What is the impact of sample size on kriging?

2 Sampling design

The sampling design refers to how you select and locate the samples for kriging. The sampling design affects the sample size for kriging in two ways: by influencing the accuracy and precision of the variogram, and by affecting the spatial coverage and representativeness of the samples. The accuracy and precision of the variogram depend on the number and distribution of sample pairs at different distances, which determine how well you can estimate the sill and the range. The spatial coverage and representativeness of the samples depend on how evenly and systematically you spread the samples over the area of interest, which determine how well you can interpolate the variable between the samples. Generally, the more accurate and precise the variogram, and the more uniform and representative the samples, the better the kriging performance, and the fewer samples you need.

3 Kriging model

The kriging model refers to how you use the variogram and the samples to estimate the variable at unsampled locations. The kriging model affects the sample size for kriging in two ways: by defining the weighting scheme and the search neighborhood for kriging, and by providing an estimation error or variance for each kriged value. The weighting scheme and the search neighborhood for kriging determine how much you rely on the nearby or distant samples, and how many samples you use for each estimation. The estimation error or variance for each kriged value measures how uncertain or confident you are about the estimation, and how well it matches the true value. Generally, the more optimal the weighting scheme and the search neighborhood, and the lower the estimation error or variance, the better the kriging performance, and the fewer samples you need.

4 Estimation error

The estimation error is the difference between the kriged value and the true value of the variable at an unsampled location. The estimation error is affected by all the factors mentioned above: the spatial variability, the sampling design, and the kriging model. The estimation error is also a function of the sample size, as it tends to decrease as the sample size increases, up to a certain point. The estimation error can be used as a criterion to optimize the sample size for kriging, by finding the minimum number of samples that achieves a desired level of accuracy or confidence. However, the estimation error is not always known or easy to calculate, as it requires either a validation dataset or a cross-validation procedure.

5 Practical guidelines

When choosing the optimal sample size for kriging, it is important to start with a preliminary variogram analysis to understand the spatial variability and the scale of the variable. The sampling design should be chosen to maximize accuracy and precision of the variogram, as well as spatial coverage and representativeness of the samples, while minimizing sampling cost and effort. Additionally, a kriging model should be selected that matches the variogram shape and sampling distribution, while minimizing estimation error or variance, and avoiding overfitting or bias. To ensure you reach your accuracy or confidence objectives, it is recommended to evaluate the kriging performance and estimation error using a validation dataset or a cross-validation procedure. Finally, adjust the sample size accordingly by adding or removing samples until you reach an optimal trade-off between kriging quality and sampling quantity.

6 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?