What is a Semivariogram? Example of a Typical Semivariogram

What is Semivariogram?

A semivariogram is a statistical curve that displays the degree of similarity between two sets of observations.

A semivariogram is a type of rectangular probability graph with the x-axis displays the horizontal distance between pairs of observations, and the y-axis displays some measure of similarity between those pairs.

The greater the similarity between observations, the higher on the graph they will be. A semivariogram can be interpreted as a graphical illustration of how close two sets of data are to being identical.

For this reason, the semivariogram can be incredibly useful in understanding how similar two groups of data are, especially when there is a large sample size to draw upon.

Semivariogram Example

According to Tobler’s First Law of Geography, “everything is related to everything else, but close things are more related than distant things.”

Closer things are more predictable and have less variability in the case of a semi-variogram. Things that are far away are less predictable and less related.

The terrain one meter ahead of you, for example, is more likely to be similar than the terrain 100 meters away.

The semi-variogram illustrates the critical concept of how sample values (pollution, elevation, noise, etc.) vary with distance.

Samples of Soil Moisture-In this example, 73 soil moisture samples were collected from a 10-acre field. The samples in the northwest corner are much wetter and have a higher water content. However, they are much dryer in the eastern quadrant.

Semivariogram Model

The semivariogram depicts the measured sample points’ spatial autocorrelation.

A model is fit through each pair of locations after they have been plotted. Certain characteristics are frequently used to describe these models.

The data from the soil moisture field are represented by the following semi-variogram.

The green region represents the area of high-water content, and the yellow represents low water content. The dots represent samples.

Model Specification

1. Start with an adequate number of data points in a model for a semivariogram to be generated. This is determined by your sample size and time period within which you will be analyzing your data set.
2. Rank each data point within the model after you have identified the pattern in which they form.
3. Determine a suitable semivariogram model by plotting all combinations of data points that are calculated, and only using those with top ranking values.
4. Build a sample size to include data points under consideration with any existing models built around that combination of data points.
5. Reject semivariograms that are not right for your data set.
6. Replace any other semivariogram models that have data points with low-ranking values, and replace them with ones that have higher ranking values than the others.
7. Repeat this process until all candidate models are removed from the sample size list.
8. Approve the new sample size that has the highest-ranking values and determine its confidence level.
9. Generate a semivariogram model that has the highest-ranking values in order to ensure you are applying the correct model to your data set.
10. Apply your semivariogram model to any future projects or research projects you may be working on as they arise.
11. Continue to analyze your data set and create other statistical models that are applicable to your project.

Semivariogram Analysis

Semivariogram analysis is the semivariogram is a statistic that assesses the average decrease in similarity between two random variables as their distance increases, which has some applications in exploratory data analysis.

To analyze a semivariogram:

1. Begin by breaking down the data points in the model that best represent your set of observations.
2. Next, determine what other models could be applied based on your data set.
3. After these are complete, determine what point of the semivariogram best represents the shape or form of your data set.
4. Analyze this shape and find stable zones that show extreme similarity between samples in order to determine where your samples’ ranges generally lie.
5. Determine why there is high variation among sample points and how this varies with distance from each other.
6. Look at the total length of the graph and see if there is a recognizable pattern among your data set.
7. Determine whether or not your project will be successful based on the shape of your graph, as well as how you are expected to gather your data.
8. Communicate this information to other parties who will assist you in applying this model to future projects or research studies that you may be performing in order to ensure accurate results.
9. Once this is complete, it is important to report your findings to management or a higher authority so that they can apply this information to your research study and make any necessary changes.

Semivariogram Formula

The goal of a semi-variogram is to demonstrate how similar two sets of data are in relation to sample values within a larger size range.

In detail, it calculates the difference between two sets of data by calculating the sum of squared differences, or the square of x minus the square of y.

The semivariogram then scales these values out to a range between 0 and 1.0 and plots them as points that follow a curve formed by their points.

No two models will be exactly alike because experimenters test new models before being used in other experiments. Each trial model is different because it is uniquely fitted to its own data set through statistical analysis.

The formula is:

where: S is the sum of squared differences dS2 = [x-y]2

Where: S is the sum of squared differences dS2 = [x-y]2 r is correlation coefficient

Response: The desired model can be demonstrated through a semivariogram graph with the use of a semi-variogram calculator.

Use this calculator to build a semi-variogram model in order to determine which one(s) best fits your data set.

From here, you will build on your semi-variogram model and gather related data points that fit the characteristics you plan to display on your graph.

This involves building a sample size that has been calculated for each semi-variogram model and then choosing the correct semi-variogram model from the list. This will be based on the values recommended by your sample size formula.

Once all these calculations are complete, you can begin to build a graph that helps to display those characteristics. If a graph is plotted, it will show your range of soil water content in relation to distance from samples of soil moisture.

From there, you can identify an expected range of values based on your data set, and whether or not your project will be a success.

This will include the type of water content your property has, and how this water content is distributed throughout the area.

You can also determine if the samples are positively correlated to each other and how long a period of time this will take to occur, as well as their response rate.

Semivariogram and Covariance

The covariance between two sets of data is calculated by subtracting the mean value from the standard deviation and then squaring the difference. The semivariogram is a scaled version of the covariance, but it uses a different measurement for its scaling.

The covariance is then multiplied by 1 – r, where r is the correlation coefficient.

In order for a semivariogram to be generated, every possible pair of observations has to be compared with every other possible pair of observations in order to determine if they are correlated or not.

The result of this analysis will create a semivariogram graph for display, which can be used to display the correlation capabilities of your data set.

This will include a range of values from 0.0 to 1.0 that are ordered from low too high in order to display your results.

This will also include the total variance generated, as well as the range of correlations that were calculated based on your data set’s ability to correlate with other sets of data.

Semivariogram and Other Methods of Analysis

Although the semivariogram is the most popular method for determining correlation between soil samples, there are other methods that can be applied to your data set if a graph is required.

These methods include:

• Correlation coefficient (r)

This is determined by the formula: r = [Sxy/(n-1) SxSx / (n-1)]

The data points that are plotted on your semivariogram graph can then be used to determine what other methods may be applied to your data set based on its correlation capabilities.

• Contingency coefficient (c)

This is determined by the formula: c = [n(n-1) / (n(2n-1))] = n(n-1)

Use this when your data is close together, or if the sample size is large. This will determine how many subgroups are matched with a similar range of soil water contents.

One way to accomplish this would be to break your data set down into subgroups and display these on your graph based on the ranges of soil water content for each subgroup.

• Partial ordination (n-1)

This is determined by the formula: n-1 = [E(X) E(Y)]

This method can be used if you have a large amount of data and a small sample size.

• Water retention curve and monotone regression model

If your research is based on the water content of soil samples and how they are affected by

rainfall, it is important to use a method of analysis that will display your data in accordance with the characteristics you are displaying on your graph.

This will help you determine how successful your project will be in the long term if it is implemented into larger systems.

Semivariogram in ArcGIS

The semivariogram can also be created in ArcGIS.

In order to do this, it is necessary to add a semi variogram calculator to the toolbox:

This can be done by copy pasting the ‘SEMIVARIOGRAM’ string into the toolbox;

select ‘Add tools > Add tool to my toolbox’; and then enter the ‘Tools Name’.

Once you have added the semi variogram calculator, you will continue by following these steps:

1. Specify the semi variogram calculator by going to ‘Append Tool > SEMIVARIOGRAM’.
2. Specify the sample size and then select the location of your sample points.
3. Use the semivariogram calculator to determine which semi-variogram model is recommended for your data set and then select it from the dropdown list ‘[Semivariogram Calculator]’.
4. Select ‘Update Layer Properties’, which will set up your curves and axes based on your choosing.
5. If necessary, change the style of your semivariogram so that it is consistent with your data set.
6. Select the “Save” button and move on to the next step.
7. Make sure that your semi-variogram model has been turned on by double clicking on it in the ‘Semivariogram’ toolbox and then select ‘Add Axis > Axis’. This will create a new layer and make it easier to work with.
8. Go to ‘Add Layer > Add Layer > Create New Axis’ and then create the axis that corresponds with the semi variogram model that was generated from the data set.
9. Select the ‘Semi-variogram Properties’ option and edit it so that it is consistent with your data set.
10. Go to ‘Edit > Select by Attributes’. This will let you select one of your semivariogram models and then add it to another layer or a new layer depending on your desired outcome.
11. Enter the name of this attribute and choose ‘OK’ to proceed.
12. Select the ‘Create’ button to end your session.
13. Select your semi-variogram model, which was generated from your data set, and then press ‘OK’. This will place it on your map in accordance with the characteristics that you set for it in ArcGIS.
14. Once you are done, the map should be displayed on your computer screen.

FAQs

What is a Semivariogram?

A semivariogram is a statistic used in spatial analysis to quantify the spatial dependence between two variables. It is a measure of how similar two points are in terms of their distance from each other.

The semivariogram is used to determine the range of spatial dependence in a dataset, and to help identify clusters and outliers.

What is a Semivariogram Nugget?

The nugget is the variogram’s y-intercept. In practice, the nugget represents the data’s small-scale variability. A portion of that short-term variability may be due to measurement error.

What does a Semivariogram show?

A semivariogram shows the correlation between two sets of data. This can be used to determine how similar the two sets of data are and whether they differ from one another or not.

What is Semivariogram kriging?

Semivariogram kriging is a method of determining the amount of correlation between two sets of data.

What is a semi-variogram?

Semi-variograms are graphical representations of the correlation between two sets of data. This allows for more information to be displayed about how similar or dissimilar a pair of data points are to each other.

What is a semi variogram’s kurtosis?

A semi-variogram’s kurtosis is the degree to which a data set can be distinguished from a random set of points. A random set of points would have a kurtosis value of 3. Because soil samples are not randomly scattered, the semi-variogram’s kurtosis value is typically greater than three.

What is a semi variogram’s range?

The semivariogram range is determined by the distance between two data points in order to show how well they correlate with one another. A larger range means a greater degree of correlation between the two data sets.

What is a semi variogram’s variance?

The variance is the degree of error that exists in assumptions about the correlation between two sets of data. A lower variance means that there is less error between separate data points.

What does the kurtosis of a semi-variogram tell you about your data?

The higher the value for the kurtosis, the more spread out and disjointed your data points are.

What is a Covariance?

The covariance is a measurement of how similar two sets of data are.

The ratio is calculated by dividing the horizontal axis by the vertical axis, which can then be squared in order to produce a scaled measurement that will determine how many units there are between each point on your semivariogram graph.

What is the difference between Semivariogram and variogram?

The difference between the semivariogram and variogram is that one of them will display the characteristics of a given data set while the other will display a range of values used to calculate a value for the data set.

The difference between them is that where the semivariogram gives you a measurement based on your data’s ability to correlate with other sets of data, it can also be used as a measurement in order to determine how well your project will work on a larger scale.

What is a Cross-correlation?

The cross-correlation is a measurement of how similar two sets of data are.

What are some other names for the semivariogram?

The semivariogram is also referred to as the ‘covariance’ and the ‘semi variance’.

What is an Edaphic Factor?

An edaphic factor is a geologic feature that helps determine how soil will respond to an environmental factor. This can include how water will move through soil, whether it will remain there, or if it will be drained.

Why is semivariogram analysis used to analyze soil water content data?

This is used to determine the range of correlation between soil samples and other data sets that are in a similar range of soil water content. It can also be used to evaluate how well samples will perform in the long term based on their correlation capabilities with other data sets.

How do I work with the semivariogram graph?

This graph is a semivariogram that is generated based on the data that you submitted. When you first start working with it, it will appear as dots. If you hover over a dot, an explanation of how the data set was analyzed will appear showing what soil property values were used in the analysis.

How do you read a semi variance?

You start by looking at your semivariogram on the bottom left of your screen and then you move it all the way to the right side, which will allow you to read off all the soil properties that were used in calculating your semivariogram.