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Hydrological system analyses are challenged by complexities of irregular nonlinearities, data uncertainties, and multivariate dependencies. Among them, the irregular nonlinearities mainly represent inexistence of regular functions for robustly simulating highly complicated relationships between variables. Few existing studies can enable reliable simulation of hydrological processes under these complexities. This may lead to decreased robustness of the constructed models, unfeasibility of suggestions for human activities, and damages to socio-economy and eco-environment. In the first of two companion papers, a discrete principalmonotonicity inference (DPMI) method is proposed for hydrological systems analysis under these complexities. Normalization of non-normally distributed samples and invertible restoration of modelling results are enabled through a discrete distribution transformation approach. To mitigate data uncertainties, statistical inference is employed to assess the significance of differences among samples. The irregular nonlinearity between the influencing factors (i.e. predictors) and the hydrological variable of interest (i.e. the predictand) is interpreted as piecewise monotonicity. Monotonicity is further represented as principal monotonicity under multivariate dependencies. Based on stepwise classification and cluster analyses, all paired samples representing the responsive relationship between the predictors and the predictand are discretized as a series of end nodes. A prediction approach is advanced for estimating the predictand value given any combination of predictors. The DPMI method can reveal evolvement rules of hydrological systems under these complexities. Reliance of existing hydro-system analysis methods on predefined functional forms is removed, avoiding artificial disturbances, e.g. empiricism in selecting model functions under irregular nonlinearities, on the modelling process. Both local and global significances of predictors in driving the evolution of hydrological variables are identified. An analysis of interactions among these complexities is also achieved. The understanding obtained from the DPMI process and associated results can facilitate hydrological prediction, guide water resources management, improve hydro-system analysis methods, or support hydrological systems analysis in other cases. The effectiveness and advantages of DPMI will be demonstrated through a case study of streamflow simulation in Xingshan Watershed, China, in another paper.

Abstract. In this research, a dual-inexact fuzzy stochastic programming (DIFSP) method was developed for supporting the planning of water and farmland use management system considering the non-point source pollution mitigation under uncertainty. The random boundary interval (RBI) was incorporated into DIFSP through integrating fuzzy linear programming (FLP) and chance-constrained programming (CCP) approaches within an interval linear programming (ILP) framework. This developed method could effectively tackle the uncertainties expressed as intervals and fuzzy sets. Moreover, the lower and upper bounds of RBI are continuous random variables, and the correlation existing between the lower and upper bounds can be tackled in RBI through the joint probability distribution function. And thus the subjectivity of decision making is greatly reduced, enhancing the stability and robustness of obtained solutions. The proposed method was then applied to solve a water and farmland use planning model (WFUPM) with non-point source pollution mitigation. The generated results could provide decision makers with detailed water supply-demand schemes involving diversified water-related activities under preferred satisfaction degrees. These useful solutions could allow more in-depth analyses of the trade-offs between humans and environment, as well as those between system optimality and reliability. In addition, comparative analyses on the solutions obtained from ICCP (Interval chance-constraints programming) and DIFSP demonstrated the higher application of this developed approach for supporting the water and farmland use system planning.

In this study, a recursive dissimilarity and similarity inferential climate classification (ReDSICC) approach is developed to provide an alternative tool for climate classification. Based on incorporation of a discrete distribution transformation (DDT) method and integration of advanced statistical inferential methods, a recursive framework of dissimilarity and similarity inferences is proposed for stepwise grouping multi‐dimensional climate‐variable observations. ReDSICC is capable of eliminating the restriction of samples being normally distributed, enabling classification of regional climates under data uncertainties and multivariate dependencies, identifying the most desired climate classification result, and avoiding subjective judgments in the classification process. To verify methodological effectiveness and facilitate related studies, ReDSICC is applied to climate classification in the Athabasca River Basin (ARB), Canada. It is revealed that the complicated dissimilarities and similarities of climatic conditions among all grids over the ARB are effectively reflected in the results of ReDSICC. A reversible transformation between an abnormal distribution and a normal distribution is achieved by DDT. The effectiveness of climate classification which is represented as the Nash coefficient for climatic features over any grid and the corresponding climate class is decreased if DDT is not employed. In comparison with daily minimum temperature, the spatial heterogeneity of daily maximum temperature is higher while that of daily cumulative precipitation is lower over the ARB. The classification result of ReDSICC varies with changes of representative climate variables and parameter values. These advantages and revelations are helpful for enhancing the reliability of climate classification results, improving the effectiveness of existing climate classification methods, and providing scientific support for the related studies in the ARB or neighbouring regions.

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Iron-based oxide with high miller index facet Fe2O3(104) effectively promotes oxygen transfer at different oxidation states for oxidizing coal molecules into CO2 and H2O during chemical looping combustion of solid fuel.