A loss function to evaluate agricultural decision‑making under uncertainty: a case study of soil spectroscopy

Modern sensor technologies can provide detailed information about soil variation which allows for more precise application of fertiliser to minimise environmental harm imposed by agriculture. However, growers should lose neither income nor yield from associated uncertainties of predicted nutrient concentrations and thus one must acknowledge and
account for uncertainties. A framework is presented that accounts for the uncertainty and determines the cost–benefit of data on available phosphorus (P) and potassium (K) in the
soil determined from sensors. For four fields, the uncertainty associated with variation in soil P and K predicted from sensors was determined. Using published fertiliser dose–yield response curves for a horticultural crop the effect of estimation errors from sensor data on
expected financial losses was quantified. The expected losses from optimal precise application were compared with the losses expected from uniform fertiliser application (equivalent to little or no knowledge on soil variation). The asymmetry of the loss function meant that underestimation of P and K generally led to greater losses than the losses from overestimation. This study shows that substantial financial gains can be obtained from sensor-based precise application of P and K fertiliser, with savings of up to £121 ha−1 for P and up to £81 ha−1 for K, with concurrent environmental benefits due to a reduction of 4–17 kg ha−1 applied P fertiliser when compared with uniform application.