Hubbry Logo
Topographic mapTopographic mapMain
Open search
Topographic map
Community hub
Topographic map
logo
8 pages, 0 posts
0 subscribers
Be the first to start a discussion here.
Be the first to start a discussion here.
Topographic map
Topographic map
Topographic map
View on Wikipedia
from Wikipedia

Sergeant Chris D. Washington checking his Topographic map during a morning deer hunt in Kilgore, Texas
A topographic map of Stowe, Vermont with contour lines
Part of the same map in a perspective shaded relief view illustrating how the contour lines follow the terrain
Sheet #535 (2013 version; second digital edition) of MTN50 Spanish National Topographic map series, covering Algete town (near Madrid) and its surroundings.
Section of topographical map of Nablus area (West Bank) with contour lines at 100-meter intervals. Heights are colour-coded.

In modern mapping, a topographic map or topographic sheet is a type of map characterized by large-scale detail and quantitative representation of relief features, usually using contour lines (connecting points of equal elevation), but historically using a variety of methods. Traditional definitions require a topographic map to show both natural and artificial features.[1] A topographic survey is typically based upon a systematic observation and published as a map series, made up of two or more map sheets that combine to form the whole map. A topographic map series uses a common specification that includes the range of cartographic symbols employed, as well as a standard geodetic framework that defines the map projection, coordinate system, ellipsoid and geodetic datum. Official topographic maps also adopt a national grid referencing system.

Natural Resources Canada provides this description of topographic maps:[2]

These maps depict in detail ground relief (landforms and terrain), drainage (lakes and rivers), forest cover, administrative areas, populated areas, transportation routes and facilities (including roads and railways), and other man-made features.

Other authors define topographic maps by contrasting them with another type of map; they are distinguished from smaller-scale "chorographic maps" that cover large regions,[3][4] "planimetric maps" that do not show elevations,[5] and "thematic maps" that focus on specific topics.[6]

However, in the vernacular and day to day world, the representation of relief (contours) is popularly held to define the genre, such that even small-scale maps showing relief are commonly (and erroneously, in the technical sense) called "topographic".[4]

The study or discipline of topography is a much broader field of study, which takes into account all natural and human-made features of terrain. Maps were among the first artifacts to record observations about topography.[7]

History

[edit]
See also: Topography § Etymology
See also: Cartography § History

Topographic maps are based on topographical surveys. Performed at large scales, these surveys are called topographical in the old sense of topography, showing a variety of elevations and landforms.[8] This is in contrast to older cadastral surveys, which primarily show property and governmental boundaries. The first multi-sheet topographic map series of an entire country, the Carte géométrique de la France, was completed in 1789.[9] The Great Trigonometric Survey of India, started by the East India Company in 1802, then taken over by the British Raj after 1857 was notable as a successful effort on a larger scale and for accurately determining heights of Himalayan peaks from viewpoints over one hundred miles distant.[10]

Global indexing system first developed for International Map of the World

Topographic surveys were prepared by the military to assist in planning for battle and for defensive emplacements (thus the name and history of the United Kingdom's Ordnance Survey). As such, elevation information was of vital importance.[11]

As they evolved, topographic map series became a national resource in modern nations in planning infrastructure and resource exploitation. In the United States, the national map-making function which had been shared by both the Army Corps of Engineers and the Department of the Interior migrated to the newly created United States Geological Survey in 1879, where it has remained since.[12][13]

1913 saw the beginning of the International Map of the World initiative, which set out to map all of Earth's significant land areas at a scale of 1:1 million, on about one thousand sheets, each covering four degrees latitude by six or more degrees longitude. Excluding borders, each sheet was 44 cm high and (depending on latitude) up to 66 cm wide. Although the project eventually foundered, it left an indexing system that remains in use.

By the 1980s, centralized printing of standardized topographic maps began to be superseded by databases of coordinates that could be used on computers by moderately skilled end users to view or print maps with arbitrary contents, coverage and scale. For example, the federal government of the United States' TIGER initiative compiled interlinked databases of federal, state and local political borders and census enumeration areas, and of roadways, railroads, and water features with support for locating street addresses within street segments. TIGER was developed in the 1980s and used in the 1990 and subsequent decennial censuses. Digital elevation models (DEM) were also compiled, initially from topographic maps and stereographic interpretation of aerial photographs and then from satellite photography and radar data. Since all these were government projects funded with taxes and not classified for national security reasons, the datasets were in the public domain and freely usable without fees or licensing.

TIGER and DEM datasets greatly facilitated geographic information systems and made the Global Positioning System much more useful by providing context around locations given by the technology as coordinates. Initial applications were mostly professionalized forms such as innovative surveying instruments and agency-level GIS systems tended by experts. By the mid-1990s, increasingly user-friendly resources such as online mapping in two and three dimensions, integration of GPS with mobile phones and automotive navigation systems appeared. As of 2011, the future of standardized, centrally printed topographical maps is left somewhat in doubt.[14][15]

Uses

[edit]
Curvimeter used to measure a distance on a topographic map

Topographic maps have many multiple uses in the present day: any type of geographic planning or large-scale architecture; Earth sciences and many other geographic disciplines; mining and other Earth-based endeavours; civil engineering and recreational uses such as hiking and orienteering.

It takes practice and skill to read and interpret a topographic map. This includes not only how to identify map features, but also how to interpret contour lines to infer landforms like cliffs, ridges, draws, etc. Training in map reading is often given in orienteering, scouting, and the military.[16]

Conventions

[edit]
Further information: contour lines § Elevation and depth

The various features shown on the map are represented by conventional signs or symbols. For example, colors can be used to indicate a classification of roads. These signs are usually explained in the margin of the map, or on a separately published characteristic sheet.[17][18][19]

Topographic maps are also commonly called contour maps or topo maps. In the United States, where the primary national series is organized by a strict 7.5-minute grid, they are often called or quads or quadrangles.

Topographic maps conventionally show topography, or land contours, by means of contour lines. Contour lines are curves that connect contiguous points of the same altitude (isohypse). In other words, every point on the marked line of 100 m elevation is 100 m above mean sea level.

These maps usually show not only the contours, but also any significant streams or other bodies of water, forest cover, built-up areas or individual buildings (depending on scale), and other features and points of interest such as what direction those streams are flowing.

Most topographic maps were prepared using photogrammetric interpretation of aerial photography using a stereoplotter. Modern mapping also employs lidar and other Remote sensing techniques. Older topographic maps were prepared using traditional surveying instruments.

The cartographic style (content and appearance) of topographic maps is highly variable between national mapping organizations. Aesthetic traditions and conventions persist in topographic map symbology, particularly amongst European countries at medium map scales.[20]

Publishers of national topographic map series

[edit]
See also: National mapping agency and Map series

Although virtually the entire terrestrial surface of Earth has been mapped at scale 1:1,000,000, medium and large-scale mapping has been accomplished intensively in some countries and much less in others.[21] Several commercial vendors supply international topographic map series.

According to 2007/2/EC European directive, national mapping agencies of European Union countries must have publicly available services for searching, viewing and downloading their official map series.[22] Topographic maps produced by some of them are available under a free license that allows re-use, such as a Creative Commons license.[23]

See also

[edit]

References

[edit]
[edit]
Revisions and contributorsEdit on WikipediaRead on Wikipedia

Topographic map

View on Grokipedia
from Grokipedia
A topographic map is a detailed cartographic representation of a portion of the Earth's surface, depicting both natural and man-made features through the use of contour lines to illustrate and , plotted to a specific scale. These maps distinguish themselves from other types by emphasizing the three-dimensional of the via contour lines drawn at regular intervals, where each line connects points of equal , allowing users to visualize hills, valleys, slopes, and other landforms. In addition to contours, topographic maps employ standardized symbols to denote elements such as rivers, forests, roads, buildings, and boundaries, providing a comprehensive view of the physical and cultural environment. Such maps are produced by national mapping agencies worldwide, including the U.S. Geological Survey and equivalents in other countries. The scale of topographic maps varies depending on their purpose, with common ratios like 1:24,000 allowing for detailed depiction of features over areas typically covering 7.5 by 7.5 minutes of latitude and longitude, known as quadrangles. This precision enables practical applications, including navigation for outdoor activities like and biking, as well as professional uses in , , and environmental assessment. For instance, these maps aid in analyzing , tracking glacial movements, and interpreting geologic history by revealing patterns in and distribution. Today, topographic maps serve as foundational layers for thematic overlays in fields like conservation, , and , underscoring their enduring value in understanding and interacting with .

Fundamentals

Definition and Purpose

A is a detailed cartographic representation of a portion of the Earth's surface that illustrates both natural and cultural features, with a primary emphasis on and . These maps depict the three-dimensional configuration of the on a two-dimensional plane, using standardized symbols and lines to convey spatial relationships and physical characteristics such as hills, valleys, rivers, roads, and buildings. The fundamental goal is to provide a scaled, accurate portrayal that enables users to visualize and interpret the without direct observation of the . The primary purpose of topographic maps is to furnish precise spatial data for comprehending landforms and facilitating informed across diverse applications. Historically, they have supported , operations, and assessment by offering reliable depictions of unknown or rugged areas. In contemporary contexts, these maps serve as essential tools in geospatial analysis, urban and , environmental management, projects, and recreational activities, allowing professionals to model for simulations, hazard assessment, and infrastructure development. By integrating elevation data with horizontal features, topographic maps bridge the gap between abstract geographic information and practical utility. Topographic maps differ from other cartographic products by their comprehensive inclusion of both hypsography—the representation of and —and planimetry—the depiction of horizontal positions of features—resulting in a holistic view of the . In contrast, thematic maps concentrate on specific variables, such as or types, without emphasizing structure. Planimetric maps, meanwhile, portray only flat, two-dimensional layouts of features like boundaries and , omitting measurable vertical dimensions. This integration of distinguishes topographic maps as versatile base layers for overlaying additional data in geographic information systems. Core principles of topographic mapping include adherence to accurate scales and appropriate projection systems to minimize and preserve spatial fidelity. In the United States, the standard scale for detailed topographic maps is 1:24,000, covering approximately 7.5 minutes of latitude and longitude per quadrangle, which balances detail and coverage for most applications. Projections such as the Universal Transverse Mercator (UTM) or Lambert Conformal Conic are commonly employed, as they are conformal and suitable for mid-latitude regions, ensuring that shapes and angles remain true over the mapped area. These elements ensure the maps' reliability for quantitative analysis and measurement.

Key Elements

Topographic maps incorporate several essential components to provide spatial reference and contextual information. Grid lines, typically based on or the Universal Transverse Mercator (UTM) system, overlay the map to enable precise location determination; for instance, USGS maps include UTM grid lines in black or marginal tick marks in blue for coordinates measured in meters. Scale bars graphically represent the ratio between map distances and ground distances, such as the common 1:24,000 scale on USGS 7.5-minute quadrangles, allowing users to measure features without recalculation. Legends detail the meaning of symbols, colors, and line styles used throughout the map, while north arrows indicate , magnetic north, and grid north to clarify orientation. Marginal information, including the map sheet name, edition date, and projection details, appears in the borders to specify the map's coverage and currency. Terrain depiction on topographic maps relies on various techniques to convey and visually. Hypsometric tinting uses color gradients, often from green for low elevations to brown or white for higher ones, to represent broad bands and patterns. Hachures consist of short, radiating lines that point downslope, with denser and thicker lines indicating steeper , a method historically employed to illustrate mountainous areas. Spot elevations provide exact height measurements at key points, such as summits or benchmarks, marked numerically to supplement broader contour representations. Hydrographic features are depicted to show water-related elements and their influence on the landscape. Water bodies like lakes and oceans are filled with blue, while rivers and use solid or dashed blue lines of varying thickness to denote or intermittent flow, with wider lines for larger waterways. Drainage patterns, including divides and flow directions, are illustrated through these line styles to highlight watershed structures. Cultural features represent human-made elements with standardized symbology for clarity. Roads appear as lines differentiated by type—solid black for highways, dashed for trails—with widths reflecting importance; for example, interstate highways are bold red lines on some USGS maps. Buildings are shown as small black rectangles for individual structures or gray tints for urban areas, while boundaries such as property lines or administrative divisions use dotted or solid lines in black or magenta. Relief shading enhances the three-dimensional perception of by applying graduated tones that mimic and shadows, typically assuming illumination from the northwest to emphasize ridges and valleys. This hill shading technique, derived from elevation data, adds depth without altering the map's scale or grid.

Historical Development

Origins and Early Maps

The earliest precursors to topographic maps appeared in ancient civilizations, where clay tablets from Babylonian scribes around 2300 BCE depicted plans of land, including features such as walls, streets, rivers, and basic terrain elements like houses and temples. These artifacts, such as the Yorgan Tepe map, represented rudimentary cadastral surveys rather than true topographic representations, focusing on practical land division without precise elevation data. In the Roman era, the , an from the CE, illustrated the empire's road network alongside settlements, rivers, mountains, and forests, providing a schematic view of terrain for travel but lacking detailed relief or scale accuracy. During the , advancements in observation and drafting led to more detailed depictions, exemplified by Leonardo da Vinci's sketches from the late . Working in the service of figures like between 1502 and 1504, da Vinci produced topographical drawings of river valleys, mountain profiles, and landscapes, such as his studies of the River and the Brembana, Trompia, and Sabbia rivers, which included distances, towns, and natural contours to aid and planning. These works marked a shift toward empirical representation of features, influencing later cartographic practices. By the , the advent of enabled the dissemination of maps with rudimentary , such as woodcut illustrations in Sebastian Münster's Cosmographia (1544), which used pictorial symbols for hills and mountains to convey landscape forms across . In the 17th and 18th centuries, military needs drove further innovations in topographic mapping, particularly in Europe where wars necessitated accurate terrain for fortification and strategy. French military engineers, including Nicolas de Fer in the early 18th century, began incorporating hachures—short lines indicating slope direction and steepness—into printed maps to depict relief more systematically, as seen in his atlases showing terrain shading alongside roads and settlements. Emanuel Swedenborg proposed the use of contour lines in 1718 as a method to represent equal elevations on maps, an idea initially aimed at mining and surveying but foundational for later topographic standards. These developments were tied to conflicts, with maps used for planning sieges and maneuvers in European wars, emphasizing qualitative terrain visualization over precise measurement. The British Ordnance Survey, established in 1791 under the Board of Ordnance, exemplified this military focus by initiating a national topographic survey to support defenses against potential Napoleonic invasion, starting with southern England. Early topographic efforts were hampered by significant limitations, including reliance on manual sketching from direct observation or rudimentary instruments like plane tables, which resulted in frequent inaccuracies in scale, proportion, and elevation. was typically conveyed qualitatively through pictorial icons or early , prioritizing visual impression over quantitative data like measurements, as precise leveling tools were unavailable until later centuries.

Evolution in the 19th and 20th Centuries

In the 19th century, topographic mapping advanced significantly through the institutionalization of national survey programs and the refinement of elevation representation techniques. The introduction of contour lines, first devised by British mathematician during his 1791 survey of mountain in , gained widespread adoption across and by the mid-1800s, enabling more precise depiction of terrain relief compared to earlier hachure methods. In the United States, the establishment of the (USGS) in 1879 marked a pivotal moment, initiating systematic topographic mapping with early quadrangle maps produced at a scale of 1:62,500 by the 1890s to support resource management and exploration. Similarly, Switzerland's Dufour Map, completed between 1844 and 1864 at a 1:100,000 scale under General Guillaume-Henri Dufour, became a global benchmark for national topographic series due to its comprehensive coverage and use of hachures for elevation, influencing subsequent European efforts. The United Kingdom's achieved a milestone with the completion of its 1:63,360 (one-inch to the mile) series for by the 1890s, incorporating initial contour lines on select sheets to enhance terrain visualization. Technological innovations in surveying instruments further propelled these developments. Theodolites, refined since Jesse Ramsden's precision model in 1787, and plane tables facilitated accurate networks across large areas, allowing surveyors to measure angles and distances with greater reliability during 19th-century campaigns. emerged as a complementary tool in the late 1800s, with balloon-based images first used for mapping in the , followed by aircraft reconnaissance during , which provided oblique views to verify ground surveys and identify features like drainage patterns. The 20th century saw accelerated progress driven by global conflicts and international collaboration. spurred the widespread adoption of photogrammetry, where overlapping aerial photographs enabled stereoscopic measurement of elevations and contours, dramatically increasing mapping efficiency for military operations and post-war reconstruction. Standardization efforts advanced through the project, initiated in 1891 and formalized with uniform specifications in the 1920s under the International Research Council (predecessor to the International Geographical Union), promoting consistent scales, symbols, and projections for 1:1,000,000 sheets worldwide. In the United States, the USGS transitioned to its iconic 7.5-minute quadrangle series in the 1940s, achieving nationwide coverage at 1:24,000 scale by the late 20th century through integrated ground and aerial methods. These evolutions also addressed key limitations in map content and accessibility. National surveys shifted from primarily purposes—where maps like early products were initially restricted—to broader public availability, as seen with USGS publications from 1879 onward, fostering civilian uses in and . Additionally, 19th- and 20th-century maps increasingly incorporated and details, such as boundaries and agricultural patterns, to reflect ecological contexts, with USGS sheets from the 1880s onward denoting timber types and USGS post-1940s quadrangles adding shaded for habitat representation.

Production Techniques

Traditional Surveying Methods

Traditional surveying methods for topographic maps rely on ground-based measurements conducted by surveyors using manual instruments to capture horizontal positions, elevations, and terrain features directly in the field. These techniques, which predate modern remote sensing, involve labor-intensive processes to establish control points and detail the landscape, ensuring the foundational data for map compilation. Key methods include , traversing, leveling, plane table surveying, and chain and surveying, each suited to different scales and precisions of topographic work. Triangulation forms the basis for establishing horizontal control networks in topographic surveying by measuring angles from known baselines to compute distances and positions across large areas using trigonometric principles. Surveyors employ theodolites to measure angles at stations, with a measured baseline serving as the initial side of a network of triangles. The distance dd between points can be calculated using the law of sines: d=b⋅sin⁡Csin⁡Ad = b \cdot \frac{\sin C}{\sin A} where bb is the baseline length, AA is the angle opposite the unknown side, and CC is the angle opposite the baseline. This method allows efficient coverage of extensive terrain with fewer distance measurements, as only angles are needed after the initial baseline. Traversing complements triangulation by connecting control points through a series of measured lines and angles, forming a closed or open polygon to verify positions and extend the network; it uses similar theodolite observations but incorporates direct distance measurements via tapes or chains for shorter segments. Both techniques minimize cumulative errors in primary control for topographic maps by distributing measurements across redundant paths. Leveling determines elevations essential for representing terrain relief on topographic maps through differential methods that establish height differences between points. Surveyors use a level instrument, such as a spirit or automatic level, mounted on a tripod, and a graduated leveling rod held at target points; readings are taken for backsights (to known elevations) and foresights (to subsequent points). The elevation difference is computed as: Δh=BS−FS\Delta h = BS - FS where Δh\Delta h is the height change, BSBS is the backsight reading, and FSFS is the foresight reading. This process is repeated in a series of setups along a level line, with temporary benchmarks set to maintain continuity, achieving vertical accuracies suitable for contour interpolation. Geodetic leveling refines this for national frameworks, incorporating corrections for Earth's curvature and refraction to support precise topographic data. Plane table surveying enables direct graphical plotting of topographic features in the field, integrating horizontal and vertical control without extensive note-taking. A flat mounted on a serves as the plane, oriented to using a or ; the , a sighting device with a , is used to sight points and draw rays on the board scaled to the . Elevations are incorporated via stadia tacheometry, where the level difference is derived from rod intercepts observed through the alidade's stadia hairs. Contours and features like ridges or streams are sketched in real-time as the table is relocated to new stations, allowing immediate visualization and adjustment for terrain details. This method excels in moderate-scale mapping where visual correlation of ground features to the is advantageous. Chain and compass methods provide a simpler, lower-precision approach for topographic surveys in rural or undeveloped areas, focusing on basic feature location without advanced instruments. Distances are measured using a surveyor's (typically 66 feet or 20 meters) stretched between points, while bearings are recorded with a prismatic or surveyor's to determine directions relative to magnetic north. Traverse lines are laid out by segments and noting offsets to features like boundaries or ; the data is later plotted using from compass bearings. Though prone to errors and less accurate for detailed , this technique suffices for preliminary or small-scale topographic sketches where high precision is not required. Accuracy in traditional is governed by error propagation through sequential measurements, necessitating careful instrument , redundant observations, and adjustments to achieve reliable topographic data. Horizontal positions from or traversing typically aim for closures within 1:5,000 to 1:10,000 of the traverse length, while vertical leveling targets differences accurate to 0.01 to 0.05 feet per mile. For a 1:5,000 scale topographic map, horizontal accuracy of about 1 meter is standard to ensure feature placement within one-half the smallest map unit. These standards mitigate cumulative errors from angular misclosures or tape sags, with least-squares adjustments often applied post-fieldwork to optimize the network. Contour generation from such data relies on this precise control to interpolate forms accurately.

Modern Digital and Remote Sensing Approaches

Modern digital and remote sensing approaches have revolutionized topographic mapping by enabling efficient, large-scale data acquisition without direct ground contact, leveraging advancements in imaging, laser technology, and computational processing to produce high-resolution digital elevation models (DEMs). These methods integrate aerial and satellite platforms with sophisticated algorithms, allowing for global coverage and rapid updates that surpass the limitations of traditional techniques. Photogrammetry, LiDAR, and satellite interferometry form the core of these approaches, often combined within geographic information systems (GIS) for contour generation and analysis. In the United States, the USGS 3D Elevation Program (3DEP) exemplifies modern production, acquiring LiDAR data at 1/3-meter resolution for the contiguous U.S. and IfSAR for Alaska and territories as of 2025. Photogrammetry utilizes overlapping stereo aerial imagery captured from aircraft or drones to reconstruct three-dimensional terrain surfaces, processed through software such as ERDAS IMAGINE to generate DEMs with vertical accuracies typically reaching sub-meter levels in optimal conditions. The technique relies on the principle of , where the apparent displacement of features between stereo pairs corresponds to elevation differences; this is quantified by the equation p=B⋅hHp = \frac{B \cdot h}{H} where pp is the , BB is the baseline distance between camera positions, hh is the difference, and HH is the flying above the . By measuring these disparities, automated stereo-matching algorithms extract , enabling the creation of detailed topographic surfaces over extensive areas. This method has been widely adopted for national mapping programs, providing seamless integration with vector for comprehensive map production. LiDAR, or Light Detection and Ranging, employs airborne laser scanning systems mounted on aircraft to emit pulses of light and measure their return times, generating dense point clouds that represent bare-earth with resolutions often exceeding 10 points per square meter. The distance to the surface is calculated using the : d=c⋅t2d = \frac{c \cdot t}{2} where dd is the distance, cc is the speed of light, and tt is the round-trip time of the pulse. Multiple returns from a single pulse allow discrimination between ground and vegetation layers, facilitating the production of digital terrain models (DTMs) that filter out non-terrain features. Airborne LiDAR systems achieve vertical accuracies of 10-15 cm in open terrain, making them indispensable for high-fidelity topographic surveys in complex environments. Satellite remote sensing has democratized global topographic data through missions like the (SRTM) launched in 2000, which used (SAR) interferometry to produce a near-global DEM at 30 m horizontal resolution, covering approximately 80% of Earth's land surface. The SRTM's C-band radar partially penetrates vegetation canopies, providing elevation estimates that reflect sub-canopy topography in forested areas with varying accuracy depending on biomass density. Subsequent missions, such as TanDEM-X (operational since 2010), have enhanced this capability with X-band SAR, yielding the WorldDEM product—a 12 m resolution global DTM achieved through bistatic and phase unwrapping, with relative vertical accuracy better than 2 m (LE90) and absolute vertical accuracy better than 4 m in most terrains. The Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) Global DEM, derived from optical stereo imagery at 30 m resolution, complements these by offering surface elevation data, though it primarily captures canopy heights in vegetated regions rather than bare earth, necessitating post-processing for topographic applications. Integration with GIS platforms, such as , allows for the of from DEMs using algorithms like (IDW) and spline methods, which estimate values at unsampled locations to create smooth, continuous surfaces suitable for mapping. IDW assigns weights inversely proportional to distance from known points, producing localized predictions ideal for irregular , while fits a flexible surface that minimizes , ensuring hydrologically correct representations. These tools enable automated contour generation at user-defined intervals, supporting scalable topographic map production with minimal manual intervention. Post-2020 advancements have further accelerated these processes through drone-based systems, which provide cost-effective, high-resolution surveys for local areas, achieving point densities up to 100 points per square meter and vertical accuracies of 5 cm over sites up to several square kilometers. Concurrently, and techniques have automated feature extraction from aerial and , using convolutional neural networks to identify and classify elements like roads, water bodies, and landforms with over 90% accuracy in benchmark studies, thereby enabling annual update cycles for dynamic topographic datasets in regions with frequent changes.

Map Conventions and Standardization

Contour Lines and Elevation Representation

Contour lines, also known as isohypses, are imaginary lines that connect points of equal on the Earth's surface relative to a reference level, such as mean . These lines represent the three-dimensional shape of on a two-dimensional , enabling visualization of hills, valleys, and slopes. Key rules govern their depiction: contour lines never cross each other, as each line maintains a unique elevation; they form closed loops around hills or depressions; and when crossing a or , they create a V-shaped pattern with the point of the V directed upstream, indicating the direction of water flow. The vertical spacing between adjacent contour lines, known as the contour interval, is selected based on the map's scale and the terrain's to effectively portray variations without overcrowding or oversimplification. For instance, on 1:50,000-scale maps, a common interval is 10 meters in areas of moderate . To aid readability, index contours—typically every fifth line—are drawn thicker and labeled with their elevation values, while intermediate contours remain thinner. Contour lines are generated through from spot heights or surveyed points, assuming a uniform between known data points. This process often employs along a connecting two points with known elevations z1z_1 and z2z_2, separated by distances d1d_1 and d2d_2 from an intermediate point. The zz at that point is calculated as: z=z1+(z2−z1)⋅d1d1+d2z = z_1 + (z_2 - z_1) \cdot \frac{d_1}{d_1 + d_2} This method estimates contour positions by prorating changes proportionally to horizontal distances. In addition to standard contours, supplementary techniques depict specific features. Depression contours, representing sinks or basins, are closed loops with short perpendicular tick marks (hachures) on their inner side, pointing toward lower elevations within the depression. Form lines, dashed or approximate contours, are used in unsurveyed or reconnaissance areas to indicate approximate relief where precise data is unavailable. Interpreting contour lines reveals terrain characteristics: closely spaced lines indicate steep slopes, as the same elevation change occurs over a short horizontal distance, while widely spaced lines denote gentle gradients. The approximate slope, or gradient, can be estimated as the contour interval divided by the horizontal distance between lines (rise over run). The pattern's orientation provides aspect, or the direction of slope facing, and cross-sectional profiles can be constructed by tracing lines along a transect to visualize elevation changes. Elevation bands may be shaded with colors for additional clarity, though detailed symbology varies by map standard.

Symbols, Colors, and Scales

Topographic maps employ standardized color conventions to distinguish natural and cultural features clearly. In (USGS) maps, brown is used for contour lines and elevation representations, blue denotes water bodies such as rivers and lakes, green indicates like forests and grasslands, and black or red highlights cultural features including roads, buildings, and boundaries. These colors enhance readability by associating visual cues with specific terrain elements, ensuring users can quickly interpret the landscape. Symbols on topographic maps are categorized into point, line, and area types to represent discrete features efficiently. Point symbols, such as triangles for benchmarks or small circles for spot elevations, mark specific locations like survey control points. Line symbols include solid lines for perennial streams, dashed lines for intermittent ones, and varying thicknesses or patterns for roads and trails to convey and type. Area patterns, like or for swamps and marshes, fill regions to depict such as urban areas or wooded zones. These symbologies are designed for minimal overlap and high contrast, facilitating accurate feature identification. Map scales in topographic representations are typically expressed as representative fractions, such as 1:24,000 for detailed USGS quadrangles where one unit on the map equals 24,000 units on the ground, or 1:100,000 for broader overviews. Projections like the polyconic, historically used for USGS topographic sheets to minimize distortion in mid-latitude regions, have largely been replaced by conformal projections such as the Transverse Mercator for modern maps, preserving shapes and angles while reducing area distortions. These choices balance accuracy across the map's extent, with scale bars often included to account for potential variations due to projection. International standards for symbology, outlined in ISO 19117, provide a conceptual schema for describing symbols and portrayal functions that map geospatial features to visual elements, promoting interoperability across mapping systems. Variations exist; for instance, while USGS maps incorporate both imperial (e.g., 1:24,000) and metric scales, European national programs like the UK Ordnance Survey uniformly adopt metric scales such as 1:25,000 for detailed topographic mapping. This ensures consistency in regions using the metric system, though core color and symbol principles remain broadly similar for global recognition. Legends and indexes on topographic maps serve as explanatory keys, detailing symbol meanings, color usages, and scale information, often located in margins or as separate insets for quick reference. In digital versions, such as USGS PDF exports and the topoBuilder application (as of 2025), layered symbology allows users to toggle features on or off and create customizable OnDemand Topo maps, enhancing interactivity while maintaining traditional legend structures for printed outputs.

Applications and Uses

Military and Navigation

Topographic maps play a critical role in operations, particularly for route planning and analysis, enabling commanders to assess mobility, concealment, and defensive positions across varied landscapes. During , Allied forces relied on detailed British and American topographic maps, including specialized geologic overlays, to evaluate soil stability, beach gradients, and inland routes for the D-Day landings on June 6, 1944, which facilitated the invasion's success by identifying suitable landing zones and potential obstacles. These maps, often supplemented with raised-relief models derived from contour data, allowed planners like to simulate assaults and mitigate risks from tidal fluctuations and features. Due to their strategic value, topographic maps are subject to security classifications, such as "Confidential" or higher, restricting access and distribution to prevent enemy exploitation. In navigation applications, topographic maps serve as foundational tools for , where users combine them with a to determine direction, distance, and position in unfamiliar by aligning map features like and landmarks with the compass needle. For off-road travel, these maps augment GPS systems by providing detailed elevation profiles and obstacle data that electronic signals alone may miss in remote or signal-denied areas, enhancing route safety and efficiency. Mobile applications like Gaia GPS integrate topographic layers, such as USGS-derived and shaded relief, to overlay real-time GPS tracks on digital maps, supporting precise navigation for adventurers and professionals alike. For , hikers use topographic maps to assess trail steepness through spacing—closely packed lines indicate rapid changes and challenging ascents, while widely spaced lines suggest gentler slopes—allowing informed decisions on route difficulty and energy expenditure. In search-and-rescue operations, data from these maps helps teams predict lost individuals' likely paths based on terrain contours, integrating with to model descent routes and prioritize high-risk zones like steep ravines. Historically, the (1804-1806) employed rudimentary topographic sketches by to document river courses, elevation shifts, and landmarks along the and Columbia Rivers, providing essential data for future navigation and territorial claims. In modern contexts, unmanned aerial vehicles (UAVs) utilize topographic maps for in military operations, employing algorithms that analyze digital elevation models to optimize low-altitude routes while avoiding obstacles in contested environments. Topographic maps face challenges in military settings, including physical degradation of paper versions in wet conditions, where moisture can render contours illegible and compromise field usability during amphibious or rainy operations. Additionally, dynamic war zones demand frequent updates to account for rapidly changing terrain from bombings or fortifications, as outdated maps can lead to navigational errors and operational failures. Digital topographic data, derived from remote sensing, addresses some of these issues by enabling real-time revisions for navigation.

Civil Engineering and Land Use Planning

Topographic maps play a pivotal role in by providing essential for in projects such as and roads, where analysis from contour lines helps identify stable terrains and minimize risks like landslides or instability. Engineers use these maps to evaluate gradient variations, ensuring that sites feature narrow valleys with suitable rock foundations and that alignments avoid excessive inclines that could increase construction costs or safety hazards. For instance, in siting, topographic integrated with GIS models assess hydrological and geological factors to prioritize locations with optimal impoundment capacities. A key application involves cut-and-fill calculations during earthwork , where contours delineate existing and proposed elevations to estimate material excavation or deposition. This process employs the average end area method, approximating as the product of the average cross-sectional area between contours and the vertical interval height, which aids in budgeting and scheduling for projects like grading. Such calculations ensure efficient by quantifying earth movement, typically using software tools that process contour intervals of 0.5 to 2 meters for accurate results on varied terrains. In , topographic maps inform decisions by highlighting -prone areas through hydrographic features like stream networks and low-lying depressions, enabling regulators to restrict development in high-risk zones to protect against inundation. These maps delineate base elevations and drainage patterns, supporting policies that designate buffer zones around waterways. For urban expansion, they guide avoidance of steep terrains by mapping slope percentages, preventing settlement on gradients exceeding 15-20% that could lead to or structural failures, thus promoting sustainable growth in flatter, accessible areas. Environmentally, topographic maps facilitate modeling by simulating over slopes and contours, predicting in vulnerable watersheds to inform conservation strategies. They also support habitat mapping by overlaying data with vegetation zones, identifying refugia for species in rugged landscapes. When integrated with GIS, these maps enable analysis of impacts, such as overlaying sea-level rise scenarios on coastal topographic digital models (DEMs) to forecast inundation of low- ecosystems up to 10 feet above mean high tide. Historical case studies underscore their utility; during the Panama Canal's planning in the early 1900s, extensive topographic surveys mapped the isthmus's elevations, valleys, and , guiding excavation volumes and lock placements across 40 miles of varied terrain. More recently, in siting, elevation data from topographic maps and DEMs have optimized locations by assessing terrain-induced wind acceleration on hills and ridges, as seen in central U.S. projects that balance energy yield with habitat preservation. Topographic maps further address gaps in disaster mitigation, particularly through their derivation into FEMA flood maps via DEMs, with post-2020 updates incorporating high-resolution data to refine special flood hazard areas and base flood elevations for numerous communities each year. These enhancements, drawing from national topographic programs, improve predictive accuracy for management and resilient design. For example, in response to events like Hurricane Helene in 2024, USGS 3D elevation models derived from topographic data aided emergency response and recovery .

National and Global Topographic Mapping Programs

Major National Publishers

In the United States, the (USGS) is the primary national publisher of topographic maps, producing the well-known 7.5-minute quadrangle series at a scale of 1:24,000, which provides detailed coverage of the , , , and U.S. territories through over 66,000 map sheets. These maps depict , , roads, and , with the USGS transitioning in 2009 from traditional printed maps to the digital US Topo format integrated into The National Map platform, enabling on-demand generation and updates. US Topo maps follow a three-year production cycle, updating one-third of the nation's coverage annually, though the program paused in 2025 for a major system and software upgrade. while underlying orthoimagery from the National Agriculture Imagery Program (NAIP) is refreshed every three years to maintain currency. Accessibility is enhanced through free downloads in GeoPDF format via the USGS Earth Explorer and topoView portals, alongside the Historical Topographic Map Collection, a digital archive of over 185,000 maps from 1884 to 2006 available for public use. In the , the (OS) serves as the national mapping agency, issuing the Explorer series at 1:25,000 scale for detailed outdoor , covering all of with emphasis on footpaths, contours, and public rights of way across approximately 400 map sheets. Complementing this, OS MasterMap provides high-resolution vector at urban scales up to 1:1,000, supporting both raster and digital formats for integration into GIS applications. Updates occur on a rolling basis, with OS MasterMap refreshed every six weeks, while Explorer raster maps are revised twice yearly to incorporate changes from field surveys and aerial imagery. Maps are accessible via free OS OpenData downloads for basic layers and paid portals for premium products, with on-demand printing available through authorized partners. Switzerland's Federal Office of Topography (swisstopo) produces the National Map series at 1:25,000 scale, renowned for its precision and aesthetic hillshading, covering the entire country and in 247 sheets that highlight alpine terrain, settlements, and . This series sets a benchmark for detail, integrating vector and raster elements derived from and orthophotos, with updates occurring annually for core datasets to reflect landscape changes. Digital access is provided through the free swisstopo geodata portal and map.geo.admin.ch viewer, supporting downloads in GeoPDF and formats, alongside on-demand printed editions. Canada's (NRCan) oversees topographic mapping via the National Topographic System, with the primary series at 1:50,000 scale offering comprehensive coverage of the country's in over 16,000 sheets that include , , and transportation features. A broader 1:250,000 series complements this for regional overviews, both now digitized as CanVec vector data and NT1 raster products. Updates are integrated periodically through the GeoGratis platform, drawing from ongoing aerial and surveys, though specific cycles vary by region with emphasis on northern territories. Free downloads in and PDF formats are available nationwide, with historical maps archived digitally for research. Australia's Geoscience Australia publishes the 1:250,000 scale topographic map series, known as NATMAP and now evolving into the AUSTopo digital format, providing national coverage across 516 sheets that capture arid interiors, coastlines, and urban areas with standardized symbols for and . This scale balances detail and overview, updated systematically since 1995 with progressive revisions incorporating satellite data and ground surveys, though full national refresh cycles span several years. Accessibility includes free online downloads via the Geoscience Australia portal in GeoPDF and web services, supporting on-demand printing and integration with initiatives.

International Initiatives and Data Sharing

International collaborative efforts in topographic mapping have been advanced by organizations like the United Nations Cartography Section, which promotes global standards for map production and data interoperability to support peacekeeping and humanitarian operations. This section focuses on enriching topographic data in crisis-prone areas through initiatives such as UN Maps, which integrate high-quality road and terrain information for operational use. Additionally, the Global Earth Observation System of Systems (GEOSS) facilitates the integration of topographic data from diverse sources, enabling coordinated observations for environmental monitoring and disaster management by providing interoperability guidelines for digital elevation models (DEMs). Open data movements have significantly enhanced accessibility to topographic resources, exemplified by the European Union's Copernicus Land Monitoring Service, which offers free, high-resolution DEMs covering global and European regions as digital surface models that include and . Complementing this, the OpenTopography portal serves as a key repository for sharing datasets, providing to high-resolution topography data for and through community-driven processing tools. International consortia play a pivotal role in standardizing and advancing topographic mapping, with the International Cartographic Association (ICA) establishing commissions dedicated to topographic mapping that develop research agendas on data integration, map projections, and coordinate systems. A landmark achievement in this domain is the TanDEM-X mission, launched in the 2010s by the in collaboration with international partners, which completed global coverage for a high-resolution DEM by 2016, encompassing over 19,000 tiles with 12-meter resolution. Post-2020 developments include the release of enhanced global DEMs like WorldDEM Neo, derived from TanDEM-X acquisitions between 2017 and 2021, offering updated elevation data at 5-meter resolution for applications in orthorectification and . However, challenges persist in data harmonization, particularly with varying vertical datums such as EGM2008, which complicate the unification of global height references across datasets from different regions and sensors. Looking ahead, crowdsourced platforms like are emerging as tools for generating topographic contours by combining volunteered geographic information with elevation data sources such as SRTM, enabling community-driven updates to global basemaps. Furthermore, technology is being explored for ensuring data provenance in shared topographic repositories, providing immutable records of data lineage to enhance trust and traceability in geospatial collaborations.

References

  1. https://pubs.usgs.gov/gip/70039399/report.pdf
  2. https://www.usgs.gov/faqs/what-a-topographic-map
  3. https://pubs.usgs.gov/gip/TopographicMapSymbols/topomapsymbols.pdf
  4. https://www.britannica.com/science/topographic-map
  5. https://www.usgs.gov/media/slideshows/a-brief-overview-usgs-topographic-maps
  6. https://www.usgs.gov/programs/national-geospatial-program/historical-topographic-maps-preserving-past
  7. https://serc.carleton.edu/mathyouneed/slope/index.html
  8. https://www.usgs.gov/educational-resources/topographic-mapping
  9. https://www.usgs.gov/programs/national-geospatial-program/topographic-maps
  10. https://pubs.usgs.gov/gip/70039400/report.pdf
  11. https://pubs.usgs.gov/gip/usgsmaps/usgsmaps.html
  12. https://pubs.usgs.gov/circ/1955/0368/report.pdf
  13. https://www.doi.gov/document-library/departmental-manual/757-dm-3-mapping
  14. https://www.usgs.gov/programs/national-geospatial-program/us-topo-maps-america
  15. https://ngmdb.usgs.gov/topoview/help/
  16. https://www.usgs.gov/publications/map-projections-used-us-geological-survey
  17. https://www.usgs.gov/media/images/utm-and-latitudelongitude-coordinates-a-topographic-map
  18. https://www.usgs.gov/faqs/how-are-utm-coordinates-measured-usgs-topographic-maps
  19. https://www.usgs.gov/media/images/scale-bar-163360-topographic-map
  20. https://www.usgs.gov/faqs/what-do-different-north-arrows-a-usgs-topographic-map-mean
  21. https://www.usgs.gov/ngp-standards-and-specifications/topographic-maps-standards-and-specifications
  22. https://pubs.usgs.gov/bul/0788e/report.pdf
  23. https://earthquake.usgs.gov/education/geologicmaps/hillshades.php
  24. https://www.usgs.gov/media/images/contour-lines-and-shaded-relief-a-us-topo-map
  25. https://www.guinnessworldrecords.com/world-records/first-clay-tablet-map
  26. https://www.researchgate.net/figure/CLAY-TABLET-MAP-EXCAVATED-AT-YORGAN-TEPE-This-is-a-cast-of-the-earliest-known-example_fig7_285762990
  27. https://www.historyofinformation.com/detail.php?id=1395
  28. https://www.unesco.org/en/memory-world/tabula-peutingeriana
  29. https://artsandculture.google.com/story/leonardo-da-vinci-cartographer-museo-galileo/xAXRtWKVrHUmJg?hl=en
  30. https://www.rct.uk/collection/912673/recto-three-sketches-of-the-course-of-the-rivers-brembana-trompia-and-sabbia-with
  31. https://static.lib.virginia.edu/exhibits/onthemap/index.php/themes/16th-century/woodcut-maps/
  32. https://archive.org/details/dr_planispheres-celeste-12201017
  33. https://publishing.cdlib.org/ucpressebooks/view?docId=ft6d5nb455&chunk.id=0&doc.view=print
  34. https://www.ordnancesurvey.co.uk/about/history
  35. https://press.uchicago.edu/books/hoc/HOC_V3_Pt1/HOC_VOLUME3_Part1_chapter29.pdf
  36. https://topostreets.com/how-historical-topo-maps-were-created/
  37. http://www.geo.hunter.cuny.edu/terrain/ter_hist.html
  38. https://mapreading.co.uk/history-of-contour-lines/
  39. https://pubs.usgs.gov/circ/1341/pdf/circ_1341.pdf
  40. https://www.esri.com/~/media/files/pdfs/library/bestpractices/125-years-of-topo-mapping.pdf
  41. https://www.swisstopo.admin.ch/en/dufour-map
  42. https://maps.nls.uk/os/one-inch-old-series/
  43. https://airandspace.si.edu/stories/editorial/beginnings-and-basics-aerial-photography
  44. https://dronecenter.bard.edu/wwi-photography/
  45. https://www.ngs.noaa.gov/wp-content/uploads/2018/06/history_of_photogrammetric_mapping-2.pdf
  46. https://www.tandfonline.com/doi/abs/10.1080/03085694.2015.974956
  47. https://mapdesign.icaci.org/2014/10/mapcarte-295365-15-minute-and-7-5-minute-quadrangle-sheets-by-usgs-1950-present/
  48. https://www.nationalarchives.gov.uk/help-with-your-research/research-guides/ordnance-survey/
  49. https://www.esri.com/news/arcnews/fall09articles/125-years.html
  50. https://geodesy.noaa.gov/INFO/history/triangulation.shtml
  51. https://pubs.usgs.gov/bul/0788b/report.pdf
  52. https://www.usgs.gov/publications/leveling
  53. https://www.ngs.noaa.gov/PUBS_LIB/GeodeticLeveling_Manual_NOS_NGS_3.pdf
  54. https://geodesy.noaa.gov/INFO/history/plane-table.shtml
  55. https://dot.ca.gov/-/media/dot-media/programs/right-of-way/documents/ls-manual/05-surveys-a11y.pdf
  56. https://www.fgdc.gov/standards/projects/accuracy/part4/FGDC-endorsed-standard
  57. https://directives.nrcs.usda.gov/sites/default/files2/1712930814/33252.pdf
  58. https://www.usgs.gov/3d-elevation-program
  59. http://academic.brooklyn.cuny.edu/geology/grocha/mapcontour/
  60. https://www.bbc.co.uk/bitesize/guides/zmb6jsg/revision/7
  61. https://ngmdb.usgs.gov/fgdc_gds/geolsymstd/fgdc-geolsym-sec30.pdf
  62. https://www.usgs.gov/educational-resources/topographic-map-symbols
  63. https://pubs.usgs.gov/fs/2002/0015/report.pdf
  64. https://pubs.usgs.gov/publication/pp1395
  65. https://pubs.usgs.gov/gip/70047422/report.pdf
  66. https://www.iso.org/standard/46226.html
  67. https://www.ordnancesurvey.co.uk/mapzone/map-skills/understanding-scale
  68. https://www.usgs.gov/faqs/where-can-i-find-a-topographic-map-symbol-sheet
  69. https://www.usgs.gov/programs/national-geospatial-program/topobuilder
  70. https://www.researchgate.net/publication/233586194_Specialist_Maps_Prepared_by_British_Military_Geologists_for_the_D-Day_Landings_and_Operations_in_Normandy_1944
  71. http://www.iapad.org/wp-content/uploads/2015/07/military_model_making_wwii_pearson_s.pdf
  72. https://www.atu.edu/rotc/docs/7_fm3_25x26.pdf
  73. https://www.rei.com/learn/expert-advice/navigation-basics.html
  74. https://www.outdoorgearlab.com/topics/camping-and-hiking/best-handheld-gps
  75. https://help.gaiagps.com/hc/en-us/articles/9067661557399-How-to-Use-Gaia-GPS
  76. https://blog.gaiagps.com/how-to-read-topographic-maps/
  77. https://www.nps.gov/articles/aps-v10-i2-c8.htm
  78. https://lewis-clark.org/sciences/geography/clarks-maps/
  79. https://www.fs.usda.gov/t-d/pubs/pdfpubs/pdf02232821/pdf02232821dpi72.pdf
  80. https://ir.library.oregonstate.edu/downloads/s1784m33n
  81. https://www.mdpi.com/2073-4441/11/9/1880
  82. https://www.researchgate.net/publication/353641729_Dam_Siting_A_Review
  83. https://aceroestudio.com/en/applications-of-topography-in-civil-engineering/
  84. https://esurveying.net/earthwork-quantity/volume-calculation-contour-method
  85. https://www.testfit.io/blog/how-to-calculate-cut-and-fill-volume
  86. https://www.huduser.gov/portal/sites/default/files/pdf/Flood-Prone-Areas-and-Land-Use-Planning.pdf
  87. https://www.fema.gov/flood-maps
  88. https://landmaps.uslandgrid.com/land-maps/topographic-maps-in-urban-planning-crucial-role/
  89. https://www.usgs.gov/science/science-explorer/climate/coasts-storms-and-sea-level-rise
  90. https://www.noaa.gov/digital-coast-sea-level-rise-viewer
  91. https://www.archives.gov/research/guide-fed-records/groups/185.html
  92. https://www.ul.com/software/ultrus/windnavigator-resource-data-maps
  93. https://www.nature.org/en-us/what-we-do/our-priorities/tackle-climate-change/climate-change-stories/site-wind-right/
  94. https://www.fema.gov/flood-maps/national-flood-hazard-layer
  95. https://msc.fema.gov/portal/search
  96. https://www.usgs.gov/news/featured-story/using-3d-elevation-models-help-response-hurricane-helene
  97. https://www.usgs.gov/faqs/how-current-are-us-topo-maps
  98. https://shop.ordnancesurvey.co.uk/maps/os-explorer-maps/
  99. https://www.ordnancesurvey.co.uk/products/os-mastermap-topography-layer
  100. https://www.ordnancesurvey.co.uk/products/os-maps-api
  101. https://www.swisstopo.admin.ch/en/national-map-1-25000
  102. https://www.swisstopo.admin.ch/en/national-maps
  103. https://myswissmap.swisstopo.admin.ch/en/
  104. https://natural-resources.canada.ca/maps-tools-publications/maps/topographic-maps
  105. https://natural-resources.canada.ca/maps-tools-publications/maps/topographic-maps/national-topographic-system-maps
  106. https://atlas.gc.ca/toporama/en/index.html
  107. https://www.ga.gov.au/scientific-topics/national-location-information/topographic-maps-data/topographic-maps
  108. https://ecat.ga.gov.au/geonetwork/srv/api/records/787cda57-ec59-41b2-9b9c-ef8ab4e38e4b
  109. https://maps.un.org/
  110. https://ceos.org/document_management/Working_Groups/WGCV/Meetings/WGCV-29/GEOSS-Interoperability-Guidance-DEM-data-V2_web.pdf
  111. https://dataspace.copernicus.eu/explore-data/data-collections/copernicus-contributing-missions/collections-description/COP-DEM
  112. https://portal.opentopography.org/
  113. https://topo.icaci.org/
  114. https://www.eoportal.org/satellite-missions/tandem-x
  115. https://space-solutions.airbus.com/imagery/3d-elevation-and-reference-points/worlddem-neo/
  116. https://gisgeography.com/topographic-maps/
  117. https://www.sciencedirect.com/science/article/pii/S1195103624000260
Add your contribution
Related Hubs
User Avatar
No comments yet.