Heavy metals concentration in soils across the conterminous USA: Spatial prediction, model uncertainty, and influencing factors

Assessment and proper management of sites contaminated with heavy metals require precise information on the spatial distribution of these metals. This study aimed to predict and map the distribution of Cd, Cu, Ni, Pb, and Zn across the conterminous USA using point observations, environmental variables, and Histogram-based Gradient Boosting (HGB) modeling. Over 9180 surficial soil observations from the Soil Geochemistry Spatial Database (SGSD) (n = 1150), the Geochemical and Mineralogical Survey of Soils (GMSS) (n = 4857), and the Holmgren Dataset (HD) (n = 3400), and 28 covariates (100 m × 100 m grid) representing climate, topography, vegetation, soils, and anthropic activity were compiled. Model performance was evaluated on 20 % of the data not used in calibration using the coefficient of determination (R2), concordance correlation coefficient (ρc), and root mean square error (RMSE) indices. Uncertainty of predictions was calculated as the difference between the estimated 95 and 5 % quantiles provided by HGB. The model explained up to 50 % of the variance in the data with RMSE ranging between 0.16 (mg kg-1) for Cu and 23.4 (mg kg-1) for Zn, respectively. Likewise, ρc ranged between 0.55 (Cu) and 0.68 (Zn), respectively, and Zn had the highest R2 (0.50) among all predictions. We observed high Pb concentrations near urban areas. Peak concentrations of all studied metals were found in the Lower Mississippi River Valley. Cu, Ni, and Zn concentrations were higher on the West Coast; Cd concentrations were higher in the central USA. Clay, pH, potential evapotranspiration, temperature, and precipitation were among the model's top five important covariates for spatial predictions of heavy metals. The combined use of point observations and environmental covariates coupled with machine learning provided a reliable prediction of heavy metals distribution in the soils of the conterminous USA. The updated maps could support environmental assessments, monitoring, and decision-making with this methodology applicable to other soil databases, worldwide.

Evaluating and Calibrating Uncertainty Prediction in Regression Tasks

Predicting not only the target but also an accurate measure of uncertainty is important for many machine learning applications, and in particular, safety-critical ones. In this work, we study the calibration of uncertainty prediction for regression tasks which often arise in real-world systems. We show that the existing definition for the calibration of regression uncertainty has severe limitations in distinguishing informative from non-informative uncertainty predictions. We propose a new definition that escapes this caveat and an evaluation method using a simple histogram-based approach. Our method clusters examples with similar uncertainty prediction and compares the prediction with the empirical uncertainty on these examples. We also propose a simple, scaling-based calibration method that preforms as well as much more complex ones. We show results on both a synthetic, controlled problem and on the object detection bounding-box regression task using the COCO and KITTI datasets.

Uncertainty in model-based treatment decision support: Applied to aortic valve stenosis

Patient outcome in trans-aortic valve implantation (TAVI) therapy partly relies on a patient's haemodynamic properties that cannot be determined from current diagnostic methods alone. In this study, we predict changes in haemodynamic parameters (as a part of patient outcome) after valve replacement treatment in aortic stenosis patients. A framework to incorporate uncertainty in patient-specific model predictions for decision support is presented. A 0D lumped parameter model including the left ventricle, a stenotic valve and systemic circulatory system has been developed, based on models published earlier. The unscented Kalman filter (UKF) is used to optimize model input parameters to fit measured data pre-intervention. After optimization, the valve treatment is simulated by significantly reducing valve resistance. Uncertain model parameters are then propagated using a polynomial chaos expansion approach. To test the proposed framework, three in silico test cases are developed with clinically feasible measurements. Quality and availability of simulated measured patient data are decreased in each case. The UKF approach is compared to a Monte Carlo Markov Chain (MCMC) approach, a well-known approach in modelling predictions with uncertainty. Both methods show increased confidence intervals as measurement quality decreases. By considering three in silico test-cases we were able to show that the proposed framework is able to incorporate optimization uncertainty in model predictions and is faster and the MCMC approach, although it is more sensitive to noise in flow measurements. To conclude, this work shows that the proposed framework is ready to be applied to real patient data.

Data worth and prediction uncertainty for pesticide transport and fate models in Nebraska and Maryland, United States

BACKGROUND

Complex environmental models are frequently extrapolated to overcome data limitations in space and time, but quantifying data worth to such models is rarely attempted. The authors determined which field observations most informed the parameters of agricultural system models applied to field sites in Nebraska (NE) and Maryland (MD), and identified parameters and observations that most influenced prediction uncertainty.

RESULTS

The standard error of regression of the calibrated models was about the same at both NE (0.59) and MD (0.58), and overall reductions in prediction uncertainties of metolachlor and metolachlor ethane sulfonic acid concentrations were 98.0 and 98.6% respectively. Observation data groups reduced the prediction uncertainty by 55-90% at NE and by 28-96% at MD. Soil hydraulic parameters were well informed by the observed data at both sites, but pesticide and macropore properties had comparatively larger contributions after model calibration.

CONCLUSIONS

Although the observed data were sparse, they substantially reduced prediction uncertainty in unsampled regions of pesticide breakthrough curves. Nitrate evidently functioned as a surrogate for soil hydraulic data in well-drained loam soils conducive to conservative transport of nitrogen. Pesticide properties and macropore parameters could most benefit from improved characterization further to reduce model misfit and prediction uncertainty.