Exploring groundwater hydrochemistry of alluvial aquifers using multi-way modeling

A three-way data set pertaining to hydrochemistry of the groundwater of north Indo-Gangetic alluvial plains was analyzed using three-way component analysis method with the purpose of extracting the information on spatial and temporal variation trends in groundwater composition. Three-way data modeling was performed using PARAFAC and Tucker3 models. The models were tested for their stability and goodness of optimal fit using core consistency diagnostic and split-half analysis. Although, a two-component PARAFAC model, explaining 50.47% of data variance, yielded 100% core consistency, it failed to qualify the validation test. Tucker3 model (3, 3, 1) captured 55.18% of the data variance and yielded simple diagonal core with three significant elements, explaining 100% of the core variability. Interpretation of the information obtained through Tucker3 model revealed that the groundwater quality in Khar watershed is mainly dominated by water hardness and related variables, whereas, water composition of the dug wells is dominated by alkalinity and carbonate/bicarbonates. Moreover, shallow groundwater sources in the region are contaminated with nitrate derived from fertilizers application in the region. The shallow aquifers are relatively more contaminated during the post-monsoon season.     

Multi-way partial least squares modeling of water quality data

A 10 years surface water quality data set pertaining to a polluted river was analyzed using partial least squares (PLS) regression models. Both the unfold-PLS and N-PLS (tri-PLS and quadri-PLS) models were calibrated through leave-one out cross-validation method. These were applied to the multivariate, multi-way data array with a view to assess and compare their predictive capabilities for biochemical oxygen demand (BOD) of river water in terms of their relative mean squares error of cross-validation, prediction and variance captured. The sum of squares of residuals and leverages were computed and analyzed to identify the sites, variables, years and months which may have influence on the constructed model. Both the tri- and quadri-PLS models yielded relatively low validation error as compared to unfold-PLS and captured high variance in model. Moreover, both of these methods produced acceptable model precision and accuracy. In case of tri-PLS the root mean squares errors were 1.65 and 2.17 for calibration and prediction, respectively; whereas these were 2.58 and 1.09 for quadri-PLS. At a preliminary level it seems that BOD can be predicted but a different data arrangement is needed. Moreover, analysis of the scores and loadings plots of the N-PLS models could provide information on time evolution of the river water quality.     

Multi-way modeling of hydro-chemical data of an alluvial river system--a case study

A large data set pertaining to water quality of an alluvial river was analyzed using multi-way data analysis methods with a view to extract the hidden information, spatial and temporal variation trends in the river water quality. Four-way data (8 monitoring sites × 22 water quality variables × 10 monitoring years × 12 sampling months) analysis was performed using PARAFAC and Tucker3 models. A two component PARAFAC model, although explained 35.1% of the data variance, could not fit to the data set. Tucker3 model of optimum complexity (2,3,1,3) explaining 39.7% of the data variance, allowed interpretation of the data information in four modes. The model explained spatial and temporal variation trends in terms of water quality variables during the study period and revealed that sampling sites in mid-stretch of the river were dominated mainly by the variables of anthropogenic origin. The results delineated the mid stretch of the river as critical from pollution point of view and also identified summer months as having high influence on river water quality in this stretch. The information regarding spatial and temporal variations in water quality generated by the four-way modeling of data would be useful in developing long-term water resources management strategies in the river basin.     

Second-order time discretization for a coupled quasi-Newtonian fluid-poroelastic system

Numerical methods are proposed for the nonlinear Stokes-Biot system modeling interaction of a free fluid with a poroelastic structure. We discuss time discretization and decoupling schemes that allow the fluid and the poroelastic structure computed independently using a common stress force along the interface. The coupled system of nonlinear Stokes and Biot is formulated as a least-squares problem with constraints, where the objective functional measures violation of some interface conditions. The local constraints, the Stokes and Biot models, are discretized in time using second-order schemes. Computational algorithms for the least-squares problems are discussed and numerical results are provided to compare the accuracy and efficiency of the algorithms.     

Synthetic Approaches to Some Polymethine Asycyanine Colorants; Impact of Functional Additives & Chain Elongation on Visible Electronic Spectra

Twenty one new chromophoric chain β‐substituted polymethine asycyanine (CCBSPA) colorants have been synthesised by catalytic condensation of (i) 4‐dimethylaminophenylbutadientylphenyl ketone; (ii) 4‐dimethylbutadienyl‐4‐nitrophenyl ketone; and (iii) 4‐dimethylaminophenylbutadienyl‐4‐methyl‐phenyl ketone with 2‐methyl quinoline methiodide and 2‐methyl‐6‐substituted quinoline methiodides using piperidine as catalyst & ethanolic DMF as solvent. These colorants were synthesized with the object to study the impact of various functional groups and chain lengthening on visible electronic spectra. All the colorants showed increase in electronic spectra whether electron withdrawing or donating. These colorants also absorb at higher wavelengths when compared to the previously reported butadienylene chain asycyanino‐colorants.