Quantifying the effect of uncertainty in an applied soil spectroscopy context A loss function approach

Abstract

Advances in sensor technology and agricultural equipment should enable farmers to improve the precision management of nutrients, water and adjusted crop density, but the decision of when to use what sensor and how many measurements to take is still ad hoc. Hence, a systematic approach to sensor use for the determination of soil conditions is necessary and could potentially reduce input use. Consequently, the aim of this thesis is to investigate the uncertainty associated with soil property predictions by spectroscopy in relation to its cost-effectiveness for soil management. To achieve this aim, four case study fields were considered in the Cambridgeshire fens (UK). A total of 747 locations were sampled for top-soil across the fields and spectral measurements were made in the visible- (V), near- (N) and mid- (M) infrared (IR) and X-ray fluorescence (XRF) regions. A subset of the soil samples has been analysed for available P , exchangeable K, pH, organic C , total N and their particle size fractions. The data collected from these fields was used to address four main topics relevant to the application of spectroscopy in soil science. Chapter 2 is concerned with the prediction of crop growth from soil NIR and MIR spectra. Crop data derived from air-borne imagery was predicted by both i.) a direct approach that used the soil spectra themselves and ii.) an indirect approach that used soil properties estimated by calibrating the spectra to reference measurements. Results show that estimated soil N, P, K and pH were significant predictors of the crop data within the indirect approach, indicating potential for the use of soil spectral data to inform precision management. Although the direct approach is advantageous for accuracy, it does not provide information on how soil properties can be managed to affect crop performance. The study concludes that there is potential for associating crop response with soil reflectance spectra for improved input management. Chapter 3 asks to what extent the effort associated with spectral measurements can be reduced at the cost of prediction accuracy associated with soil property estimates. For this purpose, the magnitude of loss in accuracy was contrasted, relative to field-scale predictions based on milled samples, by either reduced sample processing or the use of existing spectral libraries. Additionally, the predictions were performed for multiple sensors to assess whether their combined effect could minimise the loss in accuracy resulting from reduced sample processing. The study shows that reduced sample processing and spectral libraries have potential to reduce time and cost implications for predicting soil organic carbon, clay and pH from NIR and MIR spectra. Available P and K can only be predicted with moderate accuracy from the milled field-scale samples. Combined predictions from multiple sensors generally led to equal prediction accuracy or a small improvement compared to separate NIR or MIR predictions. The loss of accuracy is specific to the combination of soil property and sensor analysed. The results provide insight into the expected differences in prediction accuracy and which factors need to be taken into consideration to reduce effort for developing field-scale calibrations. Chapter 4 is concerned with quantifying the effect of accounting for uncertainty in soil property predictions from spectroscopy when making decisions about soil management. By accounting for uncertainty, it was tested whether spatial predictions of available P and K were sufficiently accurate to justify the precise application of P and K fertiliser. The effect of uncertainty (compared to using the mean kriging predictions) was quantified as an expected loss under both uniform and precise fertiliser regimes of P and K. Results show that for all four fields, there is an economic incentive for precise fertiliser application of P compared to uniform application. In the case of K, economic advantages were found in two fields. The results also indicate that in general, consideration of uncertainty led to risk-averse fertiliser application. The magnitude of the expected losses and the difference in loss between precise and uniform application were found to be dependent on (a) the kriging variance, (b) the range of the dose-response curve in terms of available P and K, (c) the range of estimated P and K values within the fields and (d) the asymmetry of the loss function. Because reduced application of P fertiliser is not only linked to economic benefits, we conclude that environmental benefits, such as reducing eutrophication of watercourses from reduced P fertiliser applications, should be included in the loss function. Chapter 5 is concerned with the uncertainty in soil available P and K estimates from spectroscopy as a function of total- and calibration sample size. The effect of uncertainty on precise fertiliser management was quantified by the difference in profit from applying fertiliser using the estimates of soil nutrient concentration, accounting for uncertainty, relative to the profit that would be gained from applying fertiliser informed by the true variation of available P and K. This difference in profit was denoted as the expected loss. Based on the observed variation in P and K in three experimental fields, 100 realisations per field were simulated for an in silico experiment. For each simulation, the fields were sampled and a calibration error was added. After kriging was performed, the fertiliser requirement needed to minimise the expected loss associated with predictions was computed together with the expected profit when data acquisition costs were accounted for. Results show that calibration sample size outweighed the effect of total sample size on the uncertainty associated with predictions. Equally, for the same calibration set size, there were large differences in the kriging variance between total sample sizes. The expected loss showed diminishing returns on investment suggesting that there is an optimum sample size. However, the expected profit in our simulations was dominated by the costs of sampling and spectroscopy. Consequently, no combination of the total- and calibration sample sizes considered would result in a financial gain and could thus be considered optimal. In case costs can be substantially reduced, spectral methods offer a promising method for informing variable rate management. The loss function approach is concluded to be an adequate method to assess whether spectroscopy is effective for informing soil management and should be applied in further case-studies to gain more robust insight in the value of applied soil spectroscop