Drainage Basin Morphometry: Terminology for UPSC Geography Optional

Drainage basin morphometry is the measurement of a river basin’s network, shape and relief through standard ratios and laws. It converts a toposheet or digital elevation model into numbers that reveal the stage of erosion, flood behaviour and erosion risk. In the exam, every parameter needs its definition, formula, typical range and meaning, and a single formula written correctly marks out a prepared candidate.

Each entry gives the definition first, then the formula in plain text, the normal range and what the value tells a planner. Entries run from the basin unit to linear, areal and relief measures. UPSC asked about watershed delineation by stream basins and divides in 2021 and the role of slope, altitude and relief in 2022.

Quick Revision Table

Term	Meaning in one line	Example
Morphometry	Quantitative measurement of a basin’s linear, areal and relief properties	Morphometric ranking of Western Ghats sub-basins
Drainage basin, watershed & drainage divide	Area draining to one outlet, bounded by a divide	Western Ghats crest divide, Arabian Sea vs Bay of Bengal
Stream order	Rank of a stream segment in the tributary hierarchy	Mississippi, 10th order at its mouth
Bifurcation ratio	Number of streams of one order divided by those of the next higher order	3–5 in undisturbed basins
Law of stream numbers	Stream numbers fall in geometric series with rising order	Horton’s 1945 law
Law of stream lengths & length ratio	Mean lengths rise in geometric series with order	Length ratio 1.5–3.5
Law of stream slopes	Mean channel slope falls in geometric series with order	Himalayan first-order torrents vs trunk rivers
Law of basin areas & area ratio	Mean basin areas rise in geometric series with order	Area ratio 3–6
Law of allometric growth	Basin parts grow in constant proportion to the whole	Hack’s law, L = 1.4 A^0.6
Drainage density	Total stream length per unit basin area	High in the Chambal ravines
Stream frequency	Number of stream segments per unit area	Fs = 0.694 Dd² (Melton)
Drainage texture	Closeness of channel spacing	Fine texture on Siwalik clays and sandstones
Length of overland flow	Mean distance water flows over land before reaching a channel	Lg = 1/(2Dd)
Constant of channel maintenance	Area needed to sustain one unit length of channel	C = 1/Dd
Form factor	Basin area divided by the square of basin length	0.785 for a circular basin
Circularity ratio	Basin area relative to a circle of the same perimeter	Near 1 for compact basins
Elongation ratio	Diameter of the equal-area circle divided by basin length	0.6–1.0 in most basins
Hypsometric curve & integral	Distribution of basin area with height; volume still uneroded	Integral above 0.6 in youthful basins
Clinographic curve	Average slope between successive contours plotted against height	Breaks of slope on the Ranchi plateau
Absolute & relative relief	Height above sea level; local height range within a unit area	Himalaya vs Ganga plain
Relief ratio	Basin relief divided by basin length	Controls sediment yield
Dissection index	Relative relief divided by absolute relief	Close to 0 on plains, high in the Himalaya
Ruggedness number	Basin relief multiplied by drainage density	High in badlands
Average slope (Wentworth’s method)	Slope from contour crossings on a grid	tan θ = (N × CI)/636.6
Slope, altitude & relief (SAR)	The three linked relief properties controlling landscape development	Himalaya, Deccan and Ganga plain compared

The Basin as a Geomorphic Unit

Morphometry (linear, areal and relief aspects)

Morphometry is the measurement and mathematical analysis of the configuration of the Earth’s surface and of the shape and dimensions of its landforms; applied to a drainage basin, it quantifies the stream network (linear aspect), the basin’s size and shape (areal aspect) and its vertical dimension (relief aspect) as dimensionless ratios comparable between basins.

• Coined by / origin: Robert Elmer Horton, an American hydraulic engineer, set out the quantitative laws of drainage composition in 1932 and 1945; Arthur Newell Strahler and his students, among them Stanley Alfred Schumm and V. C. Miller, turned them into a system in the 1950s.
• Types: Linear aspect: stream order, stream number, bifurcation ratio, stream length and length ratio (sinuosity is a channel-form measure). Areal aspect: basin area, drainage density, stream frequency, texture and shape indices. Relief aspect: basin relief, relief ratio, hypsometry, relative relief, dissection and slope.
• Method: Survey of India toposheets at 1:50,000 were the traditional base; SRTM, ASTER and CartoDEM elevation models now yield networks and divides automatically in GIS.
• Significance: Ranks sub-basins for soil conservation, flood forecasting and check-dam siting (see morphometry for planning).
• Don’t confuse with: relief morphometry of erosion surfaces, such as altimetric frequency analysis and projected profiles, which is denudation chronology.

Drainage basin, watershed and drainage divide

A drainage basin is the whole area of land whose water drains to a single outlet through one stream network; its boundary is the drainage divide (water parting), the line of highest ground from which water flows away on either side. In American and Indian planning usage the basin is also called the watershed; in older British usage “watershed” meant the divide itself.

How stream basins and divides delineate a watershed

1. Fix the outlet (pour point): a gauging site, dam site or confluence.
2. Trace the stream network upstream to its finger-tip tributaries; the channels show which way each slope drains.
3. Draw the divide across contours at right angles, joining summits, spurs and saddles so that the line never crosses a channel, and close it back on the outlet.
4. In GIS, flow-direction and flow-accumulation grids computed from a digital elevation model assign every cell draining to the pour point to the watershed.

Key features

• Open system: Inputs are precipitation and tectonic uplift; outputs are evapotranspiration and water, sediment and solutes leaving through the mouth.
• Nested hierarchy: Every basin contains sub-basins of lower order, each with its own divide. The Watershed Atlas of India divides the country into 6 water resource regions and 35 basins, then 112 catchments, about 500 sub-catchments and more than 3,200 watersheds, which are further split into sub-watersheds and micro-watersheds.
• Divide behaviour: Sharp in youthful, high-relief terrain; broad and hard to fix on old, low plains; a divide migrates when one side erodes faster, leading to river capture.
• Examples: The Western Ghats crest separates rivers flowing to the Arabian Sea from the Godavari, Krishna and Kaveri flowing to the Bay of Bengal; the Amarkantak plateau parts the Narmada from the Son; the low ground near Ambala separates the Indus and Ganga systems; the North American Continental Divide separates Pacific from Atlantic and Gulf drainage.
• Significance: Micro-watersheds of a few hundred hectares are the treatment units of India’s watershed development programmes, whose planning is dealt with under applied geomorphology.
• Sketch: A contour map with channels, a dashed divide through summits and saddles, and the outlet marked; an inset shows a sub-watershed nested within the basin.

Linear Aspects: Stream Order and Horton’s Laws

Stream order (Horton, Strahler and Shreve magnitude)

Stream order is a measure of the position of a stream segment in the hierarchy of tributaries of a drainage network, assigned by fixed rules from the finger-tip channels downstream, so that the order of the trunk stream at the outlet describes the size and branching complexity of the whole basin.

• Horton’s scheme (1945): Unbranched finger-tip streams are first order; two first-order streams make a second-order stream, and so on. The trunk stream is then renumbered back to its source, which makes the scheme tedious and subjective.
• Strahler’s scheme (1952, 1957): Horton’s scheme without renumbering. The order rises only where two streams of equal order meet; a lower-order tributary does not raise it. This “segment method” is the standard today.
• Shreve magnitude (1966): Ronald L. Shreve gave each exterior link a magnitude of 1 and each downstream link the sum of the magnitudes joining it, so every tributary counts and magnitude approximates the number of sources.
• Examples: The Mississippi is a 10th-order river and the Amazon a 12th-order river at their mouths (Strahler).
• Significance: Order depends on map scale: the same basin gains an order when mapped from 1:25,000 instead of 1:250,000, so only basins mapped at the same scale can be compared.

Bifurcation ratio

The bifurcation ratio is the ratio of the number of stream segments of a given order to the number of segments of the next higher order in a drainage basin; a dimensionless measure of how many times the network branches, it indicates structural control and the shape of the flood hydrograph.

• Formula: Rb = Nu / Nu+1, where Nu is the number of segments of order u. The mean Rb of a basin is the average over all orders, often weighted by the number of streams involved.
• Typical range: 3–5 in basins where geology does not distort the network; about 2 on flat or rolling surfaces (Horton).
• Interpretation: Values well above 5 signal strong structural control, as in elongated basins between parallel ridges; low values mark compact, weakly controlled basins.
• Significance: Low Rb concentrates tributary inflow, so the flood peak is high and sharp; high Rb staggers inflow and flattens the peak.
• Examples: Studies of basins on the Chotanagpur plateau and the Vindhyan uplands report mean ratios of 3 to 5.

Law of stream numbers

The law of stream numbers, formulated by Robert Elmer Horton in 1945, states that the numbers of stream segments of successively lower orders in a basin form a geometric series, beginning with the single segment of the highest order and increasing according to a constant bifurcation ratio.

• Formula: Nu = Rb^(k − u), where k is the order of the trunk stream. With Rb = 4 and k = 5, the numbers of segments from fifth to first order are 1, 4, 16, 64 and 256.
• Test: Plotting log Nu against order gives a straight line with a negative slope.
• Key features: First-order streams are by far the most numerous and account for most of the total stream length in any basin.
• Criticism: Ronald L. Shreve (1966) showed that topologically random networks obey the law almost automatically, so fitting it proves little about process; departures from it are more informative than conformity.
• Significance: Used to estimate the total number of channels, and hence the channel-head sources of sediment, in a basin.

Law of stream lengths and length ratio

The law of stream lengths states that the mean lengths of stream segments of successively higher orders increase in a geometric series, beginning with the mean length of first-order segments and increasing according to a constant length ratio; it was stated by Robert Elmer Horton in 1945 for cumulative mean lengths.

• Formulas: Mean length Lu = ΣLu / Nu; length ratio RL = Lu / Lu−1; law Lu = L1 × RL^(u − 1).
• Typical range: RL mostly between 1.5 and 3.5.
• Key features: Total stream length falls with rising order while mean length rises; an irregular RL between orders reveals changes of slope, rock type or stage of development.
• Significance: Mean stream length indicates the time water takes to reach the outlet; long first-order streams usually mean permeable rocks or gentle slopes.

Law of stream slopes

The law of stream slopes (law of channel slopes) states that the mean channel gradient of stream segments decreases with increasing order in an inverse geometric series with a roughly constant slope ratio, so that finger-tip channels are the steepest and the trunk stream the gentlest in a basin; Robert Elmer Horton set it out in 1945.

• Formula: Su = S1 × Rs^−(u − 1), where Su is the mean slope of order u and Rs the slope ratio.
• Mechanism: Larger streams carry more discharge and can transport their load on gentler gradients, which links this law to the concave longitudinal profile.
• Examples: First-order torrents on Himalayan slopes fall steeply, while the trunk Ganga below Haridwar descends only about 300 m in more than 2,000 km.
• Significance: Irregular slope ratios pick out knickpoints, tectonic steps and lithological barriers.

Areal Aspects: Density, Texture and Shape

Law of basin areas and area ratio

The law of basin areas states that the mean areas of drainage basins of successively higher orders increase in a geometric series, beginning with the mean area of first-order basins and increasing according to a constant area ratio; Stanley Alfred Schumm stated it in 1956, extending Horton’s law of stream lengths to areas.

• Formulas: Mean area Au = ΣAu / Nu; area ratio Ra = Au / Au−1; law Au = A1 × Ra^(u − 1).
• Typical range: Ra mostly between 3 and 6.
• Key features: Basin area is cumulative, so each basin includes all its lower-order basins plus the interbasin slopes that drain straight into its own channel.
• Significance: Area is the variable most closely tied to discharge, so the law lets hydrologists estimate the area and flow of an ungauged basin of a given order.

Law of allometric growth

The law of allometric growth, borrowed from biology, states that the parts of a drainage basin, such as stream length and basin area, grow in constant proportion to the growth of the basin as a whole, so a plot of one against the other on logarithmic axes is a straight line; Michael J. Woldenberg applied it to Horton’s laws in 1966.

• Formula: log L = log a + b log A, a power function L = aA^b.
• Hack’s law: John Tilton Hack (1957) found the length of the main stream proportional to area to the power 0.6 (L = 1.4 A^0.6, in miles); because the exponent exceeds 0.5, large basins are relatively longer and narrower than small ones.
• Significance: Allometry means basins grow by headward extension of channels and backwearing of divides at a steady rate of proportion, provided rock, climate and cover are uniform.
• Examples: The relation holds across gully systems a few hundred square metres in size and river basins of thousands of square kilometres.

Drainage density

Drainage density is the total length of all stream channels in a drainage basin divided by the area of the basin, a measure of how closely a landscape is dissected by channels; Robert Elmer Horton introduced it in 1932 and 1945, and it is the most widely used single index of basin form.

• Formula: Dd = ΣL / A, in km per km².
• Controls: Rock permeability, rainfall intensity, vegetation cover, relief and time.
• Interpretation: High Dd means impermeable rock or soil, sparse vegetation, intense rain and high relief, giving rapid runoff, flashy floods and high sediment yield. Low Dd means permeable rock, dense forest and gentle relief, giving infiltration and baseflow. Badlands record values one to two orders of magnitude above forested uplands.
• Climate link: Dd tends to peak in semi-arid climates, where storms are intense but vegetation is thin, and falls in both deserts and humid forests.
• Examples: Very high in the Chambal ravines and on Siwalik clays; low on the sandy Thar and on cavernous karst.

Stream frequency

Stream frequency (drainage frequency) is the number of stream segments of all orders per unit area of a drainage basin, defined by Robert Elmer Horton in 1932; it expresses how many channels, rather than what length of channel, a basin supports, and it rises with runoff and relief.

• Formula: Fs = ΣN / A, in segments per km².
• Relation to drainage density: Mark A. Melton (1958) found Fs = 0.694 Dd², so the two indices carry much the same information.
• Interpretation: High frequency means impermeable surfaces, steep slopes and rapid runoff; low frequency means permeable rocks and gentle slopes.
• Method: Counted in grid squares of 1 km² to map spatial variation, shown by isopleths or choropleths.
• Examples: High on the dissected Siwalik foothills; low on the Deccan basalt plateau surfaces.

Drainage texture

Drainage texture is the relative closeness of spacing of channels in a drainage basin, described as fine, medium or coarse; it expresses the combined effect of drainage density and stream frequency and reflects rock resistance, infiltration capacity, rainfall and relief.

• Formula: Horton’s texture ratio T = Nu / P, the number of streams (commonly first-order streams, or all segments) divided by the basin perimeter.
• Classes: A 1950 grading scheme calls values below 2 very coarse, 2–4 coarse, 4–6 moderate, 6–8 fine and above 8 very fine.
• Interpretation: Fine texture means weak, impermeable rock and thin vegetation; coarse texture means resistant, permeable rock such as sandstone, granite or basalt with thick soil.
• Examples: Fine texture on clay badlands and Siwalik mudstones; coarse texture on Vindhyan sandstones and granite gneiss plateaus.

Length of overland flow

The length of overland flow is the mean horizontal distance that rainwater travels over the ground surface before it enters a defined stream channel; Robert Elmer Horton regarded it as one of the most important variables affecting the hydrological and physiographic development of a basin.

• Formula: Lg = 1 / (2Dd). A basin with Dd = 2 km per km² has Lg = 0.25 km.
• Interpretation: Short Lg means closely spaced channels, quick runoff and flashy floods; long Lg means slower runoff and more time for infiltration and sheet erosion.
• Stage link: Lg is longest in early youth, shortest in late youth and early maturity when channels are most numerous, and lengthens again in old age.
• Significance: Sets the downslope length over which sheetwash and rills operate, and so the spacing of contour bunds and terraces.

Constant of channel maintenance

The constant of channel maintenance is the area of basin surface required to sustain one unit length of stream channel, the reciprocal of drainage density; Stanley Alfred Schumm introduced it in 1956 in his study of badlands at Perth Amboy, New Jersey.

• Formula: C = 1 / Dd, in km² per km.
• Interpretation: High C (low Dd) means permeable rock, dense vegetation or low relief, where a large area is needed to generate enough runoff to keep a channel open; low C means impermeable, sparsely covered, easily eroded surfaces.
• Significance: C expresses a threshold: channels form only where the contributing area exceeds it, which is why channel heads advance when forest is cleared.
• Examples: Very low on clay badlands; high on forested laterite plateaus of the Western Ghats.

Form factor

The form factor is the ratio of basin area to the square of basin length, introduced by Robert Elmer Horton in 1932 as the simplest measure of basin shape; it compares the basin with a square or circle and indicates how quickly floodwater from its tributaries reaches the outlet.

• Formula: Ff = A / Lb², where Lb is the basin length from the mouth to the farthest point on the divide.
• Range: Near 0 for very elongated basins; 0.785 (π/4) for a perfectly circular basin whose length equals its diameter.
• Interpretation: High Ff means a compact basin with a high, short flood peak; low Ff means an elongated basin with a lower, longer flood peak that is easier to manage.
• Examples: Long, narrow basins of Himalayan longitudinal rivers such as the upper Sutlej have low values; small basins on the Chotanagpur plateau are more compact.

Circularity ratio

The circularity ratio is the ratio of the area of a drainage basin to the area of a circle having the same perimeter as the basin, proposed by V. C. Miller in 1953; it measures how compact the basin is and is sensitive to indentation of the divide.

• Formula: Rc = 4πA / P², where P is the basin perimeter.
• Range: From near 0 for a thread-like basin to 1 for a perfect circle.
• Interpretation: High values mean compact basins with short travel times and sharp flood peaks, often on uniform rock; low values mean elongated or deeply indented basins, often controlled by structure, with long lag times.
• Controls: Rock type, structure, stream length and frequency, relief, slope and stage of development; Miller worked on basins in the Clinch Mountain area of Virginia and Tennessee.

Elongation ratio

The elongation ratio is the ratio of the diameter of a circle having the same area as the drainage basin to the maximum length of the basin, introduced by Stanley Alfred Schumm in 1956; it is the preferred shape index because it relates basin shape directly to relief and slope.

• Formula: Re = (2 / Lb) × √(A / π), equivalently 1.128 √A / Lb.
• Range: 0 to 1; most natural basins fall between 0.6 and 1.0.
• Interpretation: Values near 1.0 mean low relief and a circular basin; 0.6–0.8 mean high relief and steep ground slopes; below 0.6 mean strongly elongated, often structurally controlled basins.
• Commonly used classes: Circular above 0.9, oval 0.8–0.9, less elongated 0.7–0.8, elongated 0.5–0.7 and more elongated below 0.5.
• Significance: Elongated basins yield lower flood peaks and are favoured for surface storage; circular basins need stronger flood protection at the outlet.

Relief Aspects

Hypsometric curve and hypsometric integral

The hypsometric curve shows how the area of a drainage basin is distributed with height, plotting relative height (h/H) against relative area above that height (a/A); the hypsometric integral is the area under this curve, expressing the proportion of the original basin volume still unconsumed by erosion. Arthur Newell Strahler introduced the percentage curve in 1952.

• Formula: HI is measured under the curve or estimated as the elevation–relief ratio, HI = (Hmean − Hmin) / (Hmax − Hmin), which was shown in 1971 to be equivalent.
• Stage interpretation (Strahler): HI above 0.6, a convex-upward curve, marks the youthful or inequilibrium stage; 0.35–0.6, an S-shaped curve, the mature or equilibrium stage; below 0.35, a concave curve, the old or monadnock phase. Once the monadnocks are removed the integral rises back towards 0.4–0.6.
• Recent view: HI is now read mainly as a measure of uplift against erosion; it is scale-dependent and sensitive to rock resistance, so high values in active Himalayan frontal basins may record tectonics rather than youth.
• Significance: Compares the degree of dissection of basins of different sizes, and helps identify erosion surfaces through flats in the curve.
• Sketch: Three curves on axes of h/H and a/A: convex (youthful), S-shaped (mature) and concave (old).

Clinographic curve

A clinographic curve is a graph of the average slope between successive contours plotted against height, used to display the slope characteristics of a basin or relief unit; unlike area–height and hypsometric curves, it reveals breaks of slope, benches and scarps. Sebastian Finsterwalder devised it in 1890.

• Method: Average slope between two contours, tan θ = (CI × Lm) / A, where CI is the contour interval, Lm the mean length of the two contours and A the area between them; Arthur Newell Strahler’s mean-slope curve (1952) uses the mean horizontal width between contours instead.
• Key features: Steepening segments mark scarps and valley-side free faces; flattenings mark benches and possible planation levels.
• Significance: Used with superimposed profiles and altimetric analysis in denudation chronology and in slope-based land capability mapping.
• Examples: Curves for the Ranchi plateau show the steep scarp between its upper surface and the lower Chotanagpur surface.

Absolute and relative relief

Absolute relief is the height of a point or area above mean sea level, and relative relief (local relief, amplitude of available relief) is the difference between the highest and lowest points within a unit area such as a grid square; together they express the potential energy available to erosion and the degree of dissection of terrain.

• Coined by: Guy-Harold Smith introduced grid-based relative relief mapping in 1935 in a study of Ohio.
• Method: Relative relief = Hmax − Hmin in each grid square of 1 km² or a minute of latitude and longitude; values are grouped into classes and mapped as isopleths.
• Interpretation: High relative relief means deep dissection, steep slopes, active downcutting and high landslide risk; low relative relief marks plains, plateau tops and peneplains.
• Examples: Relative relief of hundreds to over a thousand metres per grid square in the Higher Himalaya; a few metres in the Ganga plain; moderate values on the Deccan plateau, whose absolute relief is high.
• Don’t confuse with: relief ratio, which relates basin relief to basin length.

Relief ratio

The relief ratio is the ratio of the total relief of a drainage basin, the difference between its highest and lowest points, to the longest dimension of the basin parallel to the main stream; introduced by Stanley Alfred Schumm in 1956, it measures the overall steepness of a basin independent of its size.

• Formula: Rh = H / Lb, dimensionless when both are in the same units.
• Interpretation: High Rh means steep basin slopes, fast runoff and high erosion; low Rh means gentle, slowly draining basins.
• Significance: Schumm showed that sediment loss from small basins rises sharply with relief ratio, so it is a quick proxy for sediment yield and reservoir silting.
• Examples: Short, steep west-flowing Western Ghats rivers have much higher ratios than the long east-flowing Godavari and Krishna.

Dissection index

The dissection index is the ratio of relative relief to absolute relief in a unit area, expressing what proportion of the height available above base level has actually been cut away by erosion; the simple form was proposed by Dov Nir in 1957, replacing laborious area-based methods.

• Formula: DI = Rr / Ra, where Rr is relative relief and Ra absolute relief in the same grid square.
• Range: 0, for an undissected flat surface, to 1, reached only on a vertical cliff descending to sea level.
• Interpretation: High values mean deep, vigorous dissection by rejuvenated or youthful streams; low values mean plains, plateau tops or old-stage surfaces.
• Examples: High on the Himalayan and Western Ghats escarpments; low on the Malwa and Karnataka plateau tops, which stand high but are little dissected.

Ruggedness number

The ruggedness number is the product of basin relief and drainage density, a dimensionless index proposed by Arthur Newell Strahler in 1958 that combines slope steepness with slope length; a basin is rugged when it is both high in relief and closely dissected by channels.

• Formula: Rn = H × Dd, with H in km and Dd in km per km².
• Interpretation: High values mean steep, closely spaced and short slopes, prone to rapid runoff, gullying and landslides; low values mean gentle, widely spaced slopes.
• Key features: If Dd rises while relief stays constant, slopes must steepen; if relief rises while Dd stays constant, slopes also steepen.
• Examples: Very high in the Siwalik badlands and the Chambal ravines; low on the Ganga plain and the Chhattisgarh basin.
• Significance: Used to rank sub-watersheds for erosion-control priority.

Average slope (Wentworth’s method)

Average slope is the mean angle of ground inclination over a unit area, and Chester Keeler Wentworth’s method (1930) derives it from a contour map by counting contour crossings along grid lines, giving a rapid estimate that avoids measuring every slope facet.

• Formula: tan θ = (N × CI) / 636.6 in metric units, where N is the average number of contour crossings per km of grid line and CI the contour interval in metres; the constant is 3,361 when N is per mile and CI in feet.
• Method: Count crossings along the sides of each grid square, often along diagonals too, average them, compute θ, classify and map as isopleths.
• Limitation: Averages mask cliffs and breaks of slope, which is why clinographic curves and slope maps from elevation models complement it.
• Significance: Slope classes guide land capability: gentle slopes suit cultivation, moderate slopes need bunding or terracing, and steep slopes should be kept under forest.
• Examples: Very gentle slopes on the Ganga plain; steep slopes on the scarps of the Rewa and Ranchi plateaus.

Slope, altitude and relief (SAR)

Slope, altitude and relief (SAR) are the three interlinked relief properties of terrain: altitude (absolute relief) is height above sea level, relief (relative relief) is the local range of height, and slope is the rate of change of height with horizontal distance; together they set the energy available for denudation and the processes that shape a landscape.

Role of each

• Altitude: Sets potential energy relative to base level and, through the fall of temperature with height, the climate. Above the snowline glacial and periglacial processes replace fluvial ones, so altitude zones process domains.
• Relative relief: Measures the energy actually available locally. Frank Ahnert (1970) found that denudation rates in mid-latitude basins rise roughly in proportion to mean local relief, so high relief means fast erosion and high sediment yield.
• Slope: Converts that energy into process: gentle slopes favour creep, wash and infiltration; steep slopes favour landslides, rockfall and rapid runoff. Later work showed that erosion rises steeply, not linearly, once hillslopes approach threshold angles of about 30°.

Interplay in landscape development

• Linked change: Uplift raises altitude; rivers incise and raise relative relief; valley sides steepen; mass movement then lowers the divides. In the Davisian model relative relief rises in youth, peaks in early maturity and declines in old age as slopes flatten (see stages of the cycle).
• Feedback: High relief and steep slopes accelerate erosion, which reduces relief unless uplift continues; in active ranges uplift and erosion approach a steady state.
• Indian examples: The Himalaya combines high altitude, very high relative relief and steep slopes, giving rapid denudation, deep gorges and frequent landslides; the Deccan plateau has high altitude but low relative relief and gentle slopes, a mature surface; the Western Ghats escarpment has moderate altitude but high relief at the scarp; the Ganga plain is low on all three and is a zone of deposition.
• Application: SAR maps underpin terrain classification, hypsometric analysis of stage, landslide hazard zonation and land-use planning.
• Sketch: A cross-section from the Ganga plain through the Siwaliks to the Higher Himalaya, labelled with altitude, relative relief and slope for each zone.

PYQs Built on These Terms

• Discuss the role of Slope, Altitude and Relief (SAR) in landscape development. (2022)
• Stream basins and drainage divides are important components to delineate a watershed area. Explain. (2021)
• How is drainage pattern determined by the water divide? (Paper II, 2014)

Frequently Asked Questions

What is the difference between a watershed and a drainage basin?

In American and Indian planning usage they mean the same thing: the whole area draining to one outlet. In older British usage, however, “watershed” meant the dividing line between two basins, now called the drainage divide. In Indian watershed programmes a watershed is usually a small drainage basin, often a micro-watershed of a few hundred hectares.

What is the normal value of the bifurcation ratio?

Between 3 and 5 in basins where geological structure does not distort the network, and about 2 on flat or rolling surfaces. A value well above 5 points to strong structural control, usually an elongated basin between parallel ridges. Low ratios mean tributaries join close together, which produces a sharper, higher flood peak at the outlet.

What does high drainage density indicate?

High drainage density indicates impermeable rock or soil, sparse vegetation, intense rainfall and high relief. Water runs off quickly through many closely spaced channels, so floods are flashy and sediment yield is high. Low density indicates permeable rock, dense forest cover or gentle relief, with more infiltration, steadier baseflow and slower flood response.

How does the hypsometric integral show the stage of a basin?

It measures the proportion of the basin’s volume still standing above its lowest point. Arthur Newell Strahler read values above 0.6 as youthful, 0.35 to 0.6 as mature and below 0.35 as old, the last applying when a few monadnocks survive above a lowered surface. Today it is treated as an index of uplift against erosion, not of age alone.

How is Strahler’s stream order different from Shreve’s magnitude?

Strahler’s order rises only when two streams of the same order meet, so small tributaries entering a large river do not change its order. Shreve’s magnitude adds up all the first-order sources upstream, so every tributary increases the value. Strahler’s scheme is simpler and suits Horton’s laws; Shreve’s tracks discharge and network size more closely.

Why is the drainage basin the ideal unit for geomorphic study?

Because it is a clearly bounded, open system: water and sediment enter as precipitation and weathered rock and leave through a single outlet, where they can be measured. Basins nest into larger basins, so studies can move between scales. Processes, forms and budgets within one divide can be linked directly, which political or administrative units cannot offer.