Important Formulas Physical Geography – Quick Recap! Relative Relief

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Formulas: Relative Relief, Drainage Density, Dissection Ratio, Ruggedness, Form| Physical Geography

Relative Relief

Steam Frequency

  • The term relative relief means the actual variation of height i.e.. different between maximum height and minimum height in per grid. Relative relief is one of the techniques which is effectively capable of presenting the relief characteristics without considering sea level.
  • Relative relief is a very important morphometric variable which is used for the overall assessment of morphological characteristics of terrain and degree of dissection.
  • Absolute relief means the maximum height of any region.
  • Stream Frequency: Number of stream segment per unit area of watershed.

Dissection Ratio

  • The dissection index, which is the ratio between relative relief and absolute relief, gives better understanding of the landscape (nature & magnitude of dissection of terrain) .
  • Equal relative altitude is not always of equal importance, since their absolute altitudes may differ. The picture gained from relative altitudes only is static, for it fails to consider the vertical distance from the erosion base, i.e.. the dynamic potential of the area studied
  • The values of dissection index vary from 0 (complete absence of dissection) to 1 (vertical cliff at sea level) - it expresses the relationship between the vertical distance of relief

from the erosion level and relative relief:

  • Very low dissection index (< 0.20) ,
  • Low dissection index (0.20 - 0.35) ,
  • Moderate dissection index (> 0.35)

Drainage Density

Ruggedness Index

  • Drainage Density (D) : Ratio of total length of all stream (L) of all order within a watershed to the total area of watershed (A)
  • A high value of the drainage density indicates a relatively high density of stream & thus a Rapid stream response
  • Ruggedness index is the ratio of the steepness of the slope. It is defined as the product of relative relief and drainage density. It is expression of texture & steepness. Ruggedness Number, Where, conversion constant (5,280 in case of mile- grid when relative relief is expressed in feet and drainage density in miles/sq. miles and 1000 when relative relief is expressed in kilometer/sq. kilometer) .
  • The topographic ruggedness index (TRI) was developed by Riley, et al. (1999) to express the amount of elevation difference between adjacent cells of a DEM. It calculates the difference in elevation values from a center cell and the eight cells immediately surrounding it. Then it squares each of the eight elevation difference values to make them all positive and averages the squares. The topographic ruggedness index is then derived by taking the square root of this average.

Bifurcation Ratio

Glacial Mass Balance

Glacial Mass Balance
  • Bifurcation ratios derived from streams ordered according to the Strahler system are not wholly independent of the stream orders from which they are computed and, within a basin, tend to decrease in a downstream direction. The bifurcation ratios computed from two successive constant orders of streams within equal-order basins increase with the area of the basin but tend to become constant where the basin reaches a certain size
  • Bifurcation ratio is defined as the ratio of the number of stream branches of a given order to the number of stream branches of the next higher order
  • According to Horton (1945, p. 290) , the bifurcation ratio varies from a minimum of 2 in “flat or rolling drainage basins” to 3 or 4 in “mountainous or highly dissected drainage basins” ; it is a parameter used in equations giving the number of streams in a basin.
  • Glacial Mass Balance: The mass balance of a glacier is the net change in its mass over a balance year or fixed year. If accumulation exceeds ablation for a given year, the mass balance is positive; if the reverse is true, the mass balance is negative.

Average Slope

Form Factor

Average Slope, . Where 636.6 is a constant derived for length in km from the original Wentworth՚s formula. Wentworth gave the following formula for computation of average slope from contour maps, using the British system.

  • This average slope map highlights the topographic expression, and inclination of slope on this basin area. It is a vital morphometric technique which helps to differentiate the surface configuration of different areas
  • Form factor (Ff) Horton expressed the shape of the basin as form factor (FO and defined it as a dimensionless ratio of the area (A) of the basin to the square of the basin length the form factor for each sub basin is measured and the minimum value is 0.1335 and the maximum value is 0.7721.

Hypsometric

Clinograph

Hypsometric Curve
  • Clinographic curves used to depict average slope between successive contour are considered as one of the best parameters for the determination of breaks in slope profiles.
  • Finsterwalder has postulated the following equation for the determination of average slope between two successive contours Average slope angle =
  • Where .
  • The hypsometric curve is the graph on the right-hand side of this page. This curve is typically used to demonstrate that the Earth has two types of crust, continental and oceanic. A hypsometric (or hypsographic) curve is one which is plotted to indicate the proportions of a given area of the earth՚s surface at various elevations or depths above or below a certain datum. The best-known example is for the entire earth՚s surface. Earth՚s surface is divided into two statistically distinct “levels” or steps, the continental platforms (about 100 meters above sea level) and the deep-sea floor (about 4700 meters below sea level) .

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