{"id":12791,"date":"2017-02-04T03:36:40","date_gmt":"2017-02-04T09:36:40","guid":{"rendered":"http:\/\/gisgeography.com\/?p=12791"},"modified":"2025-04-09T06:13:49","modified_gmt":"2025-04-09T11:13:49","slug":"kriging-interpolation-prediction","status":"publish","type":"post","link":"https:\/\/gisgeography.com\/kriging-interpolation-prediction\/","title":{"rendered":"Kriging Interpolation – The Prediction Is Strong in this One"},"content":{"rendered":"\n
\"Kriging<\/figure>\n\n\n\n
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Sculpt a Legendary Prediction Model with Kriging<\/h3>\n\n\n\n

It’s time to sculpt a prediction model of the ages. The prediction is strong in kriging<\/strong>.<\/p>\n\n\n\n

On your journey to creating a fine prediction surface, you’ll need to understand some key concepts before even getting into kriging.<\/p>\n\n\n\n

What are these concepts?<\/p>\n\n\n\n

Read below to get a step-by-step<\/em> core knowledge of kriging.<\/p>\n<\/div><\/div>\n\n\n\n

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Let’s start with some basics<\/h3>\n\n\n\n

To really understand kriging, you have to know what interpolation<\/strong> is. As with all interpolation, we’re predicting unknown values at other locations.<\/p>\n\n\n\n

With an interpolation method like inverse distance weighting<\/a>, you are making predictions without saying how certain you are.<\/p>\n\n\n\n

Here’s an example:<\/p>\n\n\n\n

We predict the purple point, by taking an inverse weighted distance of the closest three input points (The values of 12, 10, and 10). Based on the distance, we calculate how far each input point is and get a value of 11.1.<\/p>\n\n\n\n

((12\/350) + (10\/750) + (10\/850)) \/ ((1\/350) + (1\/750) + (1\/850)) = 11.1<\/strong><\/p>\n\n\n

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\"IDW<\/a><\/figure>\n<\/div>\n\n\n

This is exactly how deterministic<\/em> interpolation works. Simply, it uses a predefined function and it is what it is<\/em><\/strong>.<\/p>\n\n\n\n

But it doesn’t tell you how sure you are.<\/p>\n<\/div><\/div>\n\n\n\n

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What is Kriging Interpolation?<\/h3>\n\n\n\n

If a weatherman makes a forecast saying it’s going to rain tomorrow, how sure are you that it’s going to rain?<\/p>\n\n\n\n

In other words:<\/p>\n\n\n\n

Instead of only saying here’s how much rainfall is at specific locations, kriging also tells you the probability<\/strong> of how much rainfall is at a specific location.<\/p>\n\n\n\n

You use your input data to build a mathematical function with a semivariogram<\/strong>, create a prediction surface, and then validate your model with cross-validation.<\/p>\n\n\n\n

Not only does geostatistics<\/a> provide an optimal prediction surface, but it also delivers a measure of confidence in how likely that prediction will be true.<\/p>\n\n\n

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\"kriging<\/figure>\n<\/div>\n\n\n

Meanwhile, kriging can generate prediction surfaces and surfaces that describe how well your model predicts:<\/p>\n\n\n\n

PREDICTION<\/strong>: This surface directly predicts the values of the variable you are kriging.
ERROR OF PREDICTION<\/strong>: It depicts the standard error. You get a higher “standard of error” when there isn’t as much input data.
PROBABILITY<\/strong>: The probability surface highlights when it exceeds a threshold.
QUANTILE<\/strong>: This surface represents the best or worst-case scenarios as the 99th percentile.<\/p>\n<\/div><\/div>\n\n\n\n

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The Key to Kriging is the Semivariogram<\/h3>\n\n\n\n

Kriging relies on the semi-variogram<\/a>. In simple terms, semivariograms quantify autocorrelation<\/a> because they graph out the variance of all pairs of data according to distance.<\/p>\n\n\n\n

Chances are that closer things<\/em><\/strong> are more related and have small semi-variance. While far things<\/em><\/strong> are less related and have a high semi-variance.<\/p>\n\n\n\n

But at a certain distance (range)<\/strong>, autocorrelation becomes independent. Where that variation levels off, it’s called (sill)<\/strong>. This means there is no longer any spatial autocorrelation or relationship between the closeness of your data points. This concept is Tobler’s First Law of Geography<\/a>.<\/p>\n\n\n

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\"variogram<\/a><\/figure>\n<\/div>\n\n\n

Again, the purpose here is to fit a surface such as a polynomial that models the overall large-scale trend. Then, around that trend, we have variability with residuals where kriging comes in.<\/p>\n\n\n

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\"kriging<\/a><\/figure>\n<\/div>\n\n\n

Based on your semi-variogram<\/a> results, you can select a semivariogram that is spherical, circular, exponential, Gaussian, or linear. Alternatively, if you can make an intellectual justification for a mathematical model, then you pick that one.<\/p>\n<\/div><\/div>\n\n\n\n

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Before You Even Begin, Check Your Data<\/h3>\n\n\n\n

In our example, we use soil moisture samples taken in an agriculture field. Here is a visualization of our data points with soil moisture measurements.<\/p>\n\n\n