Flood modeling, vegetation management, geological hazards monitoring, and infrastructure planning all have one thing in common: the need for an elevation model.
The only difference is, while some use cases need an elevation model of the natural terrain (a Digital Terrain Model, DTM), others need a model that also captures surface features, like buildings and vegetation (a Digital Surface Model, DSM).
However you plan on using your elevation model, you need it to be accurate.
The source of elevation data is a key factor in the accuracy of the resulting height information stereo satellite imagery. Light Detection and Ranging (LiDAR) data are two common examples of digital elevation data sources.
In this article, we will discuss LiDAR data accuracies---including factors affecting these accuracies. We will then look at what to consider when using stereo satellite imagery for elevation modeling.
We begin by answering an important question.
What is LiDAR?
Light Detection and Ranging (LiDAR) is an Earth observation method that uses light in the form of a pulsed laser to measure ranges (variable distances). These light pulses generate 3-dimensional points, called point clouds, which are used to extract information about the shape of the Earth and its surface characteristics.
A LiDAR system consists of a laser ranging and scanning unit, an Inertial Navigation System (INS), and a Global Navigation Satellite System (GNSS) receiver. The INS and GNSS are used for positioning and orientation.
Airplanes, helicopters, and drones are the most commonly used platforms for acquiring LiDAR data for terrain modeling.
LIDAR photo of H.J. Andrews Forest by Oregon State University
Why is LiDAR Important?
Compared to traditional surveying, LiDAR sensors collect more detailed and highly accurate elevation points---faster. In addition to speed and accuracy, other factors that make LiDAR important include:
It is an active sensor, meaning data can be collected during the day or at night
In dense forests, LiDAR pulses can pass through small spaces to the ground as opposed to photogrammetry. Hence, it is important for mapping forest floors.
LiDAR sensors continuously measure surface points resulting in a more uniform height model as compared to traditional surveying.
Applications of digital terrain models from LiDAR include canopy modeling, hydrology, coastal engineering, building deformation monitoring, etc.
LiDAR Accuracy Assessment
Accuracy refers to the closeness of a measured or computed value to a standard or accepted (true) value of a particular quantity. It is commonly estimated by calculating the Root Mean Square Error (RMSE).
For LiDAR, there are two types of accuracy specifications: absolute and relative accuracy. Let us look at each.
Absolute LiDAR Accuracy
Absolute LiDAR accuracy refers to both the horizontal and vertical accuracy of LiDAR data. Absolute accuracy is assessed by comparing the LiDAR data with ground surveyed checkpoints.
Horizontal checkpoints are well-defined points/ features that are visible on the ground. Their horizontal positions are accurately surveyed with respect to a reference geodetic datum.
Vertical checkpoints, on the other hand, do not need to be visible points. They are points surveyed on flat and open terrain. This minimizes interpolation errors when comparing checkpoint elevations to elevations interpolated from the dataset. For a LiDAR dataset, the vertical accuracy achieved on flat and open terrain is known as the "fundamental" vertical accuracy.
While there's no specific method for determining the appropriate checkpoint distribution, it usually depends on land cover type and terrain. The New ASPRS 2014 Standard provides specific recommendations on checkpoint density and distribution.
Relative LiDAR Accuracy
Relative LiDAR accuracy refers to the internal quality of LiDAR elevation data without using surveyed ground control points. Relative accuracy is a measure of local differences between points in the point cloud. It is affected by LiDAR system calibration. Relative accuracy is assessed in 2 ways:
- Within-swath accuracy assessment: Assessment of data collected within the same swath or flight line. It indicates how stable the LiDAR system is.
- Swath-to-swath accuracy assessment: Assessment of data collected between swaths/ adjacent flight lines. It involves comparing overlapping sections in adjacent swaths.
"Good" relative accuracy means that individual points in your point cloud are where they are supposed to be in relation to the whole point cloud. Relative accuracy is especially important for applications such as slope and aspect which are based on the elevation of points next to each other.
What is "good" accuracy?
Well, the acceptable limits for both absolute and relative accuracy vary by application. For example, LiDAR data accuracy requirements for the detailed design of infrastructure such as a dam may be higher compared to LiDAR data for agriculture.
Digital Terrain Model (DTM) (Source).
What Factors Affect LiDAR Accuracy?
The accuracy of LiDAR-derived elevation models depends on various factors including, the calibration parameters of the LiDAR system components, the underlying point density, the flight parameters, and the data processing techniques used.
We look more closely at a few factors affecting LiDAR accuracy below.
Ground Filtering Technique Used
A LiDAR point cloud contains:
Ground points on the bare earth
Non-ground points which comprise natural features such as tree canopies and rock outcrops, and built features such as buildings bridges
Noise, which are undesired measurements, e.g., cars, airplanes, birds, etc.
When generating a digital terrain model with LiDAR data, the first step is the removal of noise. Thereafter, ground points are separated from non-ground points. This is called ground filtering. Lastly, a DTM is generated by interpolating ground points.
Ground filtering can be a challenge in regions with highly variable elevations. For example, while it may be easier to separate ground from non-ground points in flat areas, it is harder in places with a mixture of different features: variable building sizes, jagged hilly edges, short walls, and bridges.
Therefore, if the ground filtering technique used classifies non-ground points as ground points, this introduces errors in the final DTM.
LiDAR Point Density
LiDAR point density is the number of LiDAR points per unit area.
Dense point clouds improve the accuracy of derived models where the portion of the Earth's surface being mapped is complex or mountainous, i.e., where the surface elevation changes rapidly.
Additionally, in forested areas, dense point clouds increase the chances of more points penetrating through the canopy and reaching the ground. More ground points equal a more representative terrain model. Consequently, the nDSM generated will be a truer model of tree heights and canopies.
LiDAR returns photo by Environment Agency Survey Open Data.
Point Density and the Vertical Accuracy of LiDAR
Generally, higher point density results in higher vertical accuracy of the derived model.
Increased point density may not improve the accuracy in areas with flat and open terrain. Further, regardless of how dense the points are, other factors, such as GNSS and INS errors, may limit the maximum accuracy attainable.
The table below shows the American Society for Photogrammetry and Remote Sensing (ASPRS) recommended LiDAR point density for LiDAR terrain mapping.
Even though point densities are listed for specified vertical accuracies, you may select higher or lower point densities suited to your project requirements and the complexity of surfaces to be modeled.
Source: New ASPRS 2014 Standard
In the table above:
Non-vegetated vertical accuracy (NVA) is the vertical accuracy at the 95% confidence level in non-vegetated open terrain
Nominal Pulse Density (NPD) is the number of LiDAR points per unit area expressed as pulses per square meter
Nominal Pulse Spacing (NPS) is the distance between LiDAR points in meters
Flying height, flying speed, and attitude are some flight parameters that can affect the accuracy of your LiDAR data.
Flying attitude refers to the orientation of the LiDAR system (roll, pitch, and heading) with respect to a ground coordinate system during data collection. Attitude data is collected by the GNSS and IMU.
In an ideal measurement condition, sensor coordinates are in line with the ground coordinate system and the errors are insignificant. However, during data collection, the sensor may rotate randomly introducing errors in the dataset.
Flying height or altitude refers to the sensor's distance from the ground. Various studies have shown that the flight height does not have a direct impact on the accuracy but instead, affects the density of the point cloud. Lower altitudes result in dense point clouds and hence more detailed height models.
The American Society for Photogrammetry and Remote Sensing (ASPRS) specifies the following equation for estimating the horizontal accuracy of LiDAR-derived elevation data:
Computing LiDAR accuracy (Source)
The flying altitude is in meters
Global Navigation Satellite System (GNSS) errors are radial and in centimeters
IMU errors are in decimal degrees
From the above equation, the same GNSS and IMU errors will result in better horizontal accuracy of projected laser pulses at a lower flight altitude than a higher one.
Additionally, the above equation can be used to compute the flying altitude where the target horizontal accuracy and estimated GNSS and IMU errors are known.
Flying speed, on the other hand, affects the density of the point cloud. Low speeds are important for accurate mapping of complex surfaces where it is necessary to capture fine details e.g. small drainage features or to penetrate forest cover.
So far, we have focused on LiDAR-derived elevation models. But let's say you need an elevation model covering a vast area---maybe even spanning an entire country. Let's say you need this dataset regularly for monitoring. What then? That's where high-resolution stereo satellite imagery comes in.
What is Stereo Satellite Imagery?
Stereo satellite imagery refers to two (or three) images of the same location acquired by satellite sensors from different viewing angles and at approximately the same time. Different viewing angles enable the creation of 3D models over the area of interest.
High-resolution stereo satellite imagery has the advantage of generating large-scale digital elevation models and other 3D mapping products with meter-level vertical accuracy. Additionally, satellite constellations capture daily stereo imagery for monitoring applications and disaster management.
Other uses of stereo imaging include land use and cadastral mapping, and infrastructure planning.
How are High-Resolution Satellite Stereo Images Captured?
Stereo satellite images can be captured using two approaches:
- Across-track acquisition: Collection of images over the same scene on ground from different orbits yielding across-track stereo pairs. This method leads to a longer time interval between the pairs.
- Along-track stereo acquisition: Image pairs are acquired while the satellite is in the same orbit. This is achieved through an appropriate forward and backward arrangement of the sensor.
In addition to the pair, some satellites---such as Pléiades---capture a third image from a near-vertical position to avoid hidden objects in urban areas (occlusions). Such images are denoted as tri stereo imagery. Tri-stereo imagery results in a more accurate elevation model in mountainous or urban areas.
Along-track stereo image acquisition is preferred because it reduces the variability between image pairs caused by sun illumination or temporal changes---leading to higher chances of success during image matching.
Factors Affecting the Accuracy of Stereo-Derived Elevation Models
Here are some factors to keep in mind when looking at the accuracy of stereo-derived digital elevation models.
Time Lag Between Stereo Image Pairs
The time lag between the two (or three) images should be as short as possible to minimize ground and atmospheric differences that affect image matching and hence accuracy.
Base Height (B/H) Ratio
The base is the distance between satellite positions while capturing stereo imagery, whereas height is the satellite's elevation.
Illustration of B/H ratio (Source: Pléiades -user-guide)
An optimal B/H ratio ensures all objects are captured, increasing the matching accuracy of common features. A B/H of 0.25-0.4 is recommended for automatic processing.
In flat and open areas, higher than 0.4 B/H ratios may be used.
However, in areas with variable landscapes, e.g., mountains or cities with high-rise buildings, a higher B/H ratio increases the chances of areas between high mountains or buildings being missed, decreasing the matching accuracy. Luckily, using the Tri Stereo mode mitigates this risk.
LiDAR vs. High-Resolution Stereo Satellite Imagery for Terrain Modeling
The table below shows some factors you need to consider when choosing between LiDAR and high-resolution satellite imagery for terrain modeling.
|Details to be extracted||You can only extract elevations from the top surface objects, such as buildings or vegetation||Multiple returns are obtained from different height levels (e.g., top of a tree, tree branches, ground level). Multiple returns enable computation of not only surface and ground level but also intermediate levels. LiDAR is, therefore, useful when modeling forest structures|
|Area of coverage||Large regions or global coverage—including remote and inaccessible areas||Local coverage, e.g., for an infrastructure project|
|Terrain and density of vegetation or surface features||Densely vegetated areas or urban areas result in large errors in the stereo DEM. This is due to few or missing detected ground points to accurately estimate the underlying surface. The error is even worse for dense vegetation on steep slope surfaces. Luckily, in dense urban areas, the errors can be mitigated by using tri-stereo imagery||LiDAR points can be used to map ground elevations even where there’s dense vegetation|
Here's a simple test if you're deciding between LiDAR and stereo satellite imagery for your project: if you need centimeter-level accuracy, go with LiDAR. If you want meter level accuracy for vast areas, go with stereo imagery.
Putting it All Together
Elevation models are an integral component of many applications. It is therefore equally important that the underlying elevation data sources meet some minimum accuracy standard.
LiDAR data and stereo satellite images are two common examples of elevation data sources. LiDAR is more suitable for highly accurate mapping whereas stereo satellite imagery is suited for large areas which require frequent monitoring.
The accuracy of elevation models derived from either LiDAR data or stereo satellite imagery is affected by several factors which you should keep in mind while using the models.
Ultimately, choosing an elevation model is centered around understanding the problem you're trying to solve. The primary goal is to choose the best possible data for a given objective.
Looking to leverage the power of digital elevation models in your application? Explore our high-resolution elevation datasets and enrich your geospatial solutions.