Discrete principal‐monotonicity inference for hydro‐system analysis under irregular nonlinearities, data uncertainties, and multivariate dependencies. Part I: methodology development

Abstract 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 principal‐monotonicity 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. Copyright © 2016 John Wiley & Sons, Ltd.