Figure 7 Proportional contribution of four potential nitrate pollution sources (a) surface water in November 2021, (b) groundwater in November 2021, (c) surface water in April 2022, (d) groundwater in April 2022

3.5 Uncertainty Analysis and Sensitivity Analysis

Sensitivity and uncertainty analysis of Bayesian isotope mixing models are essential parts of nitrogen source apportionment research. Uncertainty analysis can evaluate the uncertainty of the nitrate source allocation results and help identify the main sources of pollution. By calculating the UI90 of each potential nitrate source, the uncertainty level of the nitrate source allocation results calculated by the SIAR model can be evaluated (Ji et al., 2017). The 5%-95% interval can control 90% of the interval and eliminate the influence of extreme values on the results. Taking the contribution rates of MS in surface water in April 2022 as an example, although the maximum contribution rate reached 0.96, the contribution rate in the 90% interval was only 0.527 (UI90=0.586). Sensitivity analysis can determine which end-members have the greatest range effect on the nitrate source allocation results, thereby helping to optimize experimental design and improve the accuracy of model predictions.
The uncertainties in the surface water and groundwater contributions for the two sampling periods are shown in Figure 8. As can be seen from Figure 8, for surface water, the percentage contribution of AD is relatively stable, with UI90 of 0.115 and 0.072 for AD in November 2021 and April 2022, respectively, ranging from 7.7% to 16.1% with 90% probability, although its maximum percentage can reach 24.8%. Larger uncertainties were associated with SN (UI90=0.584 and 0.718) and NF (UI90=0.416 and 0.737), and M&S (UI90=0.416 and 0.586) showed moderate uncertainties. For groundwater, the larger uncertainties came from SN (UI90 = 0.735 and 0.651) and NF (UI90 = 0.703 and 0.54), with M&S showing moderate uncertainties (UI90 = 0.452 and 0.623) and AD showing similarly minimal uncertainties (UI90 = 0.157 and 0.161). Groundwater has a greater uncertainty than surface water, which is related to the conditions of groundwater occurrence. Pollutants emitted by human activities pass through the unsaturated zone before entering the aquifer, during which they undergo various complex biogeochemical reactions under the influence of microorganisms. There is greater uncertainty in groundwater in April 2022 compared to November 2021, which is related to increased human activities in April such as fertilization for spring crops.