**4. Conclusions**

The SD in this work uses the Monte Carlo sampling approach which could be used to provide approximate probability of a scenario occurring in any given year considering the assumptions made earlier are true. Based on the data available in the current study, probabilities of scenarios *Sc*1, *Sc*2, *Sc*3, and *Sc*4 occurring are 0.1, 0.74, 0.02, and 0.12, respectively. The probability of dry condition (*Sc*3) occurring is lowest whereas regular condition (*Sc*2) has the highest probability of occurring (Figure 6). The SD approach implemented in the current study provides valuable results to In this work, the simulation decomposition (SD) approach is implemented with the Iowa food-energy-water (IFEW) system simulation model to better understand the impact of weather behavior on nitrogen export from Iowa. In particular, the previously developed nitrogen export model, which computes the soil nitrogen surplus, is extended with a crop weather model to include the dependence of weather in the IFEW system. The updated IFEW simulation model with SD is used to provide decomposed soil nitrogen surplus distribution in different weather scenarios.

gauge the impact of weather parameters on soil nitrogen surplus along with crop yields and nitrogen transfer in agriculture systems. However, the particular distributions used for the weather parameters are not data based, and the two input weather parameters are assumed to be independent of each during the Monte Carlo sampling process. Temperature and precipitation are correlated. Thus, there is a possibility that some combination of scenarios may not entirely occur. For example, high precipitation and high temperature may not occur at the same time because with high precipitation, the average temperature drops. Further, the probability distributions of the weather parameters are challenging to estimate as they typically do not have continuous distributions. Thus, it is advisable to use weather generators which have been trained on historical datasets to predict weather It is observed that July temperature and precipitation directly impact corn and soybean yields. Interestingly, it is observed that in the dry condition, corn yield reduces, whereas soybean yield increases compared to the yield values in regular conditions. The variation in crop yields affects nitrogen transfer in the agriculture system through fixation nitrogen (*FN*) and grain nitrogen (*GN*), affecting the soil nitrogen surplus. The SD approach provides the distribution of nitrogen surplus in various scenarios. It is observed that the regular condition covers most variation in the full distribution. Scenarios with high July temperature and low precipitation tend to produce mid to high range of nitrogen surplus values. The dry condition scenario produces the highest nitrogen surplus. Overall, the SD approach provides a deeper understanding of the cause-and-effect relationship between weather parameters and soil nitrogen surplus.

parameters rather than using continuous probability distributions. In future studies, Furthermore, the current study identified that continuous distribution on weather parameters could generate unrealistic scenarios. Thus, in future studies, highly validated weather generators will be used for estimating weather parameters, providing a more realistic distribution of soil nitrogen surplus based on weather. Additionally, the IFEW simulation model will be extended to report nitrogen loads for Iowa's nine crop reporting districts, providing spatially resolved information from the state of Iowa.

**Author Contributions:** Conceptualization, L.L. and A.K.; methodology, V.R.; software, V.R.; validation, V.R. and Y.-C.L.; writing—original draft preparation, V.R. and Y.-C.L.; writing—review and editing, V.R., Y.-C.L., L.L. and A.K.; visualization, V.R. and Y.-C.L.; supervision, L.L. and A.K. All authors have read and agreed to the published version of the manuscript.

**Funding:** The United States National Science Foundation under grant No. 1739551.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Acknowledgments:** This material is based upon work supported by the United States National Science Foundation under grant No. 1739551.

**Conflicts of Interest:** The authors declare no conflict of interest.
