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Hypsometric Curve and Hypsometric Integral

Hypsometric curve and Integral

A hypsometric curve is essentially a graph that shows the proportion of land area that exist at various elevations by plotting relative area against relative height. It gives Hypsometric integral which may be defined as the proportion lying below the curve of total square graph. When integral lies between 0.6 to 1, it would be complex curve and indicates youthful stage of dissection. 
When the integral lies between 0.35 to 0.60 it would be S shaped curve indicates maturely dissected landforms and less than 0.35 would be concave curve indicates old stage of river.


To calculate Hypsometric curve at first we have to demarcate a drainage basin and also to determine the major contours.
Suppose a drainage basin having major contours of 400m and 500m.
Then measure the total basinal area and also area below the respective contour and highest relief point and lowest relief point in the basin.
In this basin the highest relief point is 560m and lowest relief point is 360m.
Then 
Relative relief=highest relief-lowest relief
                        =560-360
                        =200
The total basin area and area below the respective contour are calculated with the help of stressing paper.
The scale of the basin map is 1:50000.
Thus 1cm = 500m and 2cm = 1Km.

When we take 2cm x 2cm area then the area will be 1 Sq Km.
Here again 1 Sq Km contains 400 small boxes.
Below 360m contour area = 0 Sq Km
Between 360 and 560m contours the total number of small boxes = 1135.
Now we know that in this stressing graph paper 400 small boxes =1 SqKm.
Hence 1 small box = 1÷400 SqKm
Therefore,
1135 small boxes = 1/400x1135 sqkm.
                                = 2.84 SqKm
Similarly,
Area between 400 & 500m=3.60SqKm.
And
Area between 500 & 560m=0.34 sqkm.
Thus total basin area
= 2.84 + 3.60 + 0.34 = 6.78 sqkm.

Now 
Relative area (a/A) 
= (Total area - Area below Respective contour)/Total area.
Relative Height (h/H) =
Relative Relief - ( Value of any contour - Lowest point of the basin)/Relative Relief


To draw the sequence of values of Relative Height (h/H) is be inversed with respect to Relative Area (a/A) values.


Then plot the Hypsometric curve as below
                 Fig. Showing Hypsometric curve.

Hypsometric Integral

Here we calculate the proportion lying below the curve to the total square graph. To calculate the proportion area we draw a horizontal and a vertical lines.
Here total 100 boxes which represents 100% of the area of the square graph. Below the Hypsometric curve there are 35 boxes and hence
35/100X100 = 35%.
Interpretation of Hypsometric curve 
Hypsometric integral is 35% and hence it is 0.35.
It indicates an old stream as 35% of basin landmass is to be old stage of dissection.

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