Roadway vertical alignment consists of grades connected by parabolic curves. Road elevation data are crucial in traffic safety analysis, roadway geometric design, fuel consumption estimation, and highway capacity analysis. Prior studies indicated that crash rates are notably higher on steep grade sections compared to level sections (Glennon, 1987; Yu & Abdel-Aty, 2014). Hamdar et al. (2016) highlighted that driver behaviour is highly influenced by the challenges posed due to the changes in roadway geometric alignment. For instance, abrupt grade changes at crest curves can significantly restrict a driver's line of sight, adversely impacting available stopping sight distance and overall roadway safety. Vertical grades and curvature directly influence sight distance, operating speed, driver workload, and vehicle dynamics, making them central to both geometric design and crash prediction. The American Association of State Highway and Transportation Officials (AASHTO) and the Federal Highway Administration (FHWA) emphasize the role of grades and crest–sag curvature in determining safe stopping distances, speed consistency, and sight limitations on vertical curves (Donnell et al., 2018). Several empirical studies further support this, showing that combinations of horizontal–vertical curvature and steep grades significantly elevate crash risk and reduce speed harmony, particularly on rural two-lane highways (Elvik & Haugvik, 2023;Ryan et al., 2022; Bauer & Harwood, 2013; Papadimitriou et al., 2019; Kar et al., 2024).

Road elevation profiles allow engineers to accurately identify steep grades that pose operational risks, particularly for heavy vehicles, assisting in targeted design interventions like crawler lanes or escape ramps. Moreover, accurate knowledge of road profiles supports safety analysis by helping identify segments with restricted visibility and elevated crash risk, enabling proactive measures such as advisory signage, speed limit adjustments, or geometric redesign. Beyond safety, vertical alignment also governs aspects such as drainage design, fuel consumption, ride comfort, and infrastructure maintenance, while precise elevation modelling facilitates 3D roadway coordination and driver visibility studies (FHWA, 2019).

Moreover, recent flood events in the US underscore the value of roadway elevation profiles in identifying flood-prone segments. Heavy rains in San Antonio and the Tri-State region in the US flooded roadways in 2025, causing fatalities and roadway closures (WTOP News, 2025; MySanAntonio, 2025; National Public Radio, 2025). Accurate vertical alignment extraction, including identification of depressed grades and shallow slopes, can reveal areas prone to ponding or runoff overflow. Integrating these profiles into drainage planning helps agencies implement effective mitigation, such as regrading, culverts, or raised embankments, to improve flood resilience.

Despite its importance, vertical alignment data remain difficult and expensive to obtain at scale. Historically, such information has resided within engineering plans and profile sheets, many of which predate digital storage and are available only in scanned or paper formats. Modern survey techniques such as Global Positioning System (GPS), Global Navigation Satellite System (GNSS), and mobile light detection and ranging (LiDAR) can yield highly precise 3-D elevation data, yet they require specialized survey vehicles, extensive field operations, and substantial financial resources, limiting their use to select corridors (Gargoum & El Basyouny, 2019). Moreover, unlike horizontal alignment, which is traceable through open geospatial databases or aerial imagery, vertical profiles cannot be easily inferred without access to elevation data, making large-scale network coverage a major challenge. This challenge is even more pronounced for older routes, where profile information may be either unavailable or outdated. As a result, estimating the parameters of roadway vertical alignment becomes essential.

Advances in remote sensing and open-access LiDAR now offer a practical solution. The U.S. Geological Survey’s 3D Elevation Program (3DEP) provides nationwide LiDAR coverage with point clouds and digital elevation models available through The National Map, enabling researchers to derive elevation and slope information for most US roads at minimal cost (USGS, 2025). Previous research demonstrates the potential of LiDAR for automated roadway geometry extraction and safety analysis (Yang & Das, 2024; Gargoum & El Basyouny, 2019; Wang et al., 2025). Yet processing large datasets, filtering roadway points, and classifying tangent versus curved segments still require robust analytical approaches.

Various datasets, such as the National Elevation Dataset from the US Geological Survey (USGS NED) (Gesch et al., 2014), Global Digital Elevation Model (GDEM) (Tachikawa et al., 2011), and LiDAR (Reutebuch et al., 2005) elevation datasets are readily available. The 3DEP from the USGS, which employs LiDAR point cloud data, has gathered extensive three-dimensional data across the US. This dataset contains over 12 trillion LiDAR point cloud records, encompassing data from more than 1,254 projects across the country (USGS, 2025).

Various techniques are available for collecting road elevation data, such as GPS, Enhanced GNSS, Inertial Navigation Systems (INS) coupled with GNSS, LiDAR (Baass & Vouland, 2005; Easa & Wang, 2010;Di Mascio et al., 2012; Higuera de Frutos & Castro, 2017; Gargoum et al., 2018; Liu et al., 2018; Zhou et al., 2021; Shams et al., 2023; Holgado-Barco et al., 2014;Yang & Das, 2024), as discussed next in the literature review section. However, these methods may not be feasible due to the cost and effort required for their implementation, especially on a larger scale.

Therefore, there is a need for estimating road elevation data indirectly from available sources, as done for road horizontal alignment (Anil & Natarajan, 2010; Easa et al., 2007;Imran et al., 2006; Yun & Sung, 2005; Xu & Wei, 2016; Bartin et al., 2019; Bartin et al., 2022; Bartin et al., 2021; Bartin et al., 2023; Findley et al., 2012; Luo et al., 2018). However, this topic has not been as extensively explored in the literature. Although various elevation data sources are available, there is a notable absence of methods for extracting roadway vertical alignment using these resources. The ones that use LiDAR data do not rely on replicable methods. In practice, many LiDAR-based studies rely on mobile mapping systems that are not freely available and are often limited to project-specific deployments. The need for advanced survey vehicles raises costs and lengthens data-collection and post-processing, which constrains scalability.

To that end, the objective of this paper is to develop an Artificial Neural Network (ANN) based approach that can accurately, quickly, and affordably extract roadway vertical alignment information and determine its geometric properties using publicly available LiDAR data in the USGS repository (USGS, 2025). However, because the ANN model requires large datasets of known vertical alignment data for training, and such data are not readily available at a large scale, the model was trained and tested using synthetically generated road vertical data. Once trained, the model was able to classify LiDAR points on a roadway as either part of a grade or a vertical curve, considering the surrounding LiDAR points. The developed ANN model was independently evaluated using the actual vertical data of Route 152, a state highway in NJ, and Route 299, a state highway in CA. Also, a case study was conducted on Route 83, a rural two-lane highway in NJ, where the model was applied to regenerate the speed profile.

Extracting roadway alignment has been the focus of numerous studies over the years, yet horizontal alignment has been the primary focus alignment (Anil & Natarajan, 2010; Easa et al., 2007;Imran et al., 2006; Yun & Sung, 2005; Xu & Wei, 2016; Bartin et al., 2019; Bartin et al., 2022; Bartin et al., 2021; Bartin et al., 2023; Findley et al., 2012; Luo et al., 2018) Various data sources were utilized for extracting roadway horizontal alignment, ranging from satellite images (Anil & Natarajan, 2010; Easa et al., 2007), GPS data (Imran et al., 2006; Yun & Sung, 2005), Geographic Information System (GIS) maps (Xu & Wei, 2016); (Bartin et al., 2019; Bartin et al., 2022; Bartin et al., 2021; Bartin et al., 2023), and mobile LiDAR mapping (Findley et al., 2012; Luo et al., 2018).

A limited number of studies focused on developing comprehensive and automated methods for extracting roadway vertical alignment. For example, Baass & Vouland, (2005) conducted a study on reconstructing vertical alignment using GPS data sources. They applied the rate of slope change between points to distinguish parabolic curves from the tangents of the vertical alignment. Initially, they used least squares approximation to fit tangents, followed by an iterative process to determine the vertical curves using least square approximations. The process required an initial value for the length of the vertical curve, which was obtained from the previously calculated tangent sections' initial and final grades. They validated the method by comparing it with exact design data and real GPS profile data from Quebec highways. To assess accuracy, they calculated the vertical distance from GPS source points and compared it to the result obtained from calculated alignments. The estimated average error was 15 cm, with a maximum error of 1.5 meters. While they applied some form of filtering to the GNSS data to address irregularities, specific details were not provided. It was acknowledged that factoring in device error would be necessary to measure the absolute error of the procedure.

Easa & Wang (2010) introduced an optimization model aimed at determining the parameters of continuous vertical alignments using GPS data. This model included multiple parabolic vertical curves and aimed to ideally fit the highway profile data through the application of the least squares method. The optimization process operated in two stages: single-curve optimization and multiple-curve optimization. Single-curve optimization employed estimated tangent parameters, derived from the controlling points defined by the operator, to approximate the length of each vertical curve. Conversely, multiple-curve optimization was applied to deduce the globally optimal parameters for both tangents and vertical curves. The model was evaluated using actual data from a 1,700-meter segment of a highway's vertical alignment. To validate the model's accuracy, the study compared the original altitude values with estimated altitudes. The average error observed was 3.8 centimeters.

Di Mascio et al. (2012) utilized a GNSS receiver mounted on a vehicle. They employed the least-squares optimization principle to identify vertical curves and lines that represent the section of the road considered with the respective mobile base. The vertical curves were examined as circular components. As a final step, they fine-tuned the results of their method using the vertical curvature profile. Higuera de Frutos & Castro (2017) developed an algorithm to reconstruct the vertical alignment of a road from the longitudinal slopes along its centerline using data from clinometers and GNSS receivers. The algorithm meticulously identified border points on the road's grade profile classified each sample point as a grade point, vertical curve point, or border point, and grouped similar points into segments. The analytical expressions for these segments were then calculated and integrated to formulate the road's vertical alignment. The efficacy of this method was validated through its application on five rural highways in Spain and the results demonstrated the algorithm's precision in recreating vertical alignments, with the results being more accurate in flat terrains compared to mountainous sections.

Recent advancements in LiDAR technology have found applications in the transportation sector, with numerous studies using LiDAR data to extract road surface characteristics, estimate roadway alignments, and analyse road cross slopes. A brief overview of LiDAR technology is provided first, followed by a review of these studies.

LiDAR operates by emitting laser pulses. As the laser pulses interact with and are reflected off objects on the Earth's surface, the LiDAR system captures the reflected signals, or returns. These returns are then utilized to generate a dense set of data points known as a “point cloud”, which represents the three-dimensional structure of the survey area. When a single laser pulse intersects various surfaces, it generates multiple reflections captured by the LiDAR sensor. These reflections are categorized as first returns, which represent the highest points, such as tree canopies or building tops, and subsequent returns, which represent lower surfaces, such as the ground beneath vegetation cover. This multi-return capability enables a detailed understanding of various landscape features.

LiDAR data can be collected via mobile and airborne systems. Mobile LiDAR Systems (MLS), usually mounted on moving vehicles, are exceptional in capturing high-resolution data at street level. They are used for road and bridge inspections, utility mapping, urban planning, and asset management, with the granularity of data being so refined in some cases as to detect asphalt cracks. Typically, the accuracy of Mobile LiDAR systems ranges between 0.05 to 0.10 meters, contingent on system configurations and environmental conditions. They can collect dense cloud data points and provide a detailed representation of the survey area.

Airborne LiDAR Systems (ALS), installed on an aircraft or a drone, cover vast areas effectively and generate digital terrain models (DTM), topographic mapping, construction of digital 3D city models, natural hazard assessment, and more. The accuracy of ALS data collected by aircraft can reach up to 10 centimeters, depending on the system and the conditions under which data are collected. On the other hand, LiDAR data collected by drones typically offer improved point density and precision due to their lower altitude operation. However, the point density of ALS may be lower compared to MLS due to the greater distance from the ground. Nonetheless, this density and accuracy are sufficient to discern road profile trajectories and estimate road grades.

Gargoum et al. (2018) proposed a method to extract the vertical profile of highways from LiDAR data. This method involved three main stages: centerline generation, road surface creation and overlaying of the centerline, and profile generation using AutoCAD Civil 3D. The centerline was generated by defining points parallel to the road's centerline, overlaying it onto a created surface from the point cloud data, and then generating the highway profile along this centerline. This method was tested on three different highway segments in Alberta, Canada, and the extracted profiles were compared with profiles generated using GPS data and manual surveys. The results demonstrated remarkable precision, with grade differences between LiDAR and manual profiles as low as 0.025% to 0.15%, and a relative elevation error of only 4%. Furthermore, when compared to GPS data, the LiDAR profiles exhibited minimal grade differences, averaging 0.023% and 0.061% on different road segments.

Liu et al. (2018) proposed a method that utilized the Digital Elevation Model (DEM), a nationwide open data source from the USGS and applied cubic smoothing splines to minimize the impact of noisy data and improve grade estimation accuracy. The selection of a key parameter (λ) in the spline method was discussed to balance smoothing noisy elevation data while retaining vertical fluctuations along the road. To validate the results, actual road grade data consisting of five highway segments and two local road segments, with a total length of 23.24 km in Atlanta, were used. The results demonstrated an average estimation error of 0.5 to 0.58 percent for local roads and 0.21 to 0.23 percent for highways.

Zhou et al. (2021) developed a method to extract highway alignments and construct 3D models using ALS data. This involved recognizing highway pavement points, extracting pavement boundaries and lane markings, and then reconstructing highway 3D models by minimizing an energy function. The method was tested on two ALS datasets from Sichuan, China. The extracted alignments achieved correctness rates of 90.67% and 99.25% and completeness rates of 87.60% and 99.55% within 10 cm and 15 cm errors, respectively. The root mean square error (RMSE) of the generated 3D models was 2.4 cm on pavement areas and 5.8 cm on hills and slopes.

LiDAR technology has also proven to be an invaluable tool for obtaining detailed insights into road aspects such as roadway cross slope extraction. Shams et al. (2023) conducted a study evaluating the effectiveness of airborne and mobile terrestrial LiDAR scanning systems in measuring pavement cross slopes. They employed end-to-end extraction and interval point extraction methods along cross-sections. The study, implemented on a 3.4-mile corridor along I-85 Business Loop in South Carolina, demonstrated LiDAR's accuracy in collecting pavement cross slopes, highlighting its suitability for large-scale applications and road surface drainage issues. Holgado-Barco et al. (2014) focused on automatically extracting geometric parameters from mobile LiDAR system datasets, with an emphasis on vertical road profiles and cross-sections. Using data from the Spanish highway A-52, the study employed segmentation and principal component analysis-based methods for processing. This approach led to a comprehensive characterization of road slopes and superelevations, showcasing LiDAR's effectiveness in road safety assessment and construction verification.

Yang and Das (2024) developed an open-source program to extract horizontal and vertical alignment information for roadways, leveraging public data and open APIs. For vertical curves, the program analyses the vertical grade profile, identifying parabolic curves and tangents by fitting piecewise linear regression models. They extracted elevation data from the USGS 3DEP, which provides high-resolution 3D elevation data across the U.S. The elevation data from 3DEP were derived from LiDAR point cloud data available at different resolutions: 30m, 10m, and 1m. The segmentation and detection of vertical curves are optimized by addressing erratic elevation data points.

In summary, previous studies in the extraction of road elevation data primarily focused on using GPS and GNSS data from vehicles equipped with advanced technologies. There are a few studies that used LiDAR data; however, the underlying datasets were often project-specific mobile or airborne LiDAR acquisitions, while relatively fewer studies leveraged publicly available, large-coverage datasets such as USGS 3DEP. In addition, the necessity of these specially equipped surveying vehicles for data collection limits their methods’ applicability to a wider scale of roadways due to significant costs and extended data collection periods.

Recognizing these constraints, this study proposes an innovative approach utilizing open-access aerial LiDAR point cloud data, offering a cost-effective and efficient solution for extracting precise roadway elevation data. The ALS data stand out as an extremely valuable resource for road grade estimation due to their easy accessibility, free availability, and nationwide coverage across the US. Despite these advantages, few studies have comprehensively addressed the detailed method of generating high-resolution road grade information from LiDAR data. This study attempts to fill this gap in the literature.

The methodology used in this study is outlined in Figure 1 and extends a previously developed ANN-based method for extracting roadway horizontal alignment data, as described in Bartin et al. (2021) and (Bartin et al., 2023). In that work, an ANN model was developed to identify horizontal tangent and curved segments using publicly available roadway GIS data. In the current study, the same ANN approach was applied to LiDAR data, which contain a significantly larger number of data points and are inherently much noisier.

To estimate the vertical alignment of a given roadway, the first step was to identify the relevant LiDAR point cloud data. The LiDAR point cloud datasets used in this study were obtained from USGS (USGS, 2025), which provides extensive coverage across the US. Each LiDAR point cloud consists of latitude, longitude, and elevation information. According to the USGS, the vertical accuracy of LiDAR data is approximately 10 centimeters (~4 inches) which is suitable for extracting roadway vertical alignment.

In the next step, the LiDAR data specific to the selected roadway were extracted. The following subsection presents the details of the two selected roadways for this study.

The selected ANN model was evaluated independently by using the aerial LiDAR data extracted along Route 152 and Route 299 centerlines. The following subsections present the results for the two study roadways separately.

Roadway vertical alignment data play a crucial role in a wide range of highway engineering and safety applications. Vertical grades and curvature shape sight distance, operating speeds, driver workload, and vehicle dynamics, and thus underpin both geometric design decisions and crash modelling. Guidance from AASHTO and FHWA highlights the decisive role of grade and crest–sag curvature in determining stopping sight distance, maintaining speed consistency, and managing visibility limitations on vertical curves (Donnell et al., 2018). Empirical evidence further shows that steep grades, combined with horizontal and vertical curvature, increase crash risk and disrupt speed uniformity, especially on rural two-lane roads (Elvik & Haugvik, 2023; Ryan et al., 2022; Bauer & Harwood, 2013; Papadimitriou et al., 2019; Kar et al., 2024). Beyond safety, vertical alignment influences drainage design, fuel consumption, ride comfort, and maintenance strategies, and supports three-dimensional roadway coordination and visibility assessments (FHWA, 2019).

Despite its importance, obtaining vertical alignment data at scale remains difficult and expensive. Legacy plans and profile sheets are often non-digital, and precision surveys using GPS, GNSS, or mobile LiDAR require specialized equipment and substantial resources, limiting corridor coverage (Gargoum & El Basyouny, 2019). While horizontal alignment can be traced using open geospatial layers or imagery, vertical profiles cannot be inferred without elevation data, which complicates coverage across large networks.

Recent advances in remote sensing help mitigate these barriers. The USGS 3DEP program provides nationwide point clouds and DEMs via The National Map, enabling low-cost derivation of elevations and slopes for most U.S. roads (USGS, 2025). Prior work demonstrates the promise of LiDAR for automated geometry extraction and safety assessment (Yang & Das, 2024; Gargoum & El Basyouny, 2019; Wang et al., 2025), but network-scale processing, roadway point isolation, and reliable classification of tangents and vertical curves still require robust, scalable analytics.

In this context, this study introduced an innovative approach to estimating vertical alignment data of roadways, which combines LiDAR data with an ANN model, addressing a critical gap by providing an efficient, scalable, and reproducible way to estimate roadway vertical alignment characteristics. Extraction of vertical alignment is known to be time-consuming and expensive, thus necessitating an efficient and rapid method due to its vital role in various traffic safety-related analyses.

Prior research on the acquisition of road elevation data has predominantly centered on the utilization of GPS and GNSS data from vehicles equipped with sophisticated technologies. Nevertheless, the requirement of such specialized surveying vehicles for data gathering has constrained the method's relevance to a broader array of road networks, owing to substantial costs and prolonged data collection periods. The proposed approach capitalizes on the aerial LiDAR data on the USGS website (USGS, 2025), which covers the majority of roads in the US.

An ANN-based approach was used to detect and identify distinct segment types along a road’s vertical alignment. First, LiDAR data were processed and the points corresponding to the study road were extracted using QGIS. Although applied to one roadway, a similar process can be repeated for multiple roads efficiently in a short period of time. Each LiDAR point's classification, indicating whether it corresponded to a vertical tangent or curved segment, was predicted through the proposed ANN model. These predicted classifications were then utilized to estimate the number and characteristics (tangent or curved) of the road segments.

To train the ANN model, synthetically generated vertical road alignment data were employed. The results of the segmentation process were used to determine essential geometric parameters such as segment length and grades. The key advantage of the presented approach is that it relies only on the labelled LiDAR data points, which makes it easily replicable for other roadway datasets.

The test dataset employed in this study comprised the vertical alignment data of Route 152 in NJ and Route 299 in CA, both two-way two-lane rural roadways. The results of the analyses demonstrated a strong agreement with the actual alignment (See Figure 7 and Figure 8). As shown in the summary of evaluation results presented in Figure 9, for Route 152, an overlap of 92.5 percent with the curved segments’ lengths and 87.9 percent with the tangent segments’ lengths was achieved, indicating a high level of concurrence between the estimated and actual segments. For Route 299, the overlap of the estimated alignment with the actual one was 83.7 percent for curved segments and 92.7 percent for tangent segments. Regarding the evaluation metrics, the average undetected segment lengths were determined to be 22.4 feet and 76.8 feet for curved and tangent segments, respectively for Route 152, while the corresponding values were 67.3 feet and 17.4 feet for curved and tangent segments, respectively, for Route 299.

Furthermore, the mean absolute error between the estimated and actual grades was found to be 0.042 percent, with variations ranging from 0 percent to 0.26 percent, for Route 152. For Route 299 the mean absolute error was 0.15 percent, with variations ranging from 0.04 percent to 0.33 percent, thus indicating a generally accurate estimation of grades in the analysis.

As mentioned earlier, roadway vertical alignment datasets are essential in various safety analyses. To demonstrate this, a case study was conducted for Route 83 in NJ and Route 299 in CA, where the extracted vertical alignment data were used to regenerate speed profiles and to identify segments requiring speed reductions. The satisfactory estimation results of this study indicate that the proposed approach can be employed for conducting large-scale analyses to estimate vertical alignment data.

Future work will involve comparing aerial and drone-based LiDAR to evaluate differences in resolution, accuracy, and cost for various roadway types. A comparison between DEM and raw point cloud data can also help determine which source better captures subtle vertical transitions. Additionally, developing an automated framework to estimate vertical alignment across multiple roadways would enable efficient, large-scale analysis and support broader safety assessments.

The contents of this paper only reflect the views of the authors, who are responsible for the facts and do not represent any official views of any sponsoring organizations or agencies.

The authors report no competing interests.

Mojibulrahman Jami: Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Writing—original draft, Writing—review & editing. Bekir Bartin: Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Writing—original draft, Writing—review & editing. Kaan Ozbay: Conceptualization, Formal analysis, Investigation, Methodology, Writing—original draft, Writing—review & editing.

This study did not involve human participants, or identifiable personal data and relied solely on publicly available geospatial datasets (e.g., USGS 3DEP LiDAR).

The study is supported by the NJDOT (FHWA-NJ-2017-007) and partially by Ozyegin University and partially by C2SMARTER, a Tier 1 UTC at New York University funded by the USDOT.

During the preparation of this work, the authors used ChatGPT (OpenAI) in order to improve the clarity, grammar, and wording of specific sections of the manuscript. The output was reviewed and revised by the authors, who take full responsibility for the content of the publication.

Handling editor: Lai Zheng, Harbin Institute of Technology, China.

Reviewers: Peijie Wu, Chongqing Jiaotong University, China; Feng Jiang, Harbin Institute of Technology, China.

Submitted: 20 October 2025; Accepted: 22 March 2026; Published: 3 April 2026.