Sensitivity and uncertainty analysis for predicted soil test phosphorus using the Annual Phosphorus Loss Estimator model

Authors: Bolster, Carl; WESSEL, BARRET - University Of Maryland; Vadas, Peter; FIORELLINO, NICOLE - University Of Maryland

Submitted to: Journal of Environmental Quality
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: 1/3/2022
Publication Date: 2/18/2022
Citation: Bolster, C.H., Wessel, B.M., Vadas, P.A., Fiorellino, N.M. 2022. Sensitivity and uncertainty analysis for predicted soil test phosphorus using the Annual Phosphorus Loss Estimator model. Journal of Environmental Quality. 51(2):216-227. https://doi.org/10.1002/jeq2.20328.
DOI: https://doi.org/10.1002/jeq2.20328

Interpretive Summary: The long-term application of inorganic fertilizer and animal manure to agricultural fields has resulted in soil test phosphorus (STP) levels that greatly exceed the agronomic critical level in many areas of the U.S. This build-up of soil P, often referred to as legacy P, can increase the risk of P being mobilized during runoff and leaching events, even years or decades after P inputs have decreased or ceased. If this mobilized P reaches P-limited surface waters, eutrophication can result, leading to serious water quality problems that can adversely impact the environment, human health, and recreational activities. Due to the cost and effort involved in soil, manure, and runoff sampling and testing, as well as implementation of best management practices, nutrient management policies and strategies are often guided by predictions from nutrient loss models. Because P mobilization is related to STP levels, it is vitally important to accurately and precisely predict how STP changes in response to changes in P application rates for addressing important P management decisions in agroecosystems. The Annual P Loss Estimator (APLE) is a spreadsheet-based, user-friendly tool that predicts field-scale P loss and changes in STP levels using inputs that are readily available or easily estimated for U.S. farmland. Because all model predictions are inherently uncertain, it is important to account for prediction uncertainty when interpreting modeling data and using modeling results to guide decision making. The objective of this study was to perform an uncertainty analysis of APLE focused on the input variables and equations used to calculate STP. This work builds on previous sensitivity and uncertainty analyses focused on predictions of P loss in surface runoff and erosion with APLE. Previously published STP data collected from three sites in Maryland are used to evaluate whether measured and assumed uncertainties in model factors result in model-prediction uncertainties that are similar in magnitude to measured variability in STP between replicates. Results from this study will improve our understanding of the strengths and limitations of using APLE and similar tools to make long-term predictions of changes in STP over time.

Technical Abstract: In this study we conducted a sensitivity and uncertainty analysis using the Annual P Loss Estimator (APLE) model focusing on model predictions of soil test phosphorus (STP). We calculated and evaluated the sensitivity coefficients of predicted STP and changes in STP using 1- and 10-yr simulations with and without P application. We also compared two methods for estimating prediction uncertainties: first-order variance approximation (FOVA) and Monte Carlo simulation (MCS). Finally, we compared uncertainties in APLE-predicted STP with uncertainties in measured STP collected from multiple sites in Maryland under different manuring and cropping treatments. Results from our sensitivity analysis showed that predicted STP and changes in STP for 1-yr simulations without P inputs were most sensitive to initial STP, whereas model STP predictions were most sensitive to manure and fertilizer application rates when sensitivity analyses included P inputs. For the 10-yr simulations without P application inputs, the range in sensitivity coefficients for crop uptake and precipitation were much greater than for the 1-yr simulations. Prediction uncertainties from FOVA were comparable to those from MCS for model input uncertainties up to 50%. Using FOVA to calculate APLE STP prediction uncertainties using the Maryland data set, the mean measured STP for nearly all site years fell within the 95% confidence intervals of the STP prediction uncertainties. Our results provide users of APLE insight into what model inputs require the most careful measurement when using the model to predict changes in STP under conditions of P drawdown (i.e., no P application) or P buildup.