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Annual Phosphorus Loss Estimator (APLE) home page
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The Annual P Loss Estimator (APLE) is a Microsoft Excel spreadsheet model that runs on an annual time step and simulates sediment bound and dissolved P loss in surface runoff and annual changes in soil test P. This empirically based model was designed for use by those without significant modeling experience and relies on a handful of commonly measured input variables. APLE considers different kinds of animal manure (beef, dairy, poultry, swine), applied either by machine or by grazing beef or dairy cattle, and highly soluble commercial fertilizers.

The APLE model was developed by Peter A. Vadas ( in 2009 and updated by Carl H. Bolster ( in 2022. 

 Major updates (ver 3.0;May 2022):

  1. Soil bulk density is now a user-defined input.
  2. Option for using the SCS Curve Number method for calculating annual runoff.
  3. Errors can be assigned to each model input. These errors are used to estimated model prediction uncertainties using Monte Carlo simulations.

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Downloads Available

APLE-Lots is a version of APLE developed specifically for simulating dissolved and particulate P loss from outdoor feedlots. 


The Wisconsin Soil Nutrient Application Planner (SnapPlus) uses many of the equations in APLE and can be accessed here



Bolster, C.H., and P.A. Vadas. 2013. Sensitivity and uncertainty analysis for the Annual Phosphorus Loss Estimator Model. Journal of Environmental Quality 42(4): 1109–1118. doi: 10.2134/jeq2012.0418.

Bolster, C.H., P.A. Vadas, and D. Boykin. 2016. Model parameter uncertainty analysis for an annual field-scale P loss model. Journal of Hydrology 539: 27–37. doi: 10.1016/j.jhydrol.2016.05.009.

Bolster, C.H., B.M. Wessel, P.A. Vadas, and N.M. Fiorellino. 2022. Sensitivity and uncertainty analysis for predicted soil test phosphorus using the Annual Phosphorus Loss Estimator model. Journal of Environmental Quality. doi: 10.1002/JEQ2.20328.

Vadas, P.A., L.W. Good, P.A. Moore, and N. Widman. 2009. Estimating Phosphorus Loss in Runoff from Manure and Fertilizer for a Phosphorus Loss Quantification Tool. Journal of Environmental Quality 38(4): 1645–1653. doi: 10.2134/jeq2008.0337.

Vadas, P.A., N.M. Fiorellino, F.J. Coale, R. Kratochvil, A.S. Mulkey, et al. 2018. Estimating Legacy Soil Phosphorus Impacts on Phosphorus Loss in the Chesapeake Bay Watershed. Journal of Environmental Quality 47(3): 480–486. doi: 10.2134/jeq2017.12.0481.

Vadas, P.A., B.C. Joern, and P.A. Moore. 2012. Simulating Soil Phosphorus Dynamics for a Phosphorus Loss Quantification Tool. Journal of Environmental Quality 41(6): 1750–1757. doi: 10.2134/jeq2012.0003.