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What are the different methods of Height Measurements? Give examples in support of your statement.

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Tree height can be measured on aerial photographs by making use of the following photo-image characteristics:

  1. Radial displacement
  2. Parallax
  3. Shadow length

Radial Displacement Method

Radial displacement (as explained in Q # 5) of the vertical photographs can be utilized for fairly accurate measurement of tree height. The degree of displacement is proportional to the height of the object and its distance from nadir.
Now if the displacement (D) of the tree-image on the aerial photograph is measured and the radial distance (R) from nadir to the top of the displaced image is known, the height of the tree can be calculated as:
ho = D ´ H / R
ho   = height of the object (tree) in feet
H  = height of the plane above the base of the object in feet
The above relationship will hold true provided the following conditions are fulfilled:

  1. When the photograph has less than 2 % tilt, so that principal point can be accepted as the nadir point.
  2. When the flight altitude above the base of the object can be precisely determined.
  • When the top and base of the object are clearly visible on the aerial photograph.
  1. When the degree of image displacement is large enough to permit accurate measurements.

Following figure indicates displaced images of the (hypothetical) objects. They are: (here scale RF = 1/1500; (focal length of camera) f = 6” and (height of air craft above ground level) H-h = 750’).

  • a = Square chimney with a radial displacement (D) = 0.70” and radial distance (R) = 4.25” measured on photo.
  • b = Eiffel Tower with a radial displacement (D) = 2” and (R) = 1.25”
  • c = Cylinder with (D) = 0.44” and (R) = 4.89”
  • d = Conifer tree with (D) = 1.31” and (R) = 4.44”

Height Measurements - Forestrypedia

  • = The height of Square Chimney:

ho = D ´ (H-h) / R
             =>         ho = 0.70 ´ 750 / 4.25
=>         ho = 123.529 feet

  • = The height of Eiffel Tower:

ho = D ´ (H-h) / R
                   =>         ho = 2 ´ 750 / 1.52
=>         ho = 986.842 feet (where as the actual height of the Eiffel Tower is 984 feet)

  • = The Height of Cylinder:

ho = D ´ (H-h) / R
=>         ho = 0.44 ´ 750 / 4.89
=>         h= 67.484 feet

  • = The height of tree:

                            ho = D ´ (H-h) / R
           =>         ho = 1.31 ´ 750 / 4.44
=>         ho = 221.283 feet

Parallax Method:

The theory of this method is based upon the differences in parallax readings at the base and top of the tall objects like trees, towers, smoke stack, etc with the help of parallax measuring instruments such as a parallax wedge or parallax bar. These measurements are taken by looking at the stereo pair under a stereoscope. The difference b/w the two readings is converted into the height of the object by means of parallax formula.
Example: Figure shows the Washington Monument:
Parallax Method - Forestrypedia
The parallax b/w the top and bottom are measured, which in this case is 1.46 inches and 2.06 inches respectively. The parallax difference (dP) is 0.60 inches. The scale of the photograph is 1:4600. Since a 12-inch focal length camera was used for taking the photograph, the height of aircraft above ground level would also be 4600 feet. The average photo base length (P) for the stereo pair is 4.40 inches.
            Here, we will be using the parallax formula:
i.e.                ho        = (H – h) dP / P + dP
here;             H-h      = 4600
dP         = 0.60
P           = 4.40
Putting values in parallax formula, we get
i.e.                ho        = 4600 ´ 0.60 / 4.40 ´ 0.60
or,                 ho          = 2760 / 5
or,                 ho          = 552 feet
Whereas, the actual height of the Washington Monument is 555 feet and 6 inches. Thus, there is a difference of approximately 3 feet which is within a reasonable limit of accuracy.
The Parallax Method of height measurement is much more accurate and reliable than the radial displacement method or the shadow method. With the parallax method, the height of most trees growing adjacent to open ground can be determined on a high-quality medium scale photography (e.g. 1:15840) with a standard error of 5 feet.
The chief advantage of parallax method lies in the fact that it requires more training and much more experience than is required for any other method.

Shadow Method:

The relationship b/w tree height and shadow length were first established as:
ho = L ´ 1 / RF tan q
ho  = height of the tree
L   = length of shadow on the aerial photograph
RF = Representative Fraction (Scale of photograph)
q   = angle of elevation of the sun
             If the length of the shadow measured on the photograph is equal to 2.8 millimeters, the scale of photography is 1:15,000 and the angle q is equal to 36O (See figure) calculate the height of the tree.
Shadow Method - Forestrypedia
The height of the object casting this shadow can be determined by the following formula:
ho = L ´ 1 / RF tan q
L = 2.8 mm            =>  L = 0.0028 m
RF = 1 / 15000
tan 36O = 0.7265
Hence; the height of the tree is:
ho = 0.0028 ´ 15000 ´ 0.7265
ho = 30.5 m
Therefore, the height of the tree is 30.5 meter or about 100 feet.

Limitations of the method:

Some of the limitations of the method are as under:

  1. The method can be accurately used provided the shadows are long and sharp so that they can be correctly measured.
  2. The object has to be located in an isolated place on level ground so that the shadow in unobstructed and free from slope effect.
  3. The time of exposure and the approximate geographic position of the locality must be known for the calculation of the inclination of the sun.
  4. The method is unsuitable for dense and fully stocked forests.
  5. The difficulty is experienced in measuring the shadow lengths of broadleaved species which have generally irregular crown shape. Usefulness of this method is therefore limited for broadleaved species.

This method is mainly used in Canada, but in Tropical and Sub-tropical countries this method is not used on account of dense vegetations.

For correction and improvements please use the comments section below.

Naeem Javid Muhammad Hassani is working as Conservator of Forests in Balochistan Forest & Wildlife Department (BFWD). He is the CEO of Tech Urdu ( Forestrypedia (, All Pak Notifications (, Essayspedia, etc & their YouTube Channels). He is an Environmentalist, Blogger, YouTuber, Developer & Vlogger.

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