# Hybrid statistical‐machine learning approach for analyzing legacy and new phosphorus losses from subsurface drainage systems

## TL;DR

This study shows that legacy phosphorus in soil is the main source of water pollution from farms, and applying organic fertilizer in winter increases new phosphorus loss.

## Contribution

A hybrid statistical-machine learning approach was used to quantify legacy and new phosphorus losses from subsurface drainage.

## Key findings

- Legacy phosphorus accounted for 84-100% of total and dissolved phosphorus losses.
- Organic fertilizer applied in winter caused significantly higher new phosphorus loss than fall applications.
- Organic fertilizers contributed more phosphorus loss than inorganic ones due to higher application rates.

## Abstract

Phosphorus (P) is essential for crop growth but leaches through subsurface drainage discharge, impacting water quality. This study's objectives are to (1) apply hybrid statistical‐machine learning to quantify the contributions of incidental (new) and legacy (old) P in drainage discharge from organic site and inorganic site and (2) evaluate the effect of manure application timing on P loss. We collected data from two on‐farm sites in southeast Michigan, USA. A linear regression equation was used to analyze P load based on drainage discharge and fertilizer application timing. The data were split into calibration and validation sets, and machine learning was used for training. The results showed strong model prediction performance. Organic fertilizers contributed approximately twice the observed total phosphorus (TP) loss (7.54 kg ha−
1 vs. 3.73 kg ha−
1) and nearly four times the dissolved reactive phosphorus (DRP) loss (4.90 kg ha−
1 vs. 1.05 kg ha−
1) compared to inorganic P loss, mainly due to the greater P application rate and higher soil test P. When applied during winter months (December–January), organic fertilizer contributed to greater new P loss, whereas early fall applications (October–November) resulted in lower new P loss, showing the importance of application timing. At the organic site, legacy P was the dominant contributor to TP and DRP losses, accounting for 84% and 79% of losses, respectively. At the inorganic site, legacy P was responsible for 97% of TP loss and the entirety (100%) of DRP loss. In conclusion, legacy P was the dominant source of P loss through drainage discharge, and winter organic fertilizer application significantly increased new P loss.

Phosphorus helps crops grow but can pollute water when it drains from fields. Most losses came from legacy phosphorus already in the soil. Winter applications of organic fertilizer caused much higher new phosphorus loss than fall applications. The timing of fertilizer application considerably influences phosphorus loss, underscoring the need for improved management practices to minimize nutrient loss.