Global Polynomial (GP) Interpolation

1. Introduction

Global Polynomial (GP) interpolation is a spatial interpolation method used in GIS (Geographic Information System) that fits a polynomial function to the data points in the study area. The polynomial function can then be used to estimate the value at unsampled locations.

The main advantages of GP interpolation are its simplicity and flexibility. It is a non-parametric method that does not require any assumptions about the underlying data distribution, and it can be used with any type of data. Additionally, it is computationally efficient and can be applied to large datasets.

Applications of Global Polynomial (GP)

The main applications of GP interpolation include:

1. Terrain modeling: GP interpolation can be used to estimate elevation and slope data for terrain modeling applications such as topographic mapping, watershed analysis, and floodplain mapping.
2. Environmental Modeling: GP interpolation can be used to estimate environmental variables such as air quality, temperature, and rainfall. These estimates can be used to identify areas with high levels of pollution or to model the spatial distribution of climate variables.
3. Demographic mapping: GP interpolation can be used to estimate population density and other demographic variables, which can be useful for planning and policy decisions.
4. Agriculture and forestry: GP interpolation can be used to estimate soil properties such as pH and nutrient content, which can be useful for agricultural management and land use planning. It can also be used to estimate biomass and timber volume in forestry applications.

3. Limitations of Global Polynomial (GP)

However, GP interpolation also has limitations that should be considered:

1. Overfitting: GP interpolation can suffer from overfitting if the polynomial degree is too high or if the data are noisy. This can result in inaccurate estimates and poor predictive performance.
2. Sensitivity to outliers: GP interpolation is sensitive to outliers in the data, which can lead to inaccurate predictions.
3. Limited to small-scale applications: GP interpolation is not well-suited for large-scale interpolation applications due to its computational complexity and sensitivity to sample distribution.
4. Difficulty in selecting the polynomial degree: Choosing an appropriate polynomial degree can be difficult and subjective, and different degrees can result in different estimates.

Overall, GP interpolation is a useful and flexible method for spatial interpolation in GIS, but its limitations should be considered in the context of the specific dataset and research question. Other interpolation methods, such as kriging or spline interpolation, may be more appropriate in some situations.