Spatial Interpolation

Short Description	Spatial interpolation is a technique used in urban health to estimate values of health-related variables or indicators at unsampled locations within an urban area.
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Category	Spatial Analysis
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Overview

Spatial interpolation is a geo-statistical method used to estimate or predict values for locations based on the values at nearby locations.

Description

Spatial interpolation methods vary, but they all operate on a common principle: the spatial autocorrelation concept, which suggests that things closer together are more likely to be similar than those farther apart. Methods can be broadly categorized into deterministic and geostatistical. Deterministic methods, such as Inverse Distance Weighting (IDW) and spline interpolation, rely on specified mathematical formulas that determine the surface. Geostatistical methods, like Kriging, consider both the distance and the degree of variation between points, offering not just an interpolated surface but also a measure of uncertainty or variance for the predictions.

Inverse Distance Weighting (IDW):

Z(x) = \frac{\sum_{i=1}^{n} \frac{Z_i}{d_i^p}}{\sum_{i=1}^{n} \frac{1}{d_i^p}}

Using data from these known points, it is possible to estimate values in the space between these points using a technique called interpolation. Interpolation can be defined as the estimation of attribute values at unsampled points from measurements made at surrounding, sampled points.

Where
$Z(x)$ is the interpolated value at location $x$ , $Z_i$ are the observed values at known locations, $d_i$ are the distances between the known locations and $x$ , $n$ is the number of known locations used in the interpolation, and $p$ is a power parameter that determines the weight of each known point based on its distance.

Kriging:
Kriging is more complex, involving the modeling of spatial autocorrelation with a semivariogram, which measures how data similarity decreases with distance. Kriging estimates are based on both the distance and the known variance, making it a preferred method for its accuracy and the ability to provide estimation error (variance) maps.

Applications in Urban Health and Wellbeing

Air Quality Monitoring: Spatial interpolation can be used to predict air quality in urban areas where direct measurements are not available. By interpolating data from air quality monitoring stations, researchers can identify pollution hotspots and assess exposure risks for urban populations.

Noise Pollution Mapping: Similar to air quality, noise measurements can be spatially interpolated to create noise pollution maps of urban areas. These maps are crucial for urban planning and implementing measures to reduce noise exposure, thereby improving residents' mental health and wellbeing.

Heat Island Effect: By interpolating temperature data, researchers can map the urban heat island effect, identifying areas that might be at greater risk during heatwaves. This information is critical for designing interventions to reduce heat exposure, such as increasing vegetation cover or modifying building materials.

Tutorial (External)

Interpolating Point Data (QGIS3) — QGIS Tutorials and Tips