Module 2.2 - Surface Interpolation

Interpolation is a Geographic Information Systems (GIS) technique that estimates values at unmeasured locations by utilizing known sample points, based on the principle that spatially proximate points exhibit similar values. This method converts point data into continuous rasters, enhancing the visualization and analysis of spatial patterns. It is applicable across numerous measurements, including elevation, rainfall, and noise levels.

In this lab assignment, three interpolation techniques, Thiessen, Inverse Distance Weighted (IDW), and Spline interpolation, were employed to analyze water quality conditions in Tampa Bay, specifically focusing on the Biochemical Oxygen Demand (BOD) measured in milligrams per liter. 

1. Thiessen Interpolation: This method is a straightforward nearest-neighbor approach that divides geographic space into polygonal regions defined by the proximity of known data points. Each polygon represents the area nearest to a particular sample point, and values are assigned throughout the polygon based on the value of the nearest known point.

2. Inverse Distance Weighted (IDW): IDW calculates values for unsampled areas by averaging values from neighboring sample points, giving more weight to closer points. This method is particularly effective with datasets that have a high density of sample points and is typically used where spatial data shows gradual changes.

3. Spline: This technique uses mathematical functions fitted to the data to minimize surface curvature. The output is a smooth surface representation ideal for depicting phenomena that show gradual variations, such as topographic gradients. Interpolation thus serves as an essential tool in GIS for analyzing and visualizing spatial data distributions effectively.

First, we started with utilizing a dataset included of samples collected from Tampa Bay over a short timeframe. An initial analysis was conducted to determine the minimum, maximum, average, and standard deviation of the BOD parameter through a non-spatial technique, which involved examining the statistics of the point data layer.

Subsequently, the Thiessen polygon tool was employed to create polygons based on the proximity to known data points. This analysis also included checking the properties of the polygons and recording the relevant statistics, including the minimum, maximum, average, and standard deviation.

Following that, IDW Spatial Analyst tool was utilized to generate a new interpolation raster, which depicted the concentration of BOD across Tampa Bay. The results were further analyzed using the Zonal Statistics as Table tool to calculate and record statistics from the newly created raster.

Lastly, the Spline tool was applied to create an alternative raster utilizing the Regularized spline method. This final raster revealed an anomaly in the northern portion of the study area, where there was a very high concentration of BOD, despite the absence of sampling points in that specific region. This observation raises questions about the accuracy and representation of the data in that area. Two nearby sampling locations showed biochemical oxygen demand (BOD) levels of 1.157 mg/L and 2.2 mg/L, with the higher reading identified as an outlier. To address this discrepancy and to avoid distorting the smooth curve, we can either remove the outlier or replace it with an interpolated value. In this case, the point corresponding to the elevated BOD reading was removed, and spline interpolation analysis was subsequently re-executed.

Map showing Spline Interpolations using Tension type