Surreal illustration of data-driven terrain model.

Unlock the Secrets of Terrain: Choosing the Right Digital Interpolation Method

Samir D’Costa in Tech & Innovation September 2025 • 4 min read.

"From drone surveys to climate models, precise terrain mapping relies on accurate interpolation. But with so many methods, which one reigns supreme?"

The Earth's surface is a complex tapestry of textures and forms, from gentle slopes to dramatic peaks and valleys. Representing this complexity in a digital format is a challenge scientists and practitioners tackle every day. Digital Terrain Models (DTMs) are the tools of choice, but creating accurate DTMs requires more than just data; it requires intelligent interpolation.

Interpolation is the process of estimating values between known data points. When building a DTM, measured data points are often sparse, and interpolation fills in the gaps to create a continuous surface. The accuracy of this process is critical, as it directly impacts any analysis or decisions based on the model.

Choosing the right interpolation method is the key. There's no 'one-size-fits-all' solution, as the best method depends on the specific terrain, the data available, and the intended application. This guide delves into the world of deterministic interpolation methods, comparing their strengths and weaknesses to help you make informed choices for your projects.

Deterministic Interpolation: A Closer Look

Surreal illustration of data-driven terrain model.

Deterministic interpolation methods rely on mathematical functions to estimate unknown values. They are considered 'deterministic' because, given the same input data, they will always produce the same output surface. This predictability makes them popular in various fields. However, the choice of method drastically affects the final result.

Researchers have explored several deterministic methods. A study focused on the Vrana Lake Nature Park compared seven distinct techniques, using elevation data gathered by aero-photogrammetry and stereo-restitution. The accuracy of each method was assessed using statistical parameters and visual analysis.

Inverse Distance Weighting (IDW): Estimates values based on the distance to known points, giving closer points more weight.
Local Polynomial (LP): Fits a polynomial equation to a local neighborhood of data points.
Radial Basis Functions (RBF): Employs various functions to interpolate values based on the distance to known points. Several RBF variations exist, including:

Thin-Plate Spline (TPS)
Spline with Tension (SWT)
Completely Regularized Spline (CRS)
Multiquadratic (MQ)
Inverse Multiquadratic (IMQ)

The study used a combination of cross-validation, split sampling, and jackknifing to rigorously test the accuracy of each method. Statistical parameters, such as root mean square error (RMSE), were calculated. Visual comparisons of the resulting surfaces further aided the assessment. By analyzing how each method performed against real-world data, the research provided valuable insights into their suitability for terrain modeling.

Making Informed Choices for Terrain Modeling

Selecting the right interpolation method is not a trivial task. Factors such as terrain complexity, data density, and desired accuracy all play a role. While the multiquadratic radial basis function (MQ-RBF) showed promise in the Vrana Lake Nature Park study, the best method for your project will depend on your specific needs and data characteristics. Rigorous testing and validation are essential to ensure the reliability of your DTM and the insights it provides.

About this Article -

This article was crafted using a human-AI hybrid and collaborative approach. AI assisted our team with initial drafting, research insights, identifying key questions, and image generation. Our human editors guided topic selection, defined the angle, structured the content, ensured factual accuracy and relevance, refined the tone, and conducted thorough editing to deliver helpful, high-quality information.See our About page for more information.

This article is based on research published under:

DOI-LINK: 10.17559/tv-20131010210942, Alternate LINK

Title: The Accuracy Of Deterministic Models Of Interpolation In The Process Of Generating A Digital Terrain Model – The Example Of The Vrana Lake Nature Park

Subject: General Engineering

Journal: Tehnicki vjesnik-Technical Gazette

Publisher: Mechanical Engineering Faculty in Slavonski Brod

Authors: Ante Šiljeg

Published: 2015-08-08

Everything You Need To Know

What is Digital Terrain Modeling (DTM) and why is interpolation crucial for creating accurate DTMs?

Digital Terrain Models (DTMs) are digital representations of the Earth's surface. They are essential for various applications, from drone surveys to climate models. Interpolation is the process of estimating values between known data points. When building a DTM, the available data points are often sparse, and interpolation fills in the gaps to create a continuous surface. The accuracy of the interpolation method directly affects the accuracy of the DTM, which impacts any analysis or decisions based on the model. Without precise interpolation, the DTM would not accurately represent the complex terrain, leading to flawed results.

What are deterministic interpolation methods, and how do they differ from other types of interpolation?

Deterministic interpolation methods rely on mathematical functions to estimate unknown values. These methods are called 'deterministic' because, given the same input data, they will always produce the same output surface. This predictability is a key characteristic. The deterministic methods include: Inverse Distance Weighting (IDW), Local Polynomial (LP), and Radial Basis Functions (RBF) like Thin-Plate Spline (TPS), Spline with Tension (SWT), Completely Regularized Spline (CRS), Multiquadratic (MQ), and Inverse Multiquadratic (IMQ). Unlike stochastic methods, which incorporate random elements, deterministic methods provide consistent results based on the input data and the chosen mathematical function.

Can you explain Inverse Distance Weighting (IDW) and how it is used in terrain modeling?

Inverse Distance Weighting (IDW) is a deterministic interpolation method. It estimates values based on the distance to known points. Closer points are given more weight in the estimation, meaning that their values have a greater influence on the interpolated value. This method is commonly used in terrain modeling to create DTMs from scattered elevation data points. The accuracy of IDW depends on the distribution of the known data points and the chosen parameters, such as the power parameter which controls the influence of distance.

What are Radial Basis Functions (RBF) and what are the different types of RBF methods used in terrain modeling?

Radial Basis Functions (RBF) are a class of deterministic interpolation methods that employ various mathematical functions to interpolate values based on the distance to known points. Several variations of RBF exist, each using a different mathematical function. These include Thin-Plate Spline (TPS), Spline with Tension (SWT), Completely Regularized Spline (CRS), Multiquadratic (MQ), and Inverse Multiquadratic (IMQ). The choice of RBF method depends on the specific terrain, the data available, and the desired level of smoothness or accuracy. The study mentioned in the text compared these RBF methods to assess their suitability for terrain modeling.

How do researchers evaluate the accuracy of different interpolation methods for Digital Terrain Modeling (DTM), and what factors influence the choice of the best method?

Researchers use various techniques to evaluate the accuracy of interpolation methods. These include statistical parameters, such as root mean square error (RMSE), and visual analysis. Cross-validation, split sampling, and jackknifing are used to rigorously test the accuracy of each method. The best method for a project depends on the specific needs and data characteristics. Factors such as terrain complexity, data density, and desired accuracy all play a role. While the multiquadratic radial basis function (MQ-RBF) showed promise in one study, the optimal method will vary depending on the project requirements. Rigorous testing and validation are essential to ensure the reliability of the DTM and the insights it provides.