💻 computer science

Gridnberg: A Topography-Aware Pedestrian Routing Dataset for New York City

This paper introduces Gridnberg, a topography-aware pedestrian routing dataset for New York City that enriches the existing network with vertex-level elevations to calculate direction-specific routing costs based on horizontal distance, comfort, and accessibility, thereby enabling more accurate terrain-aware urban analysis.

Original authors: Ariel Noyman

Published 2026-07-27

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Ariel Noyman

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine trying to navigate a city using a map that only shows the streets as flat lines on a piece of paper. This is how most computer models of cities work today; they treat the ground like a perfectly flat tabletop. But in the real world, cities are rarely flat. They have hills, ramps, stairs, and bridges that change how hard it is to walk from one place to another. Think of walking up a steep hill versus strolling on a flat sidewalk: even if the distance is the same, the hill feels much longer and more tiring. This difference matters because it changes which route a person chooses, how fast they can get somewhere, and whether a path is even possible for everyone, including those in wheelchairs or with strollers. Scientists call this "topography," which is just a fancy word for the shape and height of the land. Understanding how the ups and downs of a city affect walking is crucial for designing better, fairer, and more efficient urban spaces.

Enter Gridnberg, a new project that brings the "mountain" back into the "grid" for New York City. The researchers behind this work realized that while we have amazing digital maps of where sidewalks are, those maps usually ignore the third dimension: height. To fix this, they created a special dataset that layers real-world elevation data onto the city's pedestrian network. They didn't just guess the heights; they used a massive database of official city measurements to estimate the height of every single point on the sidewalk map.

Here is the magic trick they performed: for every tiny point on a sidewalk, they looked at all the official height measurements within a 50-meter radius (about half a football field) and took the average. This gave them a reliable "altitude" for every spot on the map. With this new 3D information, they didn't just measure how far a walk is; they calculated how "hard" it is. They created three different ways to score a route:

The "Just the Distance" score: This is the old-school way, counting only the flat distance.
The "Comfort" score: This penalizes steep hills, because climbing a steep slope feels much more tiring than walking on flat ground.
The "Accessibility" score: This is the strictest version. It heavily penalizes steep grades because they require more effort, but it does not automatically block a route just because it contains a steep step. Instead, it minimizes the total "slope cost" along the path, making it a better guide for accessibility without strictly excluding routes that have short, steep sections.

The result is a massive, open map of New York City with over 313,000 sidewalk segments, each tagged with its specific height and slope. The team found that while most of the city is relatively flat, there are significant hills, especially in areas like Park Slope and near bridges. In fact, about 12.8% of the sidewalk segments have a slope of at least 5%, and nearly 7% are steep enough (over 8.33%) to be considered challenging for many pedestrians.

One of the most interesting things the paper shows is how changing the "cost" of a route changes the path you take. For example, if you are just trying to walk the shortest distance, the computer might send you up a incredibly steep, short hill because it saves a few meters of flat walking. But if you ask the computer to find the "comfortable" or "accessible" route, it will happily take you on a slightly longer path that avoids that steep hill entirely. In one specific case in Morningside Heights, the shortest path included a "step" that the data suggested was impossibly steep (over 200% grade), which would be a vertical wall! The smart routing profiles correctly avoided this impossible path, choosing a slightly longer but realistic route instead.

The authors are careful to note that this isn't a perfect, finished product. Because they had to average heights over a 50-meter area, some very small, sharp changes in height (like a single step or a tiny ramp) might get smoothed out or mixed up with nearby bridges. They also found a few weird glitches where the math suggested a sidewalk went straight up a building, which they admit needs human review. However, they argue that this dataset is a huge leap forward because it makes the "up and down" of the city visible and measurable for everyone. It allows researchers and city planners to run the same experiments over and over again to see how terrain changes who can go where.

In short, Gridnberg is like giving a pair of 3D glasses to a flat map. It doesn't just show you where the sidewalks are; it shows you how the ground feels under your feet. By turning invisible hills into visible data, it helps us understand that in a city, the easiest way to get somewhere isn't always the shortest way—it's the one that respects the slope of the land. This tool is now available for anyone to use, helping to build a future where our cities are designed not just for the flat, but for the real, hilly, and varied world we actually live in.

Technical Summary: Gridnberg – A Topography-Aware Pedestrian Routing Dataset for New York City

Problem Statement
Urban network analysis frequently simplifies street networks into planar (2D) graphs, treating street segments as flat edges where impedance is defined solely by horizontal distance. This abstraction fails to account for elevation changes, which significantly influence walking speed, metabolic effort, and route choice. While cities like New York are often perceived as flat, they contain significant topographical variations, including hills, ramps, stairs, bridges, and depressed roadways. Existing navigation services often incorporate elevation data, but their proprietary nature prevents researchers from inspecting or reproducing their cost models. Furthermore, while sidewalk-specific networks (e.g., NYCWalks) have improved spatial fidelity, they remain planar unless enriched with elevation data.

Methodology
The paper introduces Gridnberg, a workflow that integrates topography into the NYCWalks pedestrian network. The process involves three primary stages:

Data Integration:
- Network Geometry: The base dataset is the NYCWalks network (Sevtsuk et al., 2026), containing 315,577 LineString records representing sidewalks, crosswalks, and footpaths, projected in EPSG:6538 (NAD83(2011)).
- Elevation Source: Elevation data is derived from the 2022 NYC Planimetric Database (ELEVATION class). To ensure relevance to pedestrian infrastructure, the workflow filters for roadbed spot and bridge points (Feature Code 3000), excluding building roofs and water features to prevent contamination of local mean calculations.
- Coordinate Alignment: Elevation points (originally in US survey feet and EPSG:2263) are converted to meters.
Vertex Elevation Assignment:
- For every vertex $v$ in the pedestrian network, the assigned elevation ( $z_v$ ) is calculated as the unweighted mean of all elevation observations ( $z_p$ ) within a 50-meter radius.
- Support Criteria: A vertex is considered "supported" only if at least one elevation observation exists within the radius. A segment is retained in the final dataset only if all its geometry vertices are supported. This strict criterion preserves 99.24% of the source segments (313,184 out of 315,577).
- The 50-meter radius is a trade-off between spatial specificity and source coverage; the median distance to the nearest contributing observation is 10.14 m.
Metric Calculation and Routing Costs:
- Segment Metrics: For retained segments, the workflow calculates horizontal length ( $L$ ), net elevation change ( $\Delta z$ ), and cumulative ascent ( $G^+$ ) and descent ( $G^-$ ). It also computes the maximum absolute local grade ( $g_{max}$ ), applying a 1-meter horizontal step threshold to avoid noise from extremely short geometry steps.
- Routing Cost Functions: The dataset defines three cost profiles:
  - Distance-only ( $C_0$ ): $C_0 = L$ .
  - Comfort-oriented: Applies asymmetric penalties for uphill and downhill travel based on cumulative grade ratios ( $q^+$ and $q^-$ ). It uses breakpoints at 5% ( $g_0$ ) and 8.33% ( $g_1$ ), with higher weights for steeper grades.
  - Accessibility-sensitive: Uses higher weights than the comfort profile, particularly for grades exceeding 8.33%, reflecting increased effort for mobility-impaired users.
- The cost functions are piecewise linear, penalizing segments where the cumulative grade exceeds specific thresholds. The profiles are "accessibility-sensitive" rather than "barrier-free," meaning they minimize cumulative slope-weighted cost but do not strictly exclude routes containing short, steep local steps.

Key Results

Dataset Scale: The final release contains 187,657 endpoint nodes and 313,184 physical segments (626,368 directed edges).
Topographical Distribution: Node elevations range from -0.33 m to 121.09 m. The median absolute endpoint-average grade is 0.58%, while the median maximum local absolute grade is 0.88%.
Steepness Statistics: 12.79% of segments contain a reported local grade of at least 5%, and 6.84% reach at least 8.33%. However, only 4.76% of segments incur a slope penalty in at least one direction under the routing cost logic, illustrating the difference between local maximums and segment-aggregate costs.
Network Connectivity: The dataset results in 256 connected components. The largest component contains 84.25% of nodes. Smaller components correspond to geographically separated areas like Staten Island and the Rockaway Peninsula, or areas where elevation coverage was too sparse to meet the "complete support" criterion.
Case Studies: Route comparisons demonstrate that slope-sensitive profiles often select paths that are slightly longer (e.g., 2.3% to 5.5% longer) but significantly reduce cumulative gain and maximum local grades. In some diagnostic cases, the distance-minimizing route includes edges with implausible grades (e.g., >100%), which the slope-sensitive profiles successfully avoid.

Significance and Claims
The paper positions Gridnberg as a tool for reproducible, terrain-aware analysis rather than a definitive, error-free ground truth. Its primary contributions are:

Transparency: It provides a public, inspectable implementation of how municipal elevation data can be mapped to pedestrian networks, contrasting with proprietary black-box routing engines.
Methodological Clarity: It documents the specific workflow for assigning vertex elevations, calculating direction-specific grade scores, and constructing routing cost scenarios.
Diagnostic Value: The dataset explicitly exposes unresolved cases where topography, vertical infrastructure (like bridges), and data artifacts are difficult to distinguish. For instance, the authors note that extreme grade values can arise from mixing ground and bridge-deck observations within the 50m window or from geometry artifacts.
Foundation for Improvement: The release serves as a concrete basis for improving how pedestrian networks represent elevation, enabling researchers to test how terrain affects accessibility, centrality, and foot-traffic models.

The authors remain modest regarding the dataset's limitations, acknowledging that assigned elevations are unweighted local means rather than survey-grade measurements, and that the heuristic cost functions are sensitive to feature segmentation. They emphasize that real-world application requires explicit review of edge cases, particularly where vertical connections or data mismatches occur.

Technical Summary: Gridnberg – A Topography-Aware Pedestrian Routing Dataset for New York City

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