Why does the groundwater example require quadrivariate interpolation instead of ordinary 2D or 3D interpolation?
The groundwater example requires quadrivariate interpolation because the observations are scattered in three-dimensional space and also vary over time. This involves four variables: three spatial dimensions and time. Ordinary 2D or 3D interpolation cannot capture the temporal evolution of the pollution field, so a 4D raster combining 3D space and time is needed.
Conditions
- Input values are measured at 3D points over time.
- Output is a 4D raster combining 3D space and time.
Reasoning, step by step
- Identify that the groundwater wells are scattered in horizontal and vertical directions (3D space).
- Identify that the same wells are sampled repeatedly over time.
- Conclude that the data are scattered both in space and in time, involving four variables.
- Apply quadrivariate interpolation to obtain a 4D raster representing the evolving pollution volume.
Example
The video uses a groundwater pollution dataset over 10 years, where wells have different numbers of temporal observations, to demonstrate the need for quadrivariate interpolation to create a 4D raster.
Common misconceptions
- Assuming that 3D interpolation is sufficient if the spatial data is 3D, ignoring the time dimension.
- Believing that the vertical axis in the time-distribution view represents physical depth rather than time.
Watch the explanation
Explore next
Answers are generated from source material and independently checked. Consult the original video or creator if something is unclear.