Synchronic interval Gaussian mixed-integer programming for air quality management

et al. 2016

Hydrological Processes

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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.

“…The number of nodes after PFCSA can be assumed as an integer ( Ď ) (Cheng et al ., ,,). Because the number of nodes is decreased by one in a cluster analysis, we can have Ď ≤ Ḓ .…”

Section: Discretized Characterization Of a Hydrological Systemmentioning

confidence: 99%

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

et al. 2016

Hydrological Processes

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“…Let the number of days of which meteorological conditions are dependent on streamflow be named as the cumulative days and be denoted as C . For instance, if C is equal to one, the streamflow will only rely on today's meteorology; if it is equal to two, the streamflow may depend on today as well as yesterday's meteorology (Cheng et al, , , ). Because of the complexities of hydrological processes, especially temporal variation of the response from predictors to the predictand, it is difficult to identify a representative value of C based on empirical analysis.…”

Section: Calibration and Verification Of Dpmimentioning

confidence: 99%

Discrete principal‐monotonicity inference for hydro‐system analysis under irregular nonlinearities, data uncertainties, and multivariate dependencies. Part II: Application to streamflow simulation in the Xingshan Watershed, China

et al. 2016

Hydrological Processes

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Abstract:Provision of reliable scientific support to socio-economic development and ecoenvironmental conservation is challenged by complexities of irregular nonlinearities, data uncertainties, and multivariate dependencies of hydrological systems in the Three Gorges Reservoir (TGR) region, China. Among them, the irregular nonlinearities mainly represent unreliability of regular functions for robust simulation of highly complicated relationships between variables. Based on the proposed discrete principal-monotonicity inference (DPMI) approach, streamflow generation in the Xingshan Watershed, a representative watershed in this region, is examined. Based on system characterization, predictor identification and streamflow distribution transformation, DPMI parameters are calibrated through a two-stage strategy. Results indicate that the modeling efficiency of DPMI is satisfactory for streamflow simulation under these complexities. The distribution transformation method and the twostage calibration strategy can deal with non-normality of streamflow and temporally unstable accuracy of hydrological models, respectively. The DPMI process and results reveal that both streamflow uncertainty and its rising tendency increase with flow levels. The dominant driving forces of streamflow generation are daily lowest temperature and daily cumulative precipitation in consideration of performances in global and local scales. The temporal heterogeneity of local significances to streamflow is insignificant for meteorological conditions. There is significant nonlinearity between meteorological conditions and streamflow and dependencies among meteorological conditions. The generation mechanism of low flows is more complicated than medium flows and high flows. The DPMI approach can facilitate improving robustness of hydro-system analysis studies in the Xingshan Watershed or the TGR region.

“…Besides, many existing climate classification methods rely on subjective judgments to support screening of climate variables, selection of classification thresholds, and setting of climate class sizes or numbers prior to classification practices. These issues are challenging the effectiveness of existing climate classification methods, the reliability of climate classification results, and the reasonability of climate-change impact studies or the other related ones (Dong et al, 2011(Dong et al, , 2012(Dong et al, , 2013(Dong et al, , 2014a(Dong et al, , 2014b(Dong et al, , 2014c(Dong et al, , 2015Cheng et al, 2015aCheng et al, , 2015bCheng et al, , 2015cCheng et al, , 2016aCheng et al, , 2016b.…”

Section: Introductionmentioning

confidence: 99%

Climate classification through recursive multivariate statistical inferences: a case study of the Athabasca River Basin, Canada

Intl Journal of Climatology

et al. 2017

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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.