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Fields, Isolines, Gradients and Topographic Maps. Earth Science – Notes #3. Fields. A field is any region of space, 2-D or 3-D, that has a measurable value at every point. For example, one can measure the elevation of a staircase at every stair, so the staircase is a field.

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  • A field is any region of space, 2-D or 3-D, that has a measurable value at every point.

  • For example, one can measure the elevation of a staircase at every stair, so the staircase is a field.

  • Fields may be represented graphically


  • Example: the temperature field in the oceans of the world


  • Isolines literally mean same (iso-) lines.

  • They are lines that connect points of equal value in a given field.

  • Common examples of isolines are:

    • Isotherms – temperature

    • Isobars – atmospheric pressure

    • Contour lines – elevation


  • These are isobars on a weather map


  • A gradient is the rate of change of a field value from place to place within a field.

  • Also called slope.

  • Spacing of isolines – the closer together the higher the gradient

  • Calculated by

    • gradient = change in field value


      *Page 1 in ESRT*

Topographic maps

Topographic Maps

A topographic map is a representation of a three-dimensional surface on a flat piece of paper

Topographic maps1
Topographic Maps

  • AKA Contour maps.

  • Models that show the elevation field of an area of the Earth.

  • Elevation is vertical distance above sea level.

  • Useful in many aspects of outdoor life (hiking) and environmental planning (roads, buildings, drainage)

  • Drawn with contour lines

Contour lines
Contour lines

  • Contour lines connect points of equal elevation

  • If you walk along a contour line your elevation will not change

  • The closer together the contour lines appear on a topographic map, the steeper the slope

Contour gradient
Contour Gradient

  • The rate of elevation change from place to place. Also called steepness or slope.

  • Calculated by the formula

    • gradient = change in elevation


      **The closer the lines, the steeper the land**


  • Closer

  • Steeper

  • Further

  • Gentler

Contour interval
Contour Interval

  • The vertical change in elevation between each contour line

  • 20 ft. on this map

Topographic maps misc
Topographic maps misc.

Rule of V’s

-When contour lines cross a stream they bend upstream. The stream flows opposite the V.

Topographic maps misc1
Topographic maps misc.

  • Index contours

    thicker than others

    and give elevation.

  • Benchmarks are

    permanent markers

    of elevation used

    as reference points.

Map scale
Map Scale

  • Scale is the ratio of a horizontal distance between the points on a map and the actual distance between the two points on the Earth.

  • Scales may be verbal (one inch equals a mile), fractional (1:5000), or graphical

Map direction
Map Direction

  • Top of a map is usually North, bottom is South, right is East, and left is West.

  • Maps commonly include a North arrow or compass rose.

    W E



Fields isolines gradients and topographic maps

Depression Contour Lines

  • a.k.a. hachure lines

  • Show holes or depressions in the ground surface

Contour profile
Contour Profile

  • A side-view or cross-section along a line on a map.

  • A profile is constructed by plotting elevations versus distance on a graph.

Fields isolines gradients and topographic maps

Vertical Exaggeration

  • Profiles are typically exaggerated to show vertical features

  • This is the number of times larger an object has been made to appear in the vertical direction

  • Calculated by dividing the horizontal scale by the vertical scale

Rules of contour lines some basic rules or facts about contour lines are listed below
Rules of Contour Lines — Some basic rules or facts about contour lines are listed below.

1) Where a contour line crosses a stream or valley, the contour bends to form a "V" that points upstream or valley. In the upstream direction the successive contours represent higher elevations.

2) Contours near the upper parts of hills form closures. The top of a hill is higher than the highest closed contour.

3) Hollows (depressions) without outlets are shown by closed, hatched contours. Hatched contours are contours with short lines on the inside pointing downslope. The bottom of the hollow is lower than the lowest closed contour.

Fields isolines gradients and topographic maps

  • 4) Contours are widely spaced on gentle slopes. 5) Contours are closely spaced on steep slopes. 6) Evenly spaced contours indicate a uniform slope.

  • 7) Contours do not cross or intersect each other, except in the rare case of an overhanging cliff.

  • 8) All contours eventually close, either on a map or beyond its margins.

  • 9) A single higher elevation contour never occurs between two lower ones, and vice versa. A change in slope direction is always determined by the repetition of the same elevation either as two different contours of the same value or as the same contour crossed twice.