Drainage Patterns and River Basin Analysis

23 questions

Question 1Question

Match each drainage basin morphometric property listed on the left with its corresponding geomorphic or hydrological significance on the right.

Click a left item, then click its matching right item

Items

High Drainage Density
High Bifurcation Ratio
High Form Factor
Low Stream Frequency

Matches

Show answer & explanation

Answer

High Drainage Density matches with highly impermeable surface rocks, steep relief, and fine drainage texture; High Bifurcation Ratio matches with strong structural geological control; High Form Factor matches with a circular basin shape leading to concentrated runoff and sharp peak floods; Low Stream Frequency matches with permeable underlying rock, high infiltration capacity, and coarse drainage texture.
High Drainage Density matches impermeable rocks and steep relief because runoff forms numerous channels. High Bifurcation Ratio indicates structural geological controls such as faulting. High Form Factor denotes a circular basin producing concentrated tributary runoff and sharp flood peaks. Low Stream Frequency corresponds to permeable rock where infiltration reduces stream channel generation.

Step-by-Step Solution

1
Examine the physical controls on Drainage Density (Dd=LAD_d = \frac{\sum L}{A}) and Stream Frequency (Fs=NAF_s = \frac{N}{A}).
High drainage density occurs when surface runoff is high and infiltration is low due to impermeable rock and steep slopes. Conversely, low stream frequency indicates high surface permeability where water infiltrates underground rather than forming channels.
Understanding surface runoff dynamics and bedrock permeability.
2
Analyze the geomorphic implication of the Bifurcation Ratio (Rb=NuNu+1R_b = \frac{N_u}{N_{u+1}}).
While values between 3 and 5 are typical in hydrogeologically uniform basins, values significantly higher than 5 reflect tectonic or structural geological distortion such as faulting.
Identifying structural controls in river network organization.
3
Relate Basin Form Factor (Ff=AL2F_f = \frac{A}{L^2}) to basin geometry and flood hydrographs.
Form factors approaching 1 describe circular basins where tributaries feed into the main trunk stream at similar travel times, yielding a sharp, high peak discharge.
Evaluating how basin shape governs runoff timing and flood risk.

Key Concept

Quantitative Morphometric Analysis of River Basins
Question 2Question

In a morphometric survey of a river basin using Strahler's stream ordering system, a geographer records 2424 first-order stream segments, 66 second-order stream segments, 22 third-order stream segments, and 11 fourth-order main stream channel. What is the bifurcation ratio (RbR_b) between the first-order and second-order stream segments?

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Answer: 4.04.0

Answer

The bifurcation ratio between the first-order and second-order streams is 4.04.0.
The bifurcation ratio (RbR_b) measures the degree of branching within a drainage basin and is computed by dividing the number of stream segments of a given order (N1=24N_1 = 24) by the number of stream segments of the next higher order (N2=6N_2 = 6). Dividing 2424 by 66 gives an exact ratio of 4.04.0.

Step-by-Step Solution

1
Identify the given stream segment counts for the relevant orders
First-order stream count (N1N_1) = 2424; Second-order stream count (N2N_2) = 66.
Bifurcation ratio calculation requires segment count data for adjacent stream orders.
2
Apply Strahler's bifurcation ratio formula
Rb=NuNu+1=N1N2=246=4.0R_b = \frac{N_u}{N_{u+1}} = \frac{N_1}{N_2} = \frac{24}{6} = 4.0.
The bifurcation ratio (RbR_b) is defined as the number of stream segments of a given order (NuN_u) divided by the number of stream segments of the next higher order (Nu+1N_{u+1}).

Key Concept

Bifurcation Ratio in Basin Morphometry
Estimated Time:1m 0s
Question 3Question

A morphometric study of a river basin reveals a total drainage area of 150 km2150\text{ km}^2. Quantitative stream analysis using Strahler's method identifies 1818 first-order streams, 77 second-order streams, 44 third-order streams, and 11 fourth-order stream. What is the stream frequency (FsF_s) of this river basin in streams per km2\text{km}^2?

Show answer & explanation

Answer: 0.2

Answer

The stream frequency of the river basin is 0.2 streams/km20.2\text{ streams/km}^2.
Stream frequency (FsF_s) is defined as the total number of stream segments of all orders (NN) per unit area (AA) of a drainage basin, expressed as Fs=NAF_s = \frac{N}{A}. Summing all orders yields N=18+7+4+1=30 streamsN = 18 + 7 + 4 + 1 = 30\text{ streams}. Dividing 3030 streams by the basin area of 150 km2150\text{ km}^2 gives exactly 0.2 streams/km20.2\text{ streams/km}^2.

Step-by-Step Solution

1
Calculate total number of stream segments (NN) in the basin
N=18+7+4+1=30N = 18 + 7 + 4 + 1 = 30
Stream frequency considers the total count of all stream channels of all orders within the basin.
2
Apply the stream frequency formula Fs=NAF_s = \frac{N}{A} using the total basin area A=150 km2A = 150\text{ km}^2
Fs=30150=0.2 streams/km2F_s = \frac{30}{150} = 0.2\text{ streams/km}^2
Stream frequency measures the number of stream segments per unit basin area.

Key Concept

Stream Frequency (FsF_s)
Question 4Question

A topographic map extract reveals a drainage network where major streams flow parallel to each other along elongated valleys, while short tributary streams join them at approximately right angles across alternating belts of resistant and non-resistant rock strata. Which drainage pattern is depicted, and what geological structure primarily controls its development?

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Answer: Trellis pattern, controlled by folded sedimentary rocks with alternating hard and soft strata

Answer

Trellis pattern, controlled by folded sedimentary rocks with alternating hard and soft strata
The trellis drainage pattern is characterized by parallel main channels flowing along soft-rock valleys formed by folded rock strata (synclines/anticlines), with short tributary streams cutting across resistant ridges to join the main channels at right angles.

Step-by-Step Solution

1
Analyze the spatial arrangement of the main streams and tributaries described in the scenario
Main channels are aligned in parallel valleys, and smaller tributaries join them at right angles across alternating rock belts.
Geological controls such as differential erosion of inclined or folded strata determine the pattern of river networks.
2
Match the geometric characteristics to the appropriate drainage pattern class
Parallel main streams with right-angled tributary junctions define a trellis drainage pattern.
Trellis drainage typically forms in ridge-and-valley landscapes produced by folded rock structures.

Key Concept

Trellis Drainage Pattern and Geological Structure
Question 5Question

On a topographic map extract, V-shaped contour lines crossing a river valley point towards the north-east. In which direction is the river flowing?

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Answer: South-west

Answer

The river flows towards the south-west.
On topographic maps, V-shaped contours crossing a stream valley point upstream (toward higher ground). Because the contour V's point north-east, the source of the river is to the north-east, meaning the river flows downstream toward the south-west.

Step-by-Step Solution

1
Identify the rule for contour line V-shapes in valley landforms
V-shaped contour lines point upstream towards higher land (the river source)
Water flows from high elevation to low elevation, so the apex of the 'V' points up the river valley
2
Determine the downstream flow direction from the given upstream contour orientation
Since the V-shapes point north-east (upstream), the downstream flow direction is the exact opposite
The opposite cardinal direction of north-east is south-west

Key Concept

Interpretation of V-shaped contour lines for river flow direction
Estimated Time:45s
Question 6Question

A morphometric quantitative analysis of a river basin using Strahler's stream ordering method yields the following stream segment counts:
- N1N_1 (1st-order streams) = 4040
- N2N_2 (2nd-order streams) = 1010
- N3N_3 (3rd-order streams) = 44
- N4N_4 (4th-order streams) = 11

Based on these morphometric data, what is the mean bifurcation ratio (RbR_b) of this drainage basin?

Show answer & explanation

Answer: 3.5

Answer

The mean bifurcation ratio (RbR_b) of the drainage basin is 3.5.
The mean bifurcation ratio (RbR_b) is obtained by computing the ratio of stream segments between successive orders: N1/N2=4.0N_1/N_2 = 4.0, N2/N3=2.5N_2/N_3 = 2.5, and N3/N4=4.0N_3/N_4 = 4.0. Averaging these three values gives (4.0+2.5+4.0)/3=3.5(4.0 + 2.5 + 4.0) / 3 = 3.5.

Step-by-Step Solution

1
Calculate the individual bifurcation ratios (RbR_b) between consecutive stream orders using the formula Rb=NuNu+1R_b = \frac{N_u}{N_{u+1}}.
Rb(12)=4010=4.0R_{b(1-2)} = \frac{40}{10} = 4.0, Rb(23)=104=2.5R_{b(2-3)} = \frac{10}{4} = 2.5, and Rb(34)=41=4.0R_{b(3-4)} = \frac{4}{1} = 4.0.
Bifurcation ratio measures the ratio of the number of stream segments of a given order to the number of segments of the next higher order.
2
Sum the calculated individual bifurcation ratios.
Sum =4.0+2.5+4.0=10.5= 4.0 + 2.5 + 4.0 = 10.5.
To find the average across all order transitions, the sum of all calculated ratios must first be determined.
3
Divide the total sum by the number of order transitions (k=3k = 3).
Mean Rb=10.53=3.5R_b = \frac{10.5}{3} = 3.5.
There are 3 transitions between the 4 stream orders, so dividing the sum by 3 gives the arithmetic mean bifurcation ratio.

Key Concept

Bifurcation Ratio and Stream Order Analysis in River Basins
Question 7Question

A topographical map extract drawn at a scale of 1:50,0001:50,000 delineates a drainage basin. The total area of the basin measured on the map is 160 cm2160\text{ cm}^2. Morphometric analysis reveals the following total stream segment lengths measured directly from the map across all stream orders:
- 1st-order stream segments: 48 cm48\text{ cm}
- 2nd-order stream segments: 20 cm20\text{ cm}
- 3rd-order stream segments: 12 cm12\text{ cm}
- 4th-order stream segments: 8 cm8\text{ cm}

Calculate the drainage density of the river basin in km/km2\text{km/km}^2.

Show answer & explanation

Answer: 1.1

Answer

The drainage density of the river basin is 1.1 km/km21.1\text{ km/km}^2.
Drainage density (DD) measures the ratio of total stream channel length to the total drainage basin area (D=LAD = \frac{\sum L}{A}). Converting map measurements using the scale 1:50,0001:50,000 (1 cm=0.5 km1\text{ cm} = 0.5\text{ km}), the total ground stream length is 88 cm×0.5 km/cm=44 km88\text{ cm} \times 0.5\text{ km/cm} = 44\text{ km}, and the actual ground area is 160 cm2×(0.5)2=40 km2160\text{ cm}^2 \times (0.5)^2 = 40\text{ km}^2. Dividing ground length by area produces 1.1 km/km21.1\text{ km/km}^2.

Step-by-Step Solution

1
Determine linear ground scale from map scale
1 cm on map=0.5 km on ground1\text{ cm on map} = 0.5\text{ km on ground}
Scale 1:50,0001:50,000 means 1 cm=50,000 cm=500 m=0.5 km1\text{ cm} = 50,000\text{ cm} = 500\text{ m} = 0.5\text{ km}.
2
Calculate ground area of the basin
Basin Area A=40 km2A = 40\text{ km}^2
Area conversion requires squaring the linear scale factor: 160 cm2×(0.5 km/cm)2=160×0.25=40 km2160\text{ cm}^2 \times (0.5\text{ km/cm})^2 = 160 \times 0.25 = 40\text{ km}^2.
3
Calculate total actual stream length in the basin
Total Stream Length L=44 km\sum L = 44\text{ km}
Total map stream length =48+20+12+8=88 cm= 48 + 20 + 12 + 8 = 88\text{ cm}. Ground length =88 cm×0.5 km/cm=44 km= 88\text{ cm} \times 0.5\text{ km/cm} = 44\text{ km}.
4
Compute Drainage Density (DD)
D=1.1 km/km2D = 1.1\text{ km/km}^2
Drainage density is the total channel length divided by total basin area: D=LA=44 km40 km2=1.1 km/km2D = \frac{\sum L}{A} = \frac{44\text{ km}}{40\text{ km}^2} = 1.1\text{ km/km}^2.

Key Concept

Drainage Density Calculation from Topographical Maps
Question 8Question

Match each drainage pattern type listed on the left with its primary underlying geological control or landform characteristic on the right.

Click a left item, then click its matching right item

Items

Dendritic pattern
Trellis pattern
Radial pattern
Centripetal pattern

Matches

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Answer

Dendritic pattern matches uniformly resistant rock strata; Trellis pattern matches alternating bands of hard and soft rocks with right-angle tributaries; Radial pattern matches streams flowing outward from a central dome; Centripetal pattern matches streams converging inward toward a central basin.
Dendritic drainage develops on uniform rock resistance. Trellis drainage forms where alternating hard and soft rocks cause tributaries to join main streams at right angles. Radial drainage flows outward from a dome peak, and centripetal drainage flows inward toward a central basin.

Step-by-Step Solution

1
Identify structural control for branching patterns
Dendritic pattern pairs with uniformly resistant rock strata due to uniform erosion rates.
Tree-like dendritic networks only form where rock resistance is homogeneous.
2
Identify structural control for rectangular/parallel tributary layouts
Trellis pattern pairs with alternating bands of hard and soft rocks.
Tributaries carve valleys along softer strata and meet main streams near 90-degree angles.
3
Differentiate outward vs inward flow directions
Radial matches outward flow from elevated summits, while centripetal matches inward flow into depressed basins.
Topographic highs shed water in all directions (radial), while topographic depressions collect water (centripetal).

Key Concept

Geological Controls on Drainage Patterns
Question 9Question

Two adjacent drainage basins, Basin A and Basin B, experience identical climatic conditions and precipitation levels. A geomorphic survey records the following morphometric data:

Drainage BasinTotal Channel Length (LL)Total Basin Area (AA)
Basin A180 km180\text{ km}60 km260\text{ km}^2
Basin B50 km50\text{ km}50 km250\text{ km}^2

Based on the drainage density of each basin, which of the following statements accurately compares their hydrological and geological characteristics?

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Answer: Basin A has a higher drainage density (3.0 km/km23.0\text{ km/km}^2), indicating predominantly impermeable surface rocks, higher surface runoff, and a faster flood response compared to Basin B.

Answer

Basin A has a higher drainage density (3.0 km/km23.0\text{ km/km}^2), indicating predominantly impermeable surface rocks, higher surface runoff, and a faster flood response compared to Basin B.
The option identifying Basin A as having a higher drainage density (3.0 km/km23.0\text{ km/km}^2) is correct because DdD_d is calculated by dividing total stream length (180 km180\text{ km}) by total basin area (60 km260\text{ km}^2). High values of drainage density reflect dense channel development, typical of impermeable rock strata where water cannot easily infiltrate, resulting in high surface runoff velocity.

Step-by-Step Solution

1
Calculate the drainage density (DdD_d) for Basin A using the formula Dd=LAD_d = \frac{L}{A}.
Dd(Basin A)=180 km60 km2=3.0 km/km2D_d(\text{Basin A}) = \frac{180\text{ km}}{60\text{ km}^2} = 3.0\text{ km/km}^2.
Drainage density measures the total channel length per unit basin area.
2
Calculate the drainage density (DdD_d) for Basin B.
Dd(Basin B)=50 km50 km2=1.0 km/km2D_d(\text{Basin B}) = \frac{50\text{ km}}{50\text{ km}^2} = 1.0\text{ km/km}^2.
Provides the baseline comparison value for Basin B.
3
Interpret the geomorphic and hydrological implications of high vs. low drainage density.
Basin A (3.0 km/km2>1.0 km/km23.0\text{ km/km}^2 > 1.0\text{ km/km}^2) has a higher stream network concentration, which signifies impermeable bedrock/clay soils, reduced infiltration, and rapid surface runoff leading to intense flood peaks.
High drainage density correlates with surface impermeability, sparse vegetation, and efficient surface runoff networks.

Key Concept

Drainage Density (DdD_d) and Basin Hydrology
Estimated Time:2m 0s
Question 10Question

A topographical map extract shows a series of streams radiating outward from a central dome, with subsequent tributaries capturing flow along concentric ring valleys formed on eroded sedimentary layers. Which drainage pattern is illustrated by this stream arrangement?

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Answer: Annular pattern

Answer

Annular drainage pattern
Annular drainage develops on maturely dissected domes where alternating concentric bands of hard and soft rock are exposed. Main streams flow outward from the dome, while tributary streams carve circular, ring-like channels along the softer rock belts.

Step-by-Step Solution

1
Analyze the structural landform and elevation description in the stem.
Identified a dissected dome structure with elevated center and concentric belts of contrasting rock hardness.
Geological structure dictates the structural control governing drainage network development.
2
Evaluate stream geometry and flow direction.
Streams flow outwards from the high central region, while tributary streams follow curved concentric bands of weaker rock.
Differential erosion creates circular valleys where tributaries flow along rings around the central dome.
3
Match the observed stream geometry to standard genetic drainage patterns.
The ring-like or circular pattern around a central upland is classified as annular drainage.
Annular pattern is defined by concentric ring-like stream paths formed on breached domes or maturely dissected structural domes.

Key Concept

Annular Drainage Pattern and Structural Controls
Estimated Time:1m 15s
Question 11Question

Drainage networks develop in response to specific rock structures and surface slopes. How do the following drainage pattern types match with their primary geological controls?

Click a left item, then click its matching right item

Items

Dendritic pattern
Radial pattern
Trellis pattern
Centripetal pattern

Matches

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Answer

Dendritic pattern pairs with uniform lithology and flat-lying strata; Radial pattern pairs with volcanic domes or central peaks; Trellis pattern pairs with alternating bands of hard and soft folded rocks; Centripetal pattern pairs with inward-sloping interior basins.
Each drainage pattern reflects specific surface geology: dendritic networks form on uniform rocks with equal erosion resistance, radial networks diverge outward from central domes, trellis networks align with alternating bands of folded rocks, and centripetal networks converge inward toward central basins.

Step-by-Step Solution

1
Identify the characteristic geological setting for a dendritic pattern
Dendritic drainage exhibits random branching on homogeneous rock types.
Equal resistance of underlying rock allows streams to flow in any direction without structural restriction.
2
Identify the structural control of a radial pattern
Radial drainage radiates outward from elevated peaks or domes.
High central relief forces water to flow downhill in all outward directions.
3
Identify the structural control of a trellis pattern
Trellis drainage follows alternating weak and resistant folded strata.
Main streams carve long parallel valleys in soft strata while short tributaries join at right angles across hard ridges.
4
Identify the structural control of a centripetal pattern
Centripetal drainage converges inward into a central depression.
Topography slopes downward toward a common interior low point.

Key Concept

Geological Controls on Drainage Patterns
Question 12Question

Match each specified drainage pattern with its underlying geological control or characteristic landform surface.

Click a left item, then click its matching right item

Items

Trellis drainage pattern
Rectangular drainage pattern
Radial drainage pattern
Dendritic drainage pattern

Matches

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Answer

Trellis drainage pattern matches with folded strata containing alternating hard and soft rocks; Rectangular pattern matches with faulted and jointed bedrock; Radial pattern matches with outward flow from a central dome or volcano; Dendritic pattern matches with tree-like branching on uniform rock resistance.
Each pattern corresponds directly to its bedrock control: Trellis requires alternating soft/hard folded belts, Rectangular follows structural joints and faults, Radial descends from a central highland dome or cone, and Dendritic branches randomly over uniform lithology.

Step-by-Step Solution

1
Analyze Trellis Drainage Pattern
Trellis drainage features long main streams parallel to strike valleys with short tributaries entering at right angles, characteristic of folded, tilted strata.
Differential erosion along parallel belts of soft and hard rock forces tributaries into strike valleys.
2
Analyze Rectangular Drainage Pattern
Rectangular drainage is characterized by right-angled bends in main streams and tributaries along lineaments.
Bedrock fractures, joint systems, and faults direct the line of weakest resistance for stream incision.
3
Analyze Radial Drainage Pattern
Radial drainage streams flow in all cardinal directions downward from a central peak.
Topographic highs like domes and volcanic summits direct water outward along radial slopes.
4
Analyze Dendritic Drainage Pattern
Dendritic drainage exhibits a random branching tree-like structure without structural alignment.
Uniform rock resistance (lithology) allows equal erosion in all directions.

Key Concept

Geological Controls on Drainage Network Patterns
Question 13Question

Match each river basin morphometric parameter with its corresponding quantitative definition and hydrological significance.

Click a left item, then click its matching right item

Items

Bifurcation Ratio (RbR_b)
Drainage Density (DdD_d)
Stream Frequency (FsF_s)
Form Factor (RfR_f)

Matches

Show answer & explanation

Answer

Bifurcation Ratio (RbR_b) pairs with the ratio of stream numbers between successive orders (Nu/Nu+1N_u / N_{u+1}). Drainage Density (DdD_d) pairs with the total stream length divided by basin area. Stream Frequency (FsF_s) pairs with the total number of stream segments per unit basin area. Form Factor (RfR_f) pairs with the ratio of basin area to the square of basin length.
Each morphometric parameter correctly maps to its distinct mathematical definition and hydrological role: Bifurcation Ratio relates channel counts across orders (Nu/Nu+1N_u / N_{u+1}); Drainage Density measures stream length per area (L/A\sum L / A); Stream Frequency measures individual stream counts per area (N/AN / A); and Form Factor evaluates areal shape (A/L2A / L^2).

Step-by-Step Solution

1
Identify the formula and definition for Bifurcation Ratio (RbR_b)
Bifurcation Ratio is defined as Rb=NuNu+1R_b = \frac{N_u}{N_{u+1}}, representing the ratio between stream segment counts of order uu and order u+1u+1.
This establishes the relationship between successive stream orders in Strahler's morphometric ordering.
2
Identify the formula and definition for Drainage Density (DdD_d)
Drainage Density is defined as Dd=LAD_d = \frac{\sum L}{A}, where L\sum L is the total channel length and AA is the total basin area.
It quantifies channel spacing and regional runoff dynamics per unit area.
3
Identify the formula and definition for Stream Frequency (FsF_s)
Stream Frequency is defined as Fs=NAF_s = \frac{N}{A}, counting the number of stream channels (NN) per unit area (AA).
It expresses channel density in terms of individual segment counts rather than channel length.
4
Identify the formula and definition for Form Factor (RfR_f)
Form Factor is calculated as Rf=AL2R_f = \frac{A}{L^2}, comparing basin area to the square of maximum basin length.
It measures circularity versus elongation of a river basin to predict flood hydrograph shapes.

Key Concept

Morphometric Analysis of River Basins
Question 14Question

A drainage basin outlined on a topographic map with a scale of 1:50,0001:50,000 has a total stream network length of 45 cm45\text{ cm} and a basin area of 36 cm236\text{ cm}^2 measured directly from the map sheet. What is the actual drainage density of the basin in km/km2\text{km}/\text{km}^2?

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Answer: 2.5

Answer

The actual drainage density of the river basin is 2.5 km/km22.5\text{ km}/\text{km}^2.
To calculate the true drainage density, map linear measurements and area measurements must first be converted to ground units using the scale 1:50,0001:50,000 (1 cm=0.5 km1\text{ cm} = 0.5\text{ km}, 1 cm2=0.25 km21\text{ cm}^2 = 0.25\text{ km}^2). Total ground stream length is 45×0.5=22.5 km45 \times 0.5 = 22.5\text{ km} and total ground basin area is 36×0.25=9 km236 \times 0.25 = 9\text{ km}^2. Dividing stream length by basin area yields 2.5 km/km22.5\text{ km}/\text{km}^2.

Step-by-Step Solution

1
Convert the measured total stream network length from map units (cm) to real-world kilometers.
Ground stream length L=45 cm×0.5 km/cm=22.5 kmL = 45\text{ cm} \times 0.5\text{ km/cm} = 22.5\text{ km}.
At a scale of 1:50,0001:50,000, 1 cm1\text{ cm} on the map represents 50,000 cm=0.5 km50,000\text{ cm} = 0.5\text{ km} on the ground.
2
Convert the measured basin area from square centimeters to square kilometers.
Ground basin area A=36 cm2×(0.5 km)2=36×0.25 km2=9 km2A = 36\text{ cm}^2 \times (0.5\text{ km})^2 = 36 \times 0.25\text{ km}^2 = 9\text{ km}^2.
The areal scale factor is the square of the linear scale factor (1 cm2=0.25 km21\text{ cm}^2 = 0.25\text{ km}^2).
3
Divide the total ground stream length by the total ground basin area.
Drainage density Dd=22.5 km9 km2=2.5 km/km2D_d = \frac{22.5\text{ km}}{9\text{ km}^2} = 2.5\text{ km}/\text{km}^2.
Drainage density measures stream channel length per unit area within a river basin.

Key Concept

Drainage Density and Scale Conversion in Basin Analysis
Estimated Time:2m 0s
Question 15Question

A morphometric analysis of a river basin provides the quantitative data shown below:

Morphometric ParameterValue
Total Basin Surface Area (AA)50 km250\text{ km}^2
Cumulative Stream Length (LL)125 km125\text{ km}

Based on these hydrological parameters, what is the drainage density of the basin, and what does its magnitude imply about the basin's surface runoff response?

Show answer & explanation

Answer: 2.5 km/km22.5\text{ km/km}^2, indicating a high drainage density associated with rapid surface runoff and high flood potential.

Answer

The drainage density of the basin is 2.5 km/km22.5\text{ km/km}^2, which indicates a high drainage density characterized by rapid surface runoff and high peak flood potential.
The correct answer properly calculates drainage density (DdD_d) as the total stream length divided by basin area (125 km/50 km2=2.5 km/km2125\text{ km} / 50\text{ km}^2 = 2.5\text{ km/km}^2). Hydrologically, a high drainage density (2.5 km/km22.5\text{ km/km}^2) signifies a closely knit stream network that collects and transmits storm runoff rapidly, resulting in swift hydrological response and high flood potential.

Step-by-Step Solution

1
Identify the formula for drainage density (DdD_d).
Dd=Total Cumulative Stream Length (L)Total Basin Surface Area (A)D_d = \frac{\text{Total Cumulative Stream Length } (L)}{\text{Total Basin Surface Area } (A)}
Drainage density measures the total length of stream channels per unit area of a drainage basin.
2
Substitute the given values into the formula.
Dd=125 km50 km2=2.5 km/km2D_d = \frac{125\text{ km}}{50\text{ km}^2} = 2.5\text{ km/km}^2
Dividing 125 km125\text{ km} by 50 km250\text{ km}^2 yields the linear stream length per square kilometer of basin area.
3
Interpret the hydrological significance of the calculated drainage density value.
A drainage density of 2.5 km/km22.5\text{ km/km}^2 represents a relatively high density, implying impermeable surface rocks/soils, steep slopes, minimal infiltration, rapid runoff delivery into main channels, and high flood responsiveness.
Higher drainage density values mean precipitation reaches stream channels quickly, increasing surface runoff rates.

Key Concept

Drainage Density (DdD_d) and Basin Hydrological Response
Question 16Question

On a topographical map extract, a major river stream crosses a valley where the V-shaped contour lines point towards the north-east. In which cardinal direction is the river flowing?

Show answer & explanation

Answer: South-west, because contour V-shapes point upstream towards higher elevation, meaning the river flows downstream in the opposite direction.

Answer

South-west, because contour V-shapes point upstream towards higher elevation, meaning the river flows downstream in the opposite direction.
In practical map reading, whenever contour lines cross a river valley, they form a 'V' pattern pointing toward higher ground (upstream). If the apex of the 'V' points north-east, the elevation increases toward the north-east. Because rivers flow downhill from higher to lower ground, the flow direction must be toward the south-west.

Step-by-Step Solution

1
Identify the law of V-shaped contours in valley landforms.
V-shaped contour lines crossing a stream or valley always point upstream (towards the source or higher elevation).
Topography rises as you move up a river valley, causing contour lines of higher elevation to bend upstream.
2
Determine the direction of flow based on the orientation of the contour V-apex.
Since the V-shapes point north-east (upstream), the river must flow downstream towards the south-west.
Water naturally flows from higher elevation to lower elevation, which is directly opposite to the upstream-pointing apex of the contour V-shapes.

Key Concept

Contour V-Rule for River Valley Flow Direction
Question 17Question

In a morphometric analysis of a river basin, a hydrologist counts 3232 first-order streams and 88 second-order streams using Strahler's stream ordering system. What is the bifurcation ratio between the first-order and second-order streams?

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Answer: 4

Answer

The bifurcation ratio between the first-order and second-order streams is 4.
The bifurcation ratio (RbR_b) is obtained by dividing the number of streams of a given order (N1=32N_1 = 32) by the number of streams of the next higher order (N2=8N_2 = 8). Therefore, Rb=328=4R_b = \frac{32}{8} = 4.

Step-by-Step Solution

1
Identify the number of streams of order uu and order u+1u+1
N1=32N_1 = 32 and N2=8N_2 = 8
The bifurcation ratio measures the ratio of the number of stream segments of a given order to the number of segments of the higher order.
2
Calculate the bifurcation ratio using Rb=N1N2R_b = \frac{N_1}{N_2}
Rb=328=4R_b = \frac{32}{8} = 4
Dividing the count of first-order streams by the count of second-order streams gives the ratio of stream branching.

Key Concept

Bifurcation Ratio in River Basin Morphometry
Question 18Question

On a topographical map extract drawn at a scale of 1:50,0001:50,000, a river valley features V-shaped contour lines that point consistently toward the south-west. Point X lies directly on the 450 m450\text{ m} contour line, while Point Y lies 5 km5\text{ km} further down the channel path on the 200 m200\text{ m} contour line. Based on these topographic observations, toward which direction does the river flow, and what is its average channel gradient between Point X and Point Y?

Show answer & explanation

Answer: Toward the north-east at a gradient of 1 in 201\text{ in }20

Answer

The river flows toward the north-east at an average channel gradient of 1 in 201\text{ in }20.
In topographic map interpretation, contour lines form 'V' shapes when crossing river valleys, with the apex of the 'V' pointing upstream toward higher elevation. Because the V-shapes point south-west toward the 450 m450\text{ m} contour, the river must flow downstream toward the lower 200 m200\text{ m} contour in the north-east direction. Furthermore, the gradient calculation requires dividing the Vertical Interval (450 m200 m=250 m450\text{ m} - 200\text{ m} = 250\text{ m}) by the Horizontal Equivalent (5 km=5,000 m5\text{ km} = 5,000\text{ m}), giving 2505,000=120\frac{250}{5,000} = \frac{1}{20} (or 1 in 201\text{ in }20).

Step-by-Step Solution

1
Determine flow direction from V-shaped contour lines
The river flows toward the north-east.
V-shaped contour lines crossing a river valley always point apex-upstream (toward higher ground/source). Since the V's point south-west (toward 450 m450\text{ m}), the river flows down the elevation slope toward the north-east (toward 200 m200\text{ m}).
2
Calculate Vertical Interval (VI)
VI=250 m\text{VI} = 250\text{ m}
Difference in elevation between Point X (450 m450\text{ m}) and Point Y (200 m200\text{ m}) is 450 m200 m=250 m450\text{ m} - 200\text{ m} = 250\text{ m}.
3
Convert Horizontal Equivalent (HE) to consistent units
HE=5,000 m\text{HE} = 5,000\text{ m}
The horizontal distance along the river course is 5 km=5×1,000 m=5,000 m5\text{ km} = 5 \times 1,000\text{ m} = 5,000\text{ m}.
4
Compute stream gradient ratio
Gradient=250 m5,000 m=120\text{Gradient} = \frac{250\text{ m}}{5,000\text{ m}} = \frac{1}{20} (1 in 201\text{ in }20)
Gradient is expressed as VI/HE\text{VI} / \text{HE}, simplifying 2505000\frac{250}{5000} to 120\frac{1}{20}.

Key Concept

Valley Contour Interpretation and Topographic Stream Gradient Analysis
Question 19Question

A drainage pattern where streams converge from surrounding elevated areas into a central inland depression or lake is best described as which of the following?

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Answer: Centripetal drainage pattern

Answer

Centripetal drainage pattern
Centripetal drainage pattern is defined by streams that flow inward from elevated margins toward a central depression, basin, or lake (such as Lake Chad).

Step-by-Step Solution

1
Analyze the stream flow direction described in the stem.
The streams flow from surrounding high areas inward toward a central low point (depression or lake).
Identifying the flow direction relative to topographic relief determines the structural drainage pattern type.
2
Match the flow direction to standard geological drainage pattern definitions.
Inward converging flow characterizes the centripetal drainage pattern.
The term 'centripetal' denotes moving or tending toward a center point.

Key Concept

Classification of river drainage patterns based on structural control and terrain slope
Estimated Time:45s
Question 20Question

A hydrologist conducts a morphometric analysis on a river basin using a topographic map drawn at a scale of 1:25,0001:25,000. Stream ordering reveals 2828 first-order streams, 77 second-order streams, and 11 third-order stream. If the total basin area measured on the map is 32 cm232\text{ cm}^2, what is the stream frequency (FsF_s) of the basin in streams per km2\text{streams per km}^2?

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Answer: 18

Answer

The stream frequency of the river basin is 18 streams per km218\text{ streams per km}^2.
To determine stream frequency (FsF_s), first calculate the total stream count (N=28+7+1=36N = 28 + 7 + 1 = 36). Next, convert the map area of 32 cm232\text{ cm}^2 to actual ground area using the scale 1:25,0001:25,000. Since 1 cm1\text{ cm} on the map represents 0.25 km0.25\text{ km}, 1 cm21\text{ cm}^2 represents 0.0625 km20.0625\text{ km}^2. Multiplying 32 cm232\text{ cm}^2 by 0.0625 km2/cm20.0625\text{ km}^2/\text{cm}^2 gives a basin area of 2.0 km22.0\text{ km}^2. Finally, divide the total number of streams by the basin area (36/2.0=18 streams per km236 / 2.0 = 18\text{ streams per km}^2).

Step-by-Step Solution

1
Sum the number of streams of each order to find the total stream count (NN).
N=28+7+1=36 streamsN = 28 + 7 + 1 = 36\text{ streams}.
Stream frequency considers the entire stream network comprising all stream orders in the basin.
2
Convert map area to ground area using the map scale (1:25,0001:25,000).
1 cm=0.25 km    1 cm2=0.0625 km21\text{ cm} = 0.25\text{ km} \implies 1\text{ cm}^2 = 0.0625\text{ km}^2. Actual Area A=32×0.0625=2.0 km2A = 32 \times 0.0625 = 2.0\text{ km}^2.
Stream frequency must be expressed per unit of actual ground area in km2\text{km}^2 rather than map area.
3
Divide total number of streams by actual basin area.
Fs=362.0=18 streams/km2F_s = \frac{36}{2.0} = 18\text{ streams/km}^2.
Stream frequency (FsF_s) is defined as the ratio of total number of streams to the drainage basin area.

Key Concept

Stream Frequency (FsF_s) Calculation in River Basin Morphometry
Estimated Time:2m 0s
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