = [(K₁exp{− (K₁ + K₃)t + (K₃] / (K₁ + K₃), with the decay curve asymptoting to the value K₃/ (K₁ + K₃) at equilibrium. On the soil studied this value was 5.3%. In practice, because of losses and plant removal, residual nutrient levels are usually less than the theoretical maximum. It is postulated that if the ratio of available to unavailable nutrient in a soil at equilibrium is 1 / z, then the theoretical maximum proportion of available applied nutrient at equilibrium is 1 / (z + 1). The model is likely to be most useful for major nutrients where residual effects are important in practice, e.g. phosphorus, sulphur, potassium and magnesium.