Estimating Values (Interpolating) for Non Technical GIS Users

Background source: https://www.inverse.com/article/9207-nasa-maps-show-better-air-quality-in-the-usa-worse-air-quality-in-china

From Mathematics, we have adopted an estimation method to find values between known data points. This estimation method is called interpolation. To make it approachable, let’s imagine you are a hiker. As a hiker you’d like to record your journey at each point. Each point has its own elevation (z). You recorded many of them during your hike to the Alps, around 121 points.

However, when you looked at them, they are mere points. You don’t know the elevation between them. They don’t show the track that you took because you can only look at each point. This is where interpolation helps you. When you have data points with values, in this case elevation, you can estimate the value between those points. Therefore, you will be able to see how high did you climb, and how steep. See? This is useful for many things, especially things that have spatial pattern.

One unique example is sound level in a concert. You can measure loudness (in dB) of several points in a concert and use interpolation to estimate the sound level between those points. Useful right?

You can stop here if you only want to understand the basic. However, I’ll talk about the interpolation methods in geospatial technology; not too deep, only a cheat sheet. Although I have to advise that this is a rough approach to these different methods since there is no exact rule of thumb on what kind of data suits with what method as mentioned by Wu & Hung (2016).

Interpolation Methods Cheat Sheet for Non Technical Users

Six interpolated surfaces with their parameters. N: neighbor. (a) IDW, power 2, N 10; (b) spline, tension, N 10; © kriging, circular, N 10; (d) IDW, power 4, N 20; (e) spline, thin plate, N 20; (f) kriging, exponential, N 20 (Wu & Hung, 2016).

a. Inverse Distance Weighting (IDW)

1. What is it? Uses nearby known points to guess unknown points. Closer points matter more. (IDW estimates values at unsampled locations based on a weighted average of the values available at known points. The weight is a function of the inverse distance from the unsampled location to each known point.)
2. Why use it? It’s conceptually simple and assumes that things that are closer to one another are more alike than those that are farther apart.
3. When to use it? When you believe that each data point has a local influence that diminishes with distance.
4. Where? Suitable for regions where change is gradual.
5. Usage/Field? Environmental data like temperature or precipitation where readings tend to decrease or increase gradually across a landscape.
6. How does it work? IDW calculates an average value for the unsampled location based on surrounding known values, with closer values given more influence (higher weight) than distant values.
7. Best For? Estimating things like temperature or rain amounts based on nearby measurements.
8. Not Great For? Areas with sudden changes, like city boundaries, because it’d blur those sharp edges.

b. Kriging

1. What is it? Advanced guessing using patterns between known points. (A more advanced form of interpolation that considers both the distance and the degree of variation between known data points when estimating values.)
2. Why use it? It provides more accurate results by considering spatial autocorrelation (the statistical relationship between the sampled points).
3. When to use it? When you have a good understanding of the spatial distribution and correlation of your data.
4. Where? Suitable for regions with any spatial pattern but requires a well-distributed sample.
5. Usage/Field? Often used in mining for estimating ore body, soil properties, and groundwater pollutants.
6. How does it work? Uses a semivariogram to understand the spatial relationship between points and predicts values based on this relationship.
7. Best For? Finding out things like how minerals are spread underground based on a few sample points.
8. Not Great For? Places with very few sample points or when the data doesn’t have a clear pattern.

c. Nearest Neighbor

1. What is it? Unknown point takes the value of its closest neighbor.
2. Why use it? Simplicity and suitability for categorical data (like land cover types).
3. When to use it? When data doesn’t change much between sample points or when data is categorical.
4. Where? Suitable for regions with fairly uniform distributions.
5. Usage/Field? Land use classification, determining vegetation types.
6. How does it work? Directly assigns the value of the nearest known data point to the unsampled point.
7. Best For? Picking categories, like forest vs. urban, based on the closest known point.
8. Not Great For? Smooth things like temperature maps because it’d make them look blocky.

d. Bilinear and Bicubic Interpolation

1. What is it? For image guessing; bilinear sees 4 nearby pixels, bicubic sees 16.
2. Why use it? Provides smoother results compared to nearest neighbor.
3. When to use it? Commonly used in image processing when resizing images.
4. Where? Suitable for raster image data.
5. Usage/Field? Image resampling, remote sensing.
6. How does it work? Uses a weighted average of points to determine a new value. Bicubic considers more neighboring points and results in smoother images.
7. Best For? Rescaling pictures to keep them smooth.
8. Not Great For? Maps with categories (like land types) because they can blur the distinct lines.

e. Spline Interpolation

1. What is it? A mathematical function that tries to find a smooth curve that passes through the known data points.
2. Why use it? To get a smooth surface that passes exactly through the input points.
3. When to use it? When smoothness of data is more important than exactness to input data points.
4. Where? Suitable for regions with smoothly varying surfaces.
5. Usage/Field? Elevation data, bathymetric data.
6. How does it work? Uses polynomial functions to estimate values. The curve is influenced by all sample points, giving it a smooth appearance.
7. Best For? Making smooth maps, like hills or seabed curves.
8. Not Great For? Maps with sudden changes or very noisy data, as it might exaggerate those parts.

References

Wu, Y.-H. (Eva), & Hung, M.-C. (2016). Comparison of Spatial Interpolation Techniques Using Visualization and Quantitative Assessment. InTech. doi: 10.5772/65996