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Surface variables influence our everyday life ranging from resource availability, vegetation growth, solar radiation, transportation and hydrological conditions. Various natural hazards such as erosion, flooding, landslides, and avalanches are greatly impacted by these variables too.

A few surface variables definition with its usage are outlined below:

• Elevation: Digital elevation models (DEM) is a digital representation of earth's topography or refer specifically to a raster or regular grid of spot heights. DEM are a superset of both digital terrain models (DTM) and digital surface models (DSM). Remote sensing generally captures the surface height, so the top of the tree canopy or buildings is returned, not the bare ground elevation and hence surface is called DSM. If this data is corrected to remove elements which extrude above the terrain height, the surface is called as DTM. DEM is used interchangeably with the other two terms, DTM and DSM. DEM are generally used in determining attributes of terrain, such as elevation at any point, slope and aspect or finding features on the terrain, such as drainage basins and watersheds, drainage networks and channels, peaks and pits and other landforms and in modeling of hydrologic functions, energy flux and forest fires etc.
• Slope: The slope or gradient describes steepness, incline, or grade of a surface. The slope for a particular location is computed as the maximum rate of change of elevation between that location and its surroundings. It can be expressed either in degrees or as a percentage. Slope calculation is an important aspect in hydrology, conservation, site-planning or infrastructure development studies.
• Aspect: Aspect is the orientation of slope, measured clockwise in degrees from 0 to 360, where 0 is north-facing, 90 is east-facing, 180 is south-facing, and 270 is west-facing. Aspect raster can be used in various studies such as determining direction of water flows, amount of solar illumination a site will receive, identify flat areas for emergency response etc.
• Hillshading: Hillshading is a technique used to visualize terrain as shaded relief, illuminating it with a hypothetical light source. The illumination value for each raster cell is determined by its orientation to the light source, which is based on slope and aspect.
• Curvature: Curvature is a second derivative of the surface, or it indicates the changing rate of the slope or of the orientation per unit length, in the XY plane. The unit of measure is radian/meter. When curvature surface is generated it is important to know that in which units z value is represented. If x, y and z units are same, a scale factor of 1 is defined but if values are different then conversion factor is applied. For example, if x and y are in meters and z is in feet than z factor of 0.3048 need to be set to convert units from feet to meters. There are various types of curvatures, such as profile curvature, plan curvature, tangential curvature, longitudinal curvature, maximum curvature, minimum curvature, etc. but profile and plan curvature surfaces are used frequently within GIS software for various geo-morphological studies. 

Source: http://www.spatialanalysisonline.com/HTML/index.html?profiles_and_curvature.htm

• Profile curvature (along slope): It indicates the slope variation in vertical plan and hence called as vertical curvature. A positive profile indicates that the surface is upwardly concave at that cell, a negative value indicates that the surface is upwardly convex at that cell and a value of zero indicates that the surface is linear. The Profile Curvature can be used to determine the flow velocity of water draining the surface and influences erosion and deposition. In locations with convex (negative) Profile Curvature the erosion will prevail and in locations with concave (positive) curvature the deposition will occur.
• Plan curvature (across slope): It indicates the slope variation in parallel direction and hence called as horizontal curvature. The Plan Curvature is positive for cells with concave contours and negative for cells with convex contours. Plan curvature can be used to differentiate between ridges and valleys.

Source: Scott A. Drzyzga, Shippensburg University

• Viewsheds/Visibility: Viewshed analysis (or line-of-sight) uses topographical data to determine the visibility of areas from a given point. The Viewsheds are widely used in telecommunications sector to determine placement of communication towers for maximum coverage. Besides tower placement a viewshed analysis can be used to locate fire observation stations in mountain areas so that the entire forest can be observed for possible fires.