Irrigated agriculture has important implications for achieving the United Nations Sustainable Development Goals. However, there is a lack of systematic and quantitative analyses of its impacts on food–energy–water–CO₂ nexus. Here we studied impacts of irrigated agriculture on food–energy–water–CO₂ nexus across food sending systems (the North China Plain (NCP)), food receiving systems (the rest of China) and spillover systems (Hubei Province, affected by interactions between sending and receiving systems), using life cycle assessment, model scenarios, and the framework of metacoupling (socioeconomic-environmental interactions within and across borders). Results indicated that food supply from the NCP promoted food sustainability in the rest of China, but the NCP consumed over four times more water than its total annual renewable water, with large variations in food–energy–water–CO₂ nexus across counties. Although Hubei Province was seldom directly involved in the food trade, it experienced substantial losses in water and land due to the construction of the South-to-North Water Transfer Project which aims to alleviate water shortages in the NCP. This study suggests the need to understand impacts of agriculture on food–energy–water–CO₂ nexus in other parts of the world to achieve global sustainability.

Probable maximum precipitation (PMP) is used for computing probable maximum flood (PMF), which is then used to design large hydraulic structures. A basin-scale model, based on the Hershfield method, was developed for calculating PMP and PMP uncertainty in this study. It showed that PMP from the proposed method was more consistent with the values reported by the Texas Commission on Environmental Quality (TCEQ). PMP uncertainties were more reliable than those from the previous studies because of the improvement in assumptions and methodology. Utilizing basin-wide data, the proposed method developed equations for frequency factor ($K$ ) enveloping curves and calculated and mapped 1-h, 6-h, and 24-h duration PMPs for the Brazos River basin, Texas, United States. The PMP values computed by the basin-scale method were smaller than those computed by the Hershfield method but were more consistent with the values reported by TCEQ (TCEQ results were smallest among the three). The average improvements of the difference percentages for 1-h, 6-h, and 24-h duration PMP were 53.84%, 81.04%, and 72.60%, respectively. The longer-duration PMP map showed a declining trend from east coast to west (inland) and was consistent in spatial distribution with the TCEQ map. The PMP uncertainty was determined using the delta and bootstrap methods, which produced consistent results. The uncertainty differences between the delta values and bootstrap values were 10.05%, 10.35%, and 19.02%, and between the Salas values and bootstrap values for each duration were 25.59%, 20.06%, and 27.95%, respectively, which means the delta method results were more supported by the bootstrap method results. Comparison showed that the uncertainty by other studies was smaller because uncertainty caused by $K$ and normality assumption was not considered. Using bootstrap resampling, the distribution of PMP was explored, and then PMPs with 95% confidence intervals were obtained.

Probable maximum flood (PMF) has been used in large hydraulic infrastructure design for decades. However, a complete framework for deriving PMF with uncertainty analysis is lacking. This study investigates procedures ranging from probable maximum precipitation(PMP) with uncertainty to probable maximum storm (PMS), rainfall–runoff (R-R) with uncertainty, and PMF with uncertainty. A case study of Hurricane Harvey in the lower Brazos River basin in Texas is used to calibrate the R-R model and compare it with PMF. The uncertainty of PMF stems from these three components. The updated storm records indicate that except for the area size that drives PMP, the within-storm depth-area relation can generate depths greater than that of PMP for smaller areas, which runs counter to findings of a widely cited report. The PMF peak flow derived by the average PMP value was $\mathrm{12,716}{\mathrm{m}}^3/\mathrm{s}$ , which was around three times the peak flow from Hurricane Harvey ($\mathrm{3,764}{\mathrm{m}}^3/\mathrm{s}$ ). The 95% PMP confidence interval band was 54.5 mm and resulted in a $\mathrm{3,656}{\mathrm{m}}^3/\mathrm{s}$ difference between the corresponding PMF peak flows. The return periods of PMP and rainfall of Harvey at a gauge station in Houston were around 400 years and 100 years, respectively, obtained from fitting either a generalized Pareto (GP) or generalized extreme value (GEV) probability distribution. For peak flow uncertainty, the PMP uncertainty accounted for most (81%) of the parts, while the R-R model uncertainty accounted for less (19%). The framework of this study can be expanded to other areas of interest having sufficient data sets.

A flow duration curve (FDC) is widely used for predicting water supply, hydropower, environmental flow, sediment load, and pollutant load. Among different methods of constructing an FDC, the entropy-based method, developed recently, is appealing because of its several desirable characteristics, such as simplicity, flexibility, and statistical basis. This method contains a parameter, called entropy parameter M, which constitutes the basis for constructing the FDC. Since M is related to the ratio of the average streamflow to the maximum streamflow which, in turn, is related to the drainage area, it may be possible to determine M a priori and construct an FDC for ungauged basins. This paper, therefore, analyzed the characteristics of M in both space and time using streamflow data from 73 gauging stations in the Brazos River basin, Texas, USA. Results showed that the M values were impacted by reservoir operation and possibly climate change. The values were fluctuating, but relatively stable, after the operation of the reservoirs. Parameter M was found to change inversely with the ratio of average streamflow to the maximum streamflow. When there was an extreme event, there occurred a jump in the M value. Further, spatially, M had a larger value if the drainage area was small.