Simple models for phosphorus loss from manure during rainfall

Mechanistic, predictive equations for phosphorus (P) transport in runoff from manure-applied fields constitute a critical knowledge gap for developing nonpoint-source pollution models. We derived two simple equations to describe the P release from animal manure during a rainfall event-one based on first-order P desorption kinetics and one based on second-order kinetics. The manure characteristics needed in the two kinetic equations are the maximum amount of water-extractable phosphorus (WEP) and a characteristic desorption time. Water-extractable P can be measured directly but currently the characteristic time can only be obtained by fitting experimental data. In addition, we evaluated two models usually used to estimate P loss from soil, the Elovitch equation and power function, both of which relate P loss to time. The models were tested against previously published data of P release from different manures under laboratory conditions. All equations fit the data well. Of the two kinetic equations, the second-order model showed better agreement with the data than the first-order model; for example, maximum relative differences between the model results and measured data were 2.6 and 4.7%, respectively. The characteristic times varied between 20 min for dairy manure and almost 100 min for poultry manure. The characteristic time did not appear to change with flow rate but decreased with smaller manure aggregates. The parameters for power-function relationships could not be related to measured manure characteristics. These results provide the first step to process-based approximations for predicting P release from manure with time during rainfall shortly after land application, when P losses are the greatest.