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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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Related Experiment Video

Updated: Jul 14, 2026

Visualizing Field Data Collection Procedures of Exposure and Biomarker Assessments for the Household Air Pollution Intervention Network Trial in India
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A study of spatial resolution in pollution exposure modelling.

Emilie Stroh1, Lars Harrie, Susanna Gustafsson

  • 1GIS Centre, Lund University, Sölvegatan 12, Lund, Sweden. emilie.stroh@giscentrum.lu.se

International Journal of Health Geographics
|June 6, 2007
PubMed
Summary

Choosing the right spatial resolution for air pollutant databases is crucial for health studies. Higher resolution improves accuracy, but temporal aggregation and area type (urban vs. rural) influence optimal settings for nitrogen oxides (NOx) data.

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Area of Science:

  • Environmental Science
  • Epidemiology
  • Geographic Information Systems

Background:

  • Ongoing epidemiological research in Scania, Sweden, focuses on health effects of air pollutants.
  • A critical need exists for an optimal spatial resolution in pollutant databases for epidemiological studies of varying durations.

Purpose of the Study:

  • To investigate the optimal spatial resolution for a nitrogen oxides (NOx) pollutant database.
  • To determine the impact of temporal and spatial resolution on database accuracy for epidemiological research.

Main Methods:

  • Comparison of modelled NOx concentrations at various spatial resolutions (100m to 1600m).
  • Analysis of model accuracy against measured NOx values.
  • Evaluation of spatial resolution's impact on urban versus rural areas.

Main Results:

  • Model accuracy improved with higher spatial resolution (100m fine grid).
  • Temporal aggregation (daily, weekly) significantly reduced discrepancies between resolutions.
  • Optimal spatial resolution varied considerably between urban (200-400m) and rural (approx. 1600m) areas.

Conclusions:

  • Spatial resolution choice must maintain acceptable accuracy for modelled NOx values.
  • An error exceeding 1 µg/m³ due to coarse resolution is inadvisable for daily time resolutions.
  • A flexible pollutant database allowing distinct spatial resolutions for urban and rural areas is recommended.