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Related Concept Videos

Linear Approximations01:23

Linear Approximations

For a differentiable function of two variables, linear approximation estimates values near a known point by replacing the curved surface with its tangent plane. Consider the function\begin{equation*}f(x,y)=x^2+3y^2\end{equation*}near the point (2, 1). The exact value at this point is f(2, 1) = 22 + 3(1)2 = 4 + 3 = 7.The linear approximation of f(x, y)) near (a, b) is\begin{equation*}L(x,y)=f(a,b)+f_x(a,b)(x-a)+f_y(a,b)(y-b)\end{equation*}First, compute the partial derivatives: fx(x, y) = 2x and...
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Flood risk assessment involves careful planning and analysis to ensure the safety of communities near water retention structures. Capacity contours are a vital tool in this process, as they illustrate the potential spread of water at specific levels in a given area. In the context of building a bund across a small valley, these contours play a critical role in evaluating the safety of nearby residential areas.In this example, the bund is intended to store stormwater in the valley. The engineers...

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Related Experiment Video

Updated: Jul 9, 2026

Use of Principal Components for Scaling Up Topographic Models to Map Soil Redistribution and Soil Organic Carbon
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Vertical characterization of soil contamination using multi-way modeling--a case study.

Kunwar P Singh1, Amrita Malik, Ankita Basant

  • 1Environmental Chemistry Division, Industrial Toxicology Research Centre, Post Box 80, MG Marg, Lucknow, 226 001, India. kpsingh_52@yahoo.com

Environmental Monitoring and Assessment
|November 29, 2007
PubMed
Summary

Chemometric multi-way modeling identified heavy metal contamination patterns in industrial soils. This approach revealed distinct accumulation pathways and contaminant mobility, aiding in soil remediation strategies.

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Two-Dimensional Visualization and Quantification of Labile, Inorganic Plant Nutrients and Contaminants in Soil

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Area of Science:

  • Environmental Chemistry
  • Chemometrics
  • Geochemistry

Background:

  • Industrial activities lead to soil and groundwater contamination by heavy metals.
  • Understanding contaminant pathways and mobility is crucial for effective remediation.
  • Traditional methods may not fully capture complex soil contaminant dynamics.

Purpose of the Study:

  • To apply a chemometric multi-way modeling approach for analyzing heavy metal contamination in industrial soils.
  • To assess soil/sub-soil contamination, accumulation pathways, and contaminant mobility.
  • To compare the effectiveness of multi-way modeling with traditional data analysis techniques.

Main Methods:

  • Analysis of a three-way dataset (depth, chemical variables, sites) of heavy metals in soil samples.
  • Application and validation of a three-way Tucker3 model.
  • Interpretation of model components to understand interactions across different data modes.

Main Results:

  • A two-component Tucker3 model explained 66.6% of the data variance.
  • The model provided realistic insights into horizontal and vertical contamination patterns.
  • Sites 1 and 2 showed higher heavy metal contamination compared to Site 3.
  • Distinct metal accumulation pathways were identified for shallow and deep soil layers.

Conclusions:

  • Chemometric multi-way modeling offers superior insights into soil contamination compared to traditional methods.
  • The study successfully differentiated contamination levels and accumulation pathways across sites and depths.
  • Findings provide a basis for developing targeted soil remediation strategies to prevent groundwater contamination.