Bayesian optimization of a sustainability index to reduce nitrogen losses in European cropland

Nitrogen leaching in agricultural systems is a major environmental risk resulting from irrigation-fertilization practices. Global losses of fertilized agricultural systems are estimated to be about 30% of the applied nitrogen fertilizer. As food and water security are being threatened by the effects of climate change, it is imperative to develop strategies that optimize fertilization application (and irrigation) to mitigate adverse environmental effects of nitrogen losses while maximizing production. Developing and testing such strategies remains challenging, partly because soil functions strongly depend on pedoclimatic conditions, soil degradation, and crop type; and all these parameters may be highly variable, even over relatively small distances and short periods of time. In this work, we present an approach for optimizing agricultural management based on the introduction of a sustainability index (SI). The SI is defined as a function of the net monetary system gain resulting from subtracting the estimated societal cost of soil losses of nitrogen (NO₃ leaching and N₂O emissions) and soil carbon to the brut economic gain of crop yield at current market prices. We considered a management optimization example simulating winter wheat in the United Kingdom using Historical climate simulations (1960-1980) with yearly homogeneous fertilization of 200 kg N/ha/yr applied on 11^th of March. These management variables were integrated into a probabilistic Markov Chain Monte Carlo (MCMC) approach aiming at optimizing the SI. This led to reductions of approximately 34% in annual nitrate leaching (from 44 kg/ha to 29 kg/ha) and 23% in annual nitrous oxide emissions (from 5.2 kg/ha to 4 kg/ha) by only compromising 3% of the annual crop yield (from 7.4 Mg/ha to 7.2 Mg/ha). These results are further discussed in the context of climate change and soil degradation in cropland. For this, we computed the SI for healthy and compacted soils in European cropland using winter wheat simulations under climate projections from the high-emissions climate scenario (SSP585) in the Coupled Model Intercomparison Project (CMIP6). Introducing a SI that weights economic and environmental factors of agroecosystems and utilizing it within a MCMC optimization scheme provides a powerful framework to harness agroecosystem models in order to test and optimize management strategies. Such an approach offers both estimations and uncertainty of management variables, crop yield, nitrogen losses, and the resulting net economic gain, which are crucial for informing and guiding policy-making in agriculture.